48cm
Area of rectangle is 128cm²
So use algebra to solve (remember area of rectangle = LxW)
2x * x = 128 (where 2x = length and x = width. Use 2x given length is twice width)
3x=128
2x²=128
x²=64
x=8
So perimeter = (8*4 for the length + 8*2 for the width) = 48cm
84
120 pupils
2/5ths boys = 48 boys (120/5 * 2)
3/4s of boys write in pencil = 48 * 3/4 = 36
Girls = (120-48)-72
1/3 in pen so 24.
2/3 in pencil so 48
Total in Pencil = 36 + 48 = 84
£450
£12,000 full price
Discount = 12,000 * 35/100 = £4,200
So reduced price = £12,000 – £4,200 = £7,800
£7,800 less savings of £7,350 = £450
B
£120 * 85/100 = £102
B
A+C+D = 70%. Therefore, 30% chose B.
If 25% = 320, what does 30% = ?
The approach is to use HCF of 25 and 30 which is 5%. Work out 5% first of 320
This equals 64
Then 64 * 6 (given that 30/5% = 6 times)
Total is 384
C
6+7 = 13 minutes marking.
13+2 = 15 minutes marking + checking
15 * 28 = 420minutes
420/60 = 7 hours
C
9 * 120 = 1080g
D
Work backwards. So 95+8 = 103
103-3 = 100
100/5 = 20
a) £4
200 x 2p = 400p
b) £9.50
150 x 1p + 160 x 5p
c) See below:
d) No part d in question
e) £40.60
£156.50 – (150x1p) – (200x2p)-(160x5p)-(120x20p)-(90x50p)-(55x£1)
£156.50 – £1.50 – £4 – £8 – £2.40 – £45 – £55 = £40.60
a) £5.41
b) 0.732
c) 3.3125
a) 399
b) 3,990
c) 4,389
24
Do inverse which is 624/26 = 24
a) 55%
100% – 25% – 15% – 5%
b) 5
25% of 20 = 1/4 * 20
12
Many options here
a) 15
99-84
b) 9
63 – 54
a) 20p
£2.00 – £1.20 = 80p
80p/4 = 20p
b) 6
£1.00 = 100pence
100/15=6.67
So 6 whole kiwi fruits
a) 26
b) (32+9+6)=47 * (9-6) = 141 – (9-6) = 138
a) 5
b) 3
(2×3)/2
c) 22
(3×6)+(2*2)
Substitution
c
5 hour walk at 3km/h = 15km
5 hour walk at 4 km/h = 20km
So distance could only be 19km
a) Twenty-thousand four hundred
b) -21
A + * by a – is always a –
c) 27
BIDMAS. Brackets first
d) 8
y=16/2 = 8
e)i) x = 7
e)ii) x = 5
You firstly have -x = -5 which is the same as x = 5
f) 6
g) 1:3
a) i) 1/3
3/9 = 1/3
a) ii) 30% shaded. Unshaded therefore = 70%
c) 50
10% of 500 = 50.
10/100 * 500
d) £127.50
85/100 * 150
Above formula to calculate 15% reduction
For the above, work backwards. So for example, 250-75 = 175. Etc
a) x = 6
- 3x + 7 =25
- 3x=25-7
- 3x=18
- x = 6
b) 8
- 3f – 2g
- (3*6) – (2*5)
- 18-10
a) 4
BIDMAS. Do multiplication first. So 16-12 = 4
b) 70%
When converting decimals to percentages, just move the decimal place 2 places to the right. So 0.7 becomes 70.
c) 0.6
3/5ths as a decimal. To convert denominator to 100, multiply both numerator and denom by 20. So 60/100 = 0.6
d) 18
15/100 * 120/1
e) 20 – 10 /5 = 18
Do division first according to BIDMAS. Then subtraction. So 20-2 = 18
f) 16+(32/8/2)-1 = 16 + 2 – 1 = 17
4,8 & 20
He has enough oranges
- Each orange in the pictogram is 4 oranges
- So 5 oranges above x 4 per picture = 20 oranges
- Plus half of an orange in the pictogram = 2 oranges
- So total number of oranges = 22 oranges
- 1 1/2 litres = 3 x 500ml. So 3 * 7 oranges per 500ml = 21 oranges
- He has enough in oranges
25
1 + 2 x 3 x 4 = 25
78000
Number of words = 256 * 33 * 9
Estimate = 260 * 30 * 10
= 78000
B
Number of grey tiles = 2*n where n=shape number
So for Shape 3, it would be 2*3 = 6 grey tiles
28 grey tiles = 2 * n so n = 14. Shape 14
For Shape 14, white tiles = (n+1) = 15
A
Work backwards. 23 – 3 = 20. Divide by 4 and you get 5
A
100 is not a multiple of 3
A
1680 = 1680
Quick way is you are doubling the 24 to get to 48 on the other side. Then halving the 70 and getting 35 on the other side. So no calculations required in this question
C
(22-10+8) / 4
C
- 5((6*9)+(7*3)-(8*6))
- This gives 5(54+21-48)
- This gives 5(27)
- Answer 135
12
- The first even multiple of 7 is 14. The first prime number is 2
- Therefore, answer is 12
0.006
- If not sure, remove the zeros. So make it 20 * 3 = 60 (ie multiply both numbers by the same amount until the zeros are removed. This would be x100)
- Then , because you removed 3 0s, you need to add these back in.
- So the 60 because 0.006
a) 27
8 * 9 = 72. Clotted = 27
b) 6
To give 42, reverse would be 24. So 4 * 6 = 24
c) 5 & 7
Reverse would be 35. So 2 whole numbers would be 5 & 7
Area = 200cm²
- If 2x long as wide, then need to calculate each side
- Double length v width means length is 20cm and width is 10
- Area = 200cm²
a) 160cm
b) 168cm²
600g
- 2:1 Flour:Fat
- 900g of pastry required. Given we have 3 parts, therefore each part is 300g
- Flour is 2 parts so 2 * 300 = 600g
200miles
- Calais to Paris is 320km. So 320 * 5/8 = number of miles
- 200miles. Can be done in 1 of 2 ways. Per the above or work out 1/8th which would be 40km. Then 5 * 40km = 200m
a) £102
10metres would be £10.20 * 10 = £102
b) 2.5metres
£10.20 * 2 = £20.40. This leaves £5.10 (£25.50 – £20.40)
£5.10 is exactly half of £10.20. So therefore total is 2.5 metres
a) 1/15
- Convert to the same denominator
- So this would mean Tom 3/5 = 9/15 and Jerry 1/3 = 5/15
- In total, 14/15ths has been eaten leaving 1/15
b) 250g
- If Tom had 3/5 = 150g, then 1/5 = 50g
- Therefore 5/5 = 250g
630
-
- Calculate by doing 3/4 x 840
- “of” in maths means multiply
- 3/4 * 840/1
- Simplified……..3/1 * 210/1
- 630
1596
a) 83
(14*2)+55 = 28+55 = 83
b) 13
(9*2) = 18
31-18 = 13
c) 22
d) 0
So for d), try c = 4 and 4 = 4. This will mean that 4*2 + 4 = 12 and this is equal to 4*2 + 4 as c & d are the same. So c-d or d-c = 0
£29.90
- First divide exactly by 2 as if they have 50/50. So this would be £23
- Then take 15% off Miguel and give this to Jon. So the revised share becomes 35% Miguel and 65% Jon
- So £46 * 65/100 =
462cm
Large Triangle = 16cm * 3 (all sides same as its equilateral). So 48cm
Middle Triangle = 7cm * 3 triangles * 3 sides (7 small triangles of 1cm each on the horizontal base tells us its a 7x7x7 triangle). So 63cm
Next size Triangle of which there are 3 = 3cm * 3 triangles * 3 sides = 27cm. There are 3 of them so 27cm
Smallest triangle = 36 small triangles all of 1cm per side. So 3cm *36 triangles * 3 sides = 324cm
Total of all of these is 48 + 63 + 27 + 324
16
5 numbers with mean 28 = 140 in total (5 * 28)
12 numbers with mean of 11 = 132 in total (12 * 11)
Total = 272
Mean = 272/17
a) 120
(17+13)(17-13) = 30 * 4 = 120
b) 776,000
(888+112)(888-112) = 1000 * 776 = 776000
c) 50
(7.5+2.5)(7.5-2.5) = 10 * 5 = 50
a) 12.5%
3 films = 45 degrees
45/360 = 0.125 = 12.5%
b) 7/24
Focus on left hand side (so 0,1, & 4 together = 180 degrees)
0 children = 180 degrees – 45 – 30 = 105 degrees
105/360 = 21/72 = 7/24
120
- Use BIDMAS
- 20 + (1 x 7) = 27
- (20 + 1) x 7 = 147
- 147-27
2646
90ml
- This is indirectly a question on ratios.
- So if you assume for every 10ml consumed by Jane, Alex consumes 15, the ratio is Alex 15:10 Jane
- So 150ml/25 parts = 6
- Alex = 6 *15 = 90ml
- Check would be Jane which is 10 * 6 = 60
- So confirms Alex consumes 50% more than Jane
15/26
When doing this type of question, you can’t answer 7.5/13 obviously. So the solution is to double each fraction and “force” a gap
So this becomes 14/26 and 16/26
Answer is 15/26
74
- (4+2) x 13 = 104
- 4 + (2×13) = 30
- Difference = 104 – 30
1691
a) 4
- Mean of 7 numbers = 12. Total = 84
- If 8th number added and mean is 11, total must now be 88 (8*11)
- So , the number included = 88-84 = 4
70
- Use BIDMAS. (7+3) x 11 = 10 x 11 = 110
- 7+ (3×11) = 40
- 110-40 = 70
2737
a) 8
- 30 socks – 10 white; 20 non-whites. Of the 20, 2/5th are blue
- So 20 * 2/5 = 8
b) 6 pairs
- Of the non-whites, 8 are blue so this leaves 12
- With 12 left, it could make 6 pairs
18 days
- 12 cut knees per day for 30 days = 360 cut knees over this timeframe
- To treat 20 boys, (assuming its only 1 knee that is cut per child), then this would be 360/20 = 18 days
a) £3.10
- 8 x 35p = £2.80
- If she had 30p left, her total that she had in the first place would be £2.80 + 30p = £3.10
b) 45p
- 5 lollipops @ 35p each = £1.75
- £3.10 less £1.75 = £1.35
- £1.35/3 = 45p
a) 30°
Swimming & Golf together are 90°
Therefore, Golf is 90 – 60 =30
b) 1/8
Rugby = 45/360 = 9/72 = 1/8
c) 90
- Football = 180° – 45° = 135°
- 135/360 * 240/1
d) 220
- 1320 * 60/360
3702
a) to d) below
e) See below
a) 30°
180 – Australia – Africa = 180-90-60
b) 1/8
45/360 = 9/72 = 1/8
c) 30
180/1 * 60/360 = 180*1/6 = 30
d) 1000
Degrees for Europe = 180 – USA = 180-45 = 135
1600 * 225/360. Simplified this is 1600 * 45/72 = 15/24
1600/1 * 15/24
£1.35
- 15 * 35p = £5.25
- Multipack = £3.90
- Difference = £1.35
3258
a) 1200mm²
Area of rectangle = LxW = 60mm x 20mm
b) 40 triangles
2 Triangles will joined together have dimensions of LxW = 12mmx5mm. So they form a rectangle
Therefore, in 60mm across, you get 5 “blocks” of 2 triangles. And you can go to a height of 4 blocks
So in total 5 * 4 blocks = 20 blocks. 2 triangles per block so 40 triangles
c) 1200mm
Perimeter of 1 triangle = 12+5+13=30mm
Total number of triangles = 40
Total Perimeter =1200mm
d) 1.2m
10mm = 1cm
100cm = 1m
1000mm = 1m
85p
- 12 * 65p = £7.80
- £7.80 – £6.95 = 85p
a) 1/8
45/360. Start off with 5 as the highest common denominator. Although there is a higher one
So 45/360 would become 9/72
Then 9/72 becomes 1/8
b) 40
Its the usual formula approach for this:
60/360 * 240/1
Then simplify each fraction (so 60/360 becomes 1/6)
Revised calculation is 1/6 * 240/1. Cross cancel and then multiply from there. See online videos on Youtube for 123tutors for further guidance
c) 450
Football is 135°. So 135/360 * 1200
a) 12
1/4 * 48/1
b) 2
48 * 1/2 = 24.
24 * 1/3 = 8
8 * 1/4 = 2
Remember of in maths means multiply
2184
267,120
742
53424
26748
- Add a zero on. So 267,120
- Its rearranging the formula so it becomes 742 = 26712/36
- Double the base answer of 26712 so it becomes 53424
- Add on 36 to the original answer. So its 26712 + 36 = 26748. (ie an extra 1 x 36 since number changes from 742 to 743)
Area of 1 rectangle = 15 x 5 = 75cm²
4 children
- 56 legs with 3:1 ratio dogs:children
- 12 dogs = 48 legs. 4 children = 8 legs. So thats 56 legs altogether
- For every 3 dogs there are 12 legs. For every 1 child, 2 legs. So leg ratio is 12:2 = 14 legs
- Then work up in 14s to get to 56 which takes you to 48:8
- So 8 legs = 4 children
20cm²
Its 10cm length x 2cm height. So 20cm²
18
- A=5/8; P=3/8
- Pears therefore = 3/8 * 48/1
- Pears = 18
18
- B=2 ; A=5
- If A = 45 turns, it has done 9 times as many as the “base case”
- Therefore, B will also do 9 times as many so its 18 times
£1.11
- 3mins * 7p = 21p
- 18mins * 5p = 90p
- Total cost = 111p
a) 1 hour 25mins
7.10pm – 5.35pm = 1 hour 25mins
b) 16 hours 30 mins
2 hours 45 mins converted to minutes = 165minutes
165minutes * 2 = 330mins
330mins * 3 = 990mins
990mins/ 60mins
£208
- £156/6 = £26 per night
- £26 * 8 = £208
48
- Do your 3 x 4 times table to find a number in between 41 and 51
- So 12,24,36,48
- Answer is 48
15
- 24/1 * 5/8
- Simplified = 3/1 * 5/1 = 15
6 weeks
- Per week she gets (79p-44p) profit. So this is 35p per download
- 150 downloads per day = 150x35p = £52.50 per day
- £2000/£52.50 = 38.1 days
- So this is 6 weeks as this is 42 days as she gets paid at the end of each week so you can’t use part a week
96 tiles
3metres long and 4m wide = 12m² area
You will get 12 tiles in the width from 25cm tiles (3metres = 300cm. 300cm/25 = 12 tiles)
Across you will get 8 tiles in the length from 50cm tiles ( 4metres = 400cm/50cm – 8 tiles)
12 x 8 = 96 tiles
Use BIDMAS
a) £27
Cost = ((8×3) + (3×1)) = 24+3 = 27
b) 2 adults. 3 children
Use £25 and work backwards taking off children until you get to a multiple of 8
So £16 would be the number
£25-£16 = £9. So thats 3 children
Leaving £16 so its 2 adults
£20.90
- £25.50 x 3 = £76.50
- £1.30 x 2 = £2.60
- Total = £79.10
- Change = £100 – £79.10
a) 24
Half of the 48 students so 24
b) 1/4
c) 4
Pizza is about 1/3 of 1/4.
1/4 = 12 children given 1/2 = 24
So 1/3 of 12 = 4
25,100 millimetres
- 25.1metres = 25.1 x 100 = 2,510 centimetres
- 2,510 x 10 = 25,100 millimetres
858
- 22 x 39
- 858
36
-
-
- 15/100 * 240/1
- Simplify…3/20 * 240/1
- 3/1 * 12/1
- 36
-
£15.96
Buy 2 get 3rd free so only pay for 2
£5.32
£15.96/3 to get equivalent price per bottle
a) £120
Car Hire £45
Over 200km is 150km extra driven
Cost is £0.5 per km so total cost is 150 x £0.50 = £75 extra
Total cost is £45 + £75
b) 390km
Cost for Daryl £140. Less 200km covered for £45.
This leaves £95
Total mileage from this would be 95/0.5 = 190km
Add base 200km so total distance travelled is 390km
38
- Triple 16 = 48 points. Double 20 = 40 points
- Total so far is 88 points
- He therefore needs 38 with this final dart
175
- To paint houses, 14 days per house x 14 houses = 168 days
- Add 4 days holiday = 172
- Add 3 days sick leave = 175
20 students
- Work on basis 6 students = 30°
- Therefore, 2 students = 10°
- So, 100° = 20 students
9,600cm³
Volume = length x width x height
Volume = 3.2 x 1.5 x 2
Volume = 6.4 x 1.5
Volume = 9.6 (this is in metres. Convert to centimetres)
9.6litres
1 litre = 1000cm³
321
279
20
- It is one extra “21” So 321
- It is one less “21”. So 279
- It is 20
£6.42
- If 9 pairs cost £19.26, work out the cost of 1 pair first via division
- This would be £2.14
- Cost of 3 pairs would be £6.42
- Or you look at 9 pairs and 3 pairs. HCF is 3. Just divide the £19.26 by 3
a) 5
b) 26
c) 112
Apply the rules of BIDMAS. Brackets, Indices, Division, Multiplication, Addition, Subtraction
a) 3.5 hours
Time = Distance/Speed = 420/120
b) 180 miles
Distance = 180miles
120mph so after 1.5 hours, train will travel 180 miles
72 stickers
- 80/10 = 8
- 45/5 = 9
- 8 * 9 = 72
a) 672
b) 264
c) 1,081
d) 843
E
- £1.99 x 6 = £11.94
- Change would be £20.00 – £11.94
D
- Use BIDMAS. Therefore…
- 32-8
- 24
D
- 60 seconds per minute. 4 minutes = 60 x 4 – 240
a) 12 seconds
- After 2 seconds, Gary is at 20metres which is when Andy starts running
- So Andy has 20 metres to make up
- It will take him 10 seconds to close this gap as he makes up 2 metres per second
- Add the initial 2 second start that Gary had over Andy
b) 120 metres
- Distance = Speed x Time
- Therefore = 12m/s x 10 seconds = 120 metres
a) 4 & 58 which would give an answer of 232
b) 30 ( 120/4)
Test 1
- 60/80 = 75% (60/80 *100/1)
- 70/100 = 70% (70/100 * 100/1)
a. £22.50
- 2 Adults = £6.25 * 2 = £12.50
- 4 Children = £2.50 * 4 = £10.00
- Total = £22.50
b. 8 children
- 4 adults = £5 * 4 = £20.00
- Remaining is £24
- £24/£3 = 8 children
a. 10 seconds
If turn is 360 degrees every 40 seconds, 90 degrees as a right angle would take 1/4 of 40 = 10 seconds
b. 84 turns
In 56 minutes, the sails make 56/1 * 60/40 turns
Again, use of fractions to calculate these types of questions
6 & 8
- Think about numbers that multiply to give 48. Thats going to be starting with low numbers, 2 * 24, 3 * 16, 4* 12, 6 * 8 etc
- Answer is 6 * 8 as these numbers when added give 14 and multiplied, give 48
Start with Sneezy as this is given as 24 and work from there
Grumpy gets 1 more so is on 25 etc etc
116cm
- Number of days = 5
- Height sunflower grows is (68 – 48) = 20cm
- Per Day growth therefore = 4cm
- Taking 21st August through to 2nd September = 12 days
- Therefore, growth during this period is 48cm
- Adding on the height as of 21st August of 68cm = 116cm
28th July
- Work Backwards. 4cm per day = 12 days
- Therefore, 12 days from 16th August 4th August
- Then take a week off this and you get 28th July
180
- 23 – 13 = 10.
- 23 – 5 = 18
- 10 x 18 = 180
13, 5
- 13 as the first number. So he would end up with zero
- Or for the second number, 5 so he ends up with zero for the second number
5 Pens 4 Pencils
- Whatever you buy in pens, just end in a 5 or 0. So the only number this applies to between 0 and 55 is 35
- So its 5 Pens. This leaves 20p
- 20p is for pencils @ 5p each
- So 4 pencils
£14.90
1. £2.98 * 5
2. Multiplication question in words
£32
- Working backwards, 25% discount would mean discount on ticket cost was 25/75 * 30/1 = £10
- Full Price Child = £40
- Senior Citizen therefore pays 80/100 * 40/1 = £32
36
8, 12, 16
Use the inverse operation of 17 * 11 = 187
3 Hours
If it takes 4 people 6 hours, (24 man hours) then 8 people will take half this time.
10 Hours
twice the length = 48 hours.
48/5 = 9.6 which is near enough to 10 hours
E
Use substitution of values:
Orange costs 10p, Apple costs 5p
A – 35p (2 x 10p) + (3 x 5p)
B – 35p
C – 35p (1 x 10p) + (5 x 5p)
D – 35p (3 x 10p) + (1 x 5p)
E – 40p
95p
- 85p x 3 = £2.55
- 30p x 5 = £1.50
- Total Cost = £4.05
- Change = £5.00 – £4.05 = 95p
£4.20
- Work on HCF route. 12 eggs and 18 eggs
- HCF = 6. Therefore, first calculate what 6 eggs costs
- If 12 costs £2.80, 6 costs £1.40
- Therefore, 18 would be 3x what 6 costs. So £4.20
See below
45km
1817 – 1747 = 30 minutes. If train travels 90km/h, it will travel half this distance in 30 minutes
1917
Detailed workings to follow
£660
120/100 * 550/1
Simplify the calculation per normal rules of simplification and cross cancellation and then calculate
£1000
100/120 * 1200/1
70 hours
Process:
- If Lazy Living = 2/7ths, Celeb Gossip is 5/7
- 5/7 * 98/1
- Simplified this is = 5/1 * 14/1
- This is 70
0.4
Process:
- One option is to change 0.08 to 8. So x 100
- Then multiply 8 by 5
- This gives 40
- Then to divide the answer by 100 as you originally multipied the question x 100
- This gives 0.4
52,272
product means multiplication
150ml
- Ratios question. 1R:2O:3A = 6 parts
- Each party is 50ml
- So 3 parts is 150ml
Total Cost of Family of 2 adults and 3 children = £6,020
- Calculate each component at a time;
- Read the question carefully as infants (children <2) travel free;
- So real cost is 2 adults and 2 children;
- (2 x 1550) + (2×900) + (2×320) + (2×240) = £6,020
Difference of cost to stay at Portomento Bay = £790
- Calculate the cost of each sub part;
- Portomento Bay = £2050 + £1040 + £320 + £240 = £3,650
- South Seas = £1,450 + £850 + £320 + £240 = £2,860
- Difference = £790
By buying online, they save £300
- 25% of …..So 25/100 * [(320×3) + (240)]
- Therefore, 25% of £1,200
- £300
Holiday Mill
- This is because 3 adults cost (3×1550) = £4,650
- Cost of child = £900
- Therefore, cost is £5,550
See below
The trick here is to substitute the actual scenarios with a given value. For example, assume the value costs £4.
Then use this figure in every single option to see which one works
48cm
- You have to think about times tables;
- So the shortest length will be the LCM of 6 & 8;
- This is 48cm
£1.64
- Use the HCF Principle. This always works if there is a HCF
- So the HCF of 9 & 12 is 3. Find the cost of 3 bananas first
- This is £1.23 / 3 = £0.41 for 3 (divide by 3 because there are 3 lots of 3 in 9)
- For 12 bananas, the cost is £0.41 * 4 = £1.64
a) 45,670
b) 8,101
- 4567 x 5 x 2
- (40,505 / 25) x 5
160
- Always convert the words to numbers and interpret the question
- This is the trick with these questions. Being able to convert words to numbers
- Its simply 32 x 5
258
Use the proper method:
a) i See below
a) ii See below
b) 13,20,24
- 4=2² with difference as 2
c) 0,1,4 & 9
- 0²=0; 1²=1; 2²=4; 3²=9
d) See below
a) See below
b) See below
c) 40
10 x 4
d) 5,050
This can be done with the following calculation
(100×101)/ 2 = 101 x 50 = 5,050
a) 8g
- If each tea leaves weighs 0.008g, then multiply this by 1000 to get weight of 1000 tea leaves
- Move the decimal place 3 places (number of zeros after the 1) to the right. 1000x.008g
- This would give 8
b) 125,000
- The number of leaves = 125 x 1000
c) 100
- A tea bag = (250 x 0.008) + 0.5g = 2.5g
- 250/2.5g = 100
64cm³
The volume of Cube A is 8cm³. So this is 2x2x2. For 64cm, think of cube numbers. So 2x2x2 = 8. 3x3x3 = 27. 4x4x4=64
So double the side of Cube A is 4 so its 64cm³
a) 48cm
See labelling below
b) 108cm²
Area = WxL. 6×18
c) 18
In 18cm across, she can fit 6 (18/3). Given its 6cm tall, she can fit 3 high. So in total 3 rows each with 6 in each row 18
a) 300ml
8 * 150ml = 1,200ml
- Always worth converting everything to the denomination in which the answer is required.
- So 1,5 litres = 1,500ml.
- 1,500ml – 1,200ml = 300ml
b) 6 full jugs
- 2 Litres * 5 bottles = 10,000ml.
- 10,000 / 1,500 = 6 full jugs = 9,000ml.
- There will be 1,000ml remaining/ left over
- Read the question carefully as it asks for FULL jugs
a) 2.4kg
Key is to understand what each marker is worth. The answer to this is 0.2kg. Therefore, 2.4kg
b) 2400g
“k” means 1000. Therefore, 1000g = 1kg
12
Consider the various options to multiply to get to 72.
2 x 36; 3 x 24; 9 x 8, 12 x 6
12 x 6 is the only option which meets the criteria
a i) 80
ii) 23
Work backwards. 120/4 = 30. 30 minus 7 = 23
b) x2 -6 OR -3 x2
1.5
1/10 * 5 = 0.5 (Move decimal one place to the left when dividing
1/5 of 10 = 2
So difference is 1.5
>
112 is the Left Hand side. 102 is the Right Hand Side. Missing sign is greater than
a) 2040
Move the decimal 2 places to the right when multiplying
b) 1050
- You can do the inverse operation here and multiply 1000 x 1.05 to get to the answer
- If not sure, then do the calculation in 2 parts:
- 1000 x 1 = 1000
- 1000 x 0.05 = 50 (Remember 0.1 = 10% = 100. So 0.05 = 5% = 50)
- Then add both numbers together
128
Use the following method and remember “of” means multiply in maths
3/4 * 1/96
This gives
3/384
Simplified….
128/1
22,374
a) 9
Work backwards. 47 – 2 = 45. 45/5 = 9
b) 48
Work backwards. 5 + 3 = 8. x 6 = 48
c) 12
(50-x)/2 = 19
50-x = 38
x=12
d) 8
100 – (x + x) = 36
x² = 100 – 36
x² = 64
x = 8
See below
Ensure BIDMAS rules are applied
£2,636
Classic maths questions whereby its just converting all the words to numbers
a) 24
- Give that Cats = 48 = 120º
- Hamsters = 60º. Therefore, they are half of cats = 24
The true way to look at this question is to say if 120º = 48, then what is the HCF of 60 & 120. This is 60. Therefore, take the 120 and say how many 60s go into 120. This is 2. Therefore, 60 = 24
b) 60
- Cats 120º + Hamsters 60º + Other 30º = 210º
- Remainder is 360 – 210 = 150º
- Again, HCF principle. Given you know 60º = 24, what is 150º?
- HCF = 30. So 30 is half of 60 so it equals 12
- Then how many 30s into 150 = 5
- Therefore 5 * 12 = 60
- The easiest way to complete these questions is to think about the HCF multiple.
- Look at how many cupcakes you have ingredients for. Its 8. You need to complete for 12.
- HCF of 8 & 12 is 4. Therefore, if you work out the ingredients for 4 cupcakes, then you can multiply up by 3x to get to 12
- So for 4, its half of what is required for 8
- So butter would be 75g.
- x3 would give you butter for 12 cakes etc
36
3 x 4 is 12 so think of multiples of 12 between 30 and 40
a) 5
1/7 * 35/1
Always cross cancel. So the 7 and 35 can be simplified further….
1/1 * 5/1
b) 21
The best approach is given that the answer to a) is 7, then 3/7ths would be 3 * 7 = 21
0,0,1,1
22,352
a) 6
(9×4)/6 = 36/6 =6
b) 2
(36×2)/(9×4) = 2
a) 8
-
-
-
- If 64 cars in total, then the following equation will be used to calculate the number of red cars
- 64/1 * 45/360.
- After cross cancellation, this is simplified to:
- 64/1 * 5/40
- Further cross cancellation:
- 8/1 * 1/1
-
-
b) 3/8
- The key here is to remember that the opposite angles when 2 lines cross, create equal angles
- So given Black and Red are 45º each, this gives 90° in total
- So remaining in the circle is 360 – 90 = 270
- Each angle must therefore be 270/2 = 135
- Every 45 degrees = 1/8th. So 135 = 3/8
a) 330 minutes
6 x 55 minutes = 330 minutes
b) £19.80
- 330 minutes / 60 = 5 hours 30 minutes
- Per Hour = £3.60.
- Therefore £3.60 x 5.5 hours = £19.80
30
A classic question on the concept of fractions. If Ravi is left with 12 sweets and this equals 2/5, then you have to calculate what 1/5 equals. This is 12/2 so it equals 6 sweets
Therefore, each 1/5 = 6 sweets. There were therefore 30 sweets to start with in the box
a) £25.80
- Cost of Tickets – 2 Adults + 2 Children. (£6.50 x 2) + (£3.00 x 2) = £19
- Popcorn – 2 Small bags + 1 Large Bag. (£1.50 x 2) + (£2.20) = £5.20
- Total Cost is £24.20
- Change is therefore £50.00 – £24.20
b) 1 hour 5 minutes
- 14:30 + 3 hours = 17:30.
- So 17:30 less 16:25 leaves 1 hour 5 minutes
9 & 4
- The way to tackle this question is think of multiples of 36. This would be 1,2,3,4,6,9,12,18,36
- The 2 numbers with a difference of 5 are 9 & 4
18
Work these questions always with the following approach:
3/8 * 48/1
Then simplify to:
3/1 * 6/1
Easier to get to the answer of 18
a) 5
Applying the rules, = 3 x 3 – 4
b) 6
Working backwards, 32+4 =
So 36 = 6 x 6
c) 9
Slightly trickier. But you need a multiple of 72 with one option being 9
x² – x – 72 = 0
24
- 36 sweets between them. This is a question on ratios:
- D = 1, H = 2 (Because hannah has twice as many has Dominic)
- A = 6 because Abdul has 3 times as many as Hannah
- So 1:2:6. Total parts = 9. Each part is therefore 36/9 = 4 sweets per part
- Total for Abdul = 6 parts * 4 sweets per part
a) 18
- Comedy represents 1/4 of the total pie. This is 25%.
- The pie is worth 72 students in total
- So 1/4 x 72 = 18
b) 50º
- 360 – 90 – 160 – 60 = 50
a) 15mins
- 30 mins / 2 = 15 mins if you have 2 hoses
b) 15mins
- To fill 10cm, it takes 1 hose 15mins. So to fill 30cm, I need 45mins for 1 hose.
- With 3 hoses therefore, the time is 15mins (45/3)
a) 23C
- Assess what each marker represents. This is 2C
- Therefore, answer is 23C
b) -12C (Minus 12C)
c) 35C
d) i) 68F
20/5 = 4 * 9 = 36 + 32 = 68
d) ii) 15C
- Work backwards
- 59F – 32 = 27 / 9 =3 * 5 = 15
£563
- There are 3 free adult tickets because you get 1 free adult ticket with every 10 student tickets
- So its 32 student tickets + 1 adult ticket to buy
- (32 * 14) + (15 * 1) = 448 + 15 = 563
a) 168cm
140/1 * 6/5
b) 90cm
105/1 * 6/7
b) x by 7 and then +3
a) 5 coins £2, 20p, 5p, 2p, 1p
b) £5.44
2 magazines cost £2.28 * 2 = £4.56.
£10.00 – £4.56
144
You can take the factor tree route per this article:
https://123tutors.co.uk/finding-the-lowest-common-denominator/
63
Just go through 9x table. 63
41,096
a) 50
- Substitute into the “rules” per the example. So this would give (10 x 10) / (1 + 1) = 100/ 2 =50
b) 5
- First solve (3☺4) = (4×4) / (3+1) = 16/4 = 4
- Then (4☺5) = (5×5)/ (4+1) = 25/5 = 5
c) 7
- Have to solve with algebra. 6 ☺ y = (y x y ) / (6 + 1) = y² / 7
- So y² / 7 = 7. Therefore, rearranging,
- y² = 7 x 7 . So y² = 49
- Therefore , y =7
6
Xp + Yp = 38. Where X = 4 page letter and Y = 3 page letter
- Some points to remember. The 3 page letter number of penpals should be an even number of penpals. This is because a 4 page letter * any number of penpals will always given an even number. Therefore, the 3 page letter can only be * 2, * 4, * 6 or * 8.
- The answer is * 6 (So 6 * 3 = 18) + (5 * 4 = 20) = 38
5 cubes
- Tall Cube. Number of cubes is W * L * H. This equals 2 * 2 * 8. = 32
- Small Cube. Number of cubes is W * L * H. This equals 3 * 3 * 3 = 27
Change from £5 = £5-£1.39 = £3.61
55p + 84p = £1.39
500g of Sugar. £1.10 per kg. Therefore 500/1000 = 1/2 so 1/2 * £1.10 = 55p
750g of flour. £1.12 per kg. Therefore 750/1000 * 112/1. Think of HCF though. The HCF of 750 *& 1000 is 250. Therefore, given you know what 1000g (1kg) costs, you can work out 250g.
This would be £1.12/4 = 28p per 250g
So 750g of flour = 28p * 3 = 84p
12
If 3/5 were eaten and this represents 18, then each 1/5 is equal to 6. (18/3). Therefore, there were 30 sweets to start with and 12 remain uneaten
£18
50 calls @ 17p per call = £8.50. Plus £9.50 for the fixed charge
a) 750g
With these types of questions, ALWAYS think of HCF. So for 12 cookies, you need ingredients per above. For 30 you need…..
Well you take the HCF of 12 & 30 which is 6.
Step 1: Calculate what you need for 6 cookies first. 12 cookies requires 300g so 6 requires 150g plain chocolate.
Step 2: 30 is a multiple of 6. So take what you had for 6 cookies and * by 5. To give you chocolate for 30 cookies. So 150g * 5 = 750g
b) £2.70
26p x 30 = £7.80. Less £5.10 cost = £2.70 profit
20
Calculate the Right hand side first which gives 12. Then re arrange. Take “-8” over to the right hand side from left so it becomes a positive. So 12 + 8 = 20.
578
Simple multiplication question
a) 555
Given 6*37 answer and 9*37, 15 * 37 will be these 2 answers added together
b) 888
(9*37 + 3*37) * 2
c) 499.5
(9*37)*3 = 999.
999/2
d) 962
(6*37) * 4 = 888. So this is 24 lots of 37. To get another 2 lots of 37, you take 1/3 of the answer for 6 * 37.
So 222/3 = 74. Then 888 + 74
a) 20
W 10 – 5 =X + 5 = Y * 2= 10 + 10 = Zoe
b) 2
Work backwards: Zoe calls out 4. Take away 10 as she added 10 to the number. This gives minus 6. Therefore, Yana must have had minus 3. Xanthe must have had 2.
c) 6.5
If Yana whispers 3, she was originally given 1.5. Xanthe must have had 6.5 from Wendy
d) 0
e) 9
f) 16
£2.65
250g bags cost £3.90 each. So 1kg = £15.60
100g costs £1.85. Buy 6 bags and he gets 3 free. This equals 9. Therefore, he has to buy 7 bags in total
7 * £1.85 = £12.95
Saving is £15.60 – £12.95
a) 1224
Will be half of 2448 . So 1224
b) 2496
Will be 48 greater than 2448. So 2496
c) 2.448
The numbers moved by a combined 3 decimal places. So move the decimal place in the original answer by 3 places
d) 51
Do 2448 ÷ 48 = 51. Then move decimal place 1 place to the left. This is because you multiplied 24.48 x 100 and 4.8 x 10. Therefore, the difference is 1 decimal place to adjust the number by
a) 27
540 ÷ 20
b) 50ml
20ml is added to 4 litres of water. Therefore, think in HCF of 4 & 10. This is 2. So first calculate 2 litres which would be 10ml. Therefore, 10 litres would be 5 * 10ml = 50ml
c) 3 weeks
6 litres of water would be 30ml of Kleeno per day. Therefore if a bottle contains 540ml, this would be equivalent to:
540 ÷ 30 = 18 daily cleans.
Given that the floor is cleaned every day apart from 1 day, then 1 week is 6 days of cleaning. Therefore this represents 3 weeks of cleaning
a) 876,512
b) 876,215
c) 2,568
The Rule for 6: The prime factors of 6 are 2 and 3. So for a number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3.
d) 6,198
Largest 4 Digit Number is 8765. Smallest 4 Digit Number is 2567. Difference is
12 & 5
Think first of multiples of 60. 6 * 10, 12 * 5, 30 * 2, 60 * 1. And so on. The answer being 12 * 5 since 12 -5 gives 7
27
3/8 * 72/1 = 3/1 * 9/1 = 27
36 & 64
Think of all the square numbers over 64….
81,100,121,144,169
36 + 64 = 100
a)0.569
Move decimal 2 places to the left when going smaller.
b) 2.007
1997 + 10
Write it out as a maths operations question per above
4,781
Simple multiplication question
a) 5
10T = 18 papers per teacher over the 3 hour timeframe. Which equals 6 papers per teacher per hour
To mark 90, requires total of 15 hours. Therefore 5 teachers
10/180 * T/90 = (10*90)/180 = T. T=5
b) 5
3 x 10 = T x 5 = 30/5
c) 120
6 papers per hour * 20 Teachers = 120 papers
850g
Total Mass = 2.5kg.
Try and convert to the same metric to work through the calculation. So 2,500g
2 Bags of Carrots = 250g x 2
1 Cabbage = 750g
Total of Carrots + Cabbage = 1,250g . Plus 4oog for shopping bag = 1,650g in total
Therefore, Potatoes = 2,500g – 1,650g = 850g
a) 70g
If 18 oatcakes requires 140g, then 9 would require half of this
b) 90 oatcakes
Need to think of factors. This is the trick to all of these styles of questions. So 80 ml makes 18 oatcakes. Therefore, if she only has 400 ml, then its how many “lots of” 80 do you get into 400. This would be 5 lots. So 5 lots of 18 oatcakes=90
c) See below:
Again, think of factors. Starting point is 18 and this question asks for 27. Therefore HCF of 18 & 27 is 9. If 18 requires X Ingredients, what does 9 require? This is your starting point. 9 requires half of what 18 requires. Therefore, 27 requires 3 times what 9 requires
a) 56
Work backwards. 20 MINUS 6 = 14 MULTIPLY BY 4 = 56
Sense check and work through from 56. 56/4 + 6 = 20
b) 7.5
6/4 = 1.5 + 6
c) even and multiples of 4
d) 48
18 minus 6 = 12. Multiply by 4 = 48
e) 216
Work backwads twice. 9 MINUS 6 = 15 X 4 = 60. Then again. 60 minus 6 = 54 x 4 = 216
a) 11
Work out RHS first = 26. Then rearrange formula if needed. ? = 26 – 15. Therefore ? =11
b) 5
2+20 = 27 – ?
BIDMAS
c) 0.5
18/3 = 6. ? x 12 = 6. This would bee 0.5
8 & 7
Best way is to think about multiples of 56. So this might be 28 & 2, 8 & 7 etc. 8&7 is the combination that multiplies to give 56 and added gives 15
36
Remember, “of” means multiplication in maths. So the simple way is 2/3 x 54/1. ALWAYS Cross Cancel where possible:
2/1 x 18/1 = 36
a) 800
Move decimal 3 places to the right. So it becomes 800
b) 3.49
Move decimal 2 places to the left
34
Do the inverse.
17 = 2 x ?
4,571
Simple multiplication question
29
He has 20 bars which means he gets 6 free bars. So 20/3 = 18 Remainder 2
He then has 6 free bar wrappers + 2 reminder = 8 bars
He then uses these 8 wrappers to get 2 free bars and this also leaves a remainder of 2
Then he uses the 2 remainder + 2 new wrappers he gets from the 2 free bars to get 1 more bar
So total is 20 + 6+ 2 + 1
a) 19
(5 x 4) -1
b) 8
Remember that normally, it would be takeaway 6 on the left hand side. If you take this to the other side, it will become addition. So lets do this:
m ? = 26 + 6
m ? = 32. So given its ? x 4, ? must be 8
c) 7
5 ? (4 * 4 – 3)
5 ? – (13) = 5 * 4 – (13) = 20 – 13 = 7
d) 9
[(6 X 4) – p ] x 4 = 56
[24 – p] x 4 – 4= 56
96 -4p-4 = 56
-4p=56-96+4
-4p = -36
p=9
Just read one statement at a time and use it to complete the table where possible
- 35 Boys. Therefore , 45 girls
- 2/3 of girls play stringed instrument. So 45 x 2/3 = 30. Which means 15 do not
- 38 do not play stringed instrument. Therefore, for boys, its 38 – 15 = 23
a) See below
b) See below
c) 9
Always one more than the pattern number
d) 15
Spot the pattern? Divide lines by 2 to get to the pattern number
e) 60
Formula would be : (Dots x 2) – 2 = number of lines. 31 * 2 = 2 = 60
3.6kg
Try doing the question in the same metric. So in this case, probably grams is easier to work with
Basket = 500g
Kitten = (600*4) = 2400g
Cat therefore = 6,500g (6.5kg) – 2400 – 500
Total = 3,600g.
Then convert back to KG
a) 87
She always tells the truth and the answer has to fulfill each statement. Given that its a multiple of 29 and is <100, its logical to start with going through multiples of 29. So 29,58,87
b) 60
She never tells the truth. So:
The number is less than 100. It is a multiple of 10. It does divide by 3 exactly and it has NO remainder when divided by 4.
Think of multiples of 10 and those multiples that divide exactly by 3 and are less than 100. These are 30,60 & 90. Of these the only number that is a multiple of 4 leaving no remainder is 60
4.5m
Freda Frog = 25 x 30 = 750
Teddy Toad = 40 x 30 = 1200
Remember to convert to metres.
a) 11
2 x 3 + 5 = 11
b) 13
2 x 5 + 3
c) 6
Work backwards. Output = 23 minus 5 = 18. Divide by 3
d) 1
a) 18
3=40p. Therefore, number of 40p’s in £2.40. 6 times.
b) £4.40
If 3 stickers cost 40p, then 3’s into 33 = 11x . Therefore 40p x 11
11 & 6
Start with 66 and think of multiples of 66. So 11 & 6
a) 31
Reverse Maths. 87 – 56
b) 2
54/6 = 9. Therefore, X + 7 has to be 2
c) 10,000
Question on how many places you have to move the decimal. Its 4 places
30
Use the approach of 5/8 * 48/1
Then cross cancellation etc and simplify this to 5/1 * 6/1
Cross cancellation is essential as it makes the calculation far easier overall and reduces error rates
63
Think about the multiples of 7 & 9 between 60 & 70
a) 1920
If not sure, write down the initial number, 2020. Then take away 100 from this. Its simply subtraction in words
b) 220
2.2 as the starting point. Move decimal 2 places to the right. So this gives 220
2,303
a) Approx 8cm. (Range 6 – 8cm is acceptable as it depends on the size of the online image or print out)
b) 35
8s into 280 . Use bus stop
c) £32.50
Firstly calculate number of weeks for 2 Years. This is 52 * 2 = 104
Next , number of “8 week batches” in 104 weeks. = 13
So cost is £2.50 x 13
d) 3,500
4 squeaks per minute. Therefore, 240 per hour
For 14 hours, its 240 * 14 = 3,360. Nearest 500 = 3,500
a) 15 laps
Convert the 6km to m which gives 6000m. 400 into 6000
Remove like for like zeros to make it easier to work through. So it becomes 4 into 60. This gives 15 laps
b) 13.8km
Always step by step on what you know:
- Marathon 13.4km
- Running Track 3 laps @ 400m = 1.2km
- Total of the above is 14.6km
- This leaves 42.2-14.6 as the town run. Which is 27.6km
- Half of this town run (as its 2 laps) would give 13.8km per town run lap
a) 9,180
The approach is to take 17 x 2. Given that you already have 17 x 538, its just another 17 x 2 that needs to be added onto the answer. So add 34 to 9146
b) 14,526
The change is from 17 to 27. So just take the difference of 10 and multiply by 538. This is 5380. Add this to the original answer
c) 269
Re-arrange the formula. 9146/17 = 538. So 9146/34 is half of the prior answer
a) 250/2 = 125g (amount for 6 waffles) x 3 = 375g
Think about HCF for 12 waffles v 18 waffles. The HCF for 12 & 18 is 6. Therefore, the best approach is to take 250/2 (to give 6 waffles). Then x that result by 3
b) 2eggs = 12 waffles. Therefore 1egg=6 waffles. 5 will therefore = 30 waffles
Again think about HCF of 2 & 5 which is 1. Therefore, the best way is to work out how many waffles you get for 1 egg and proceed from there
c) 75g
1oz = 25g. So 13oz = 13 * 25 = 325g
325 – 250 = 75g more
a) 9874
These questions do catch some students out. Start with the highest number and work digit by digit
b) 4987
c) 985
d) 9784
If any number ends in a two digit number that you know is divisible by 4 (e.g. 24, 04, 08, etc.), then the whole number will be divisible by 4 regardless of what is before the last two digits. Alternatively, one can simply divide the number by 2, and then check the result to find if it is divisible by 2.
a) See below…
(6×4)-3 = 21
(33+3) / 4 = 9 (need to work backwards so therefore, reverse the signage)
(-1+3) / 4 = 0.5
b) x2 + 2
Try with the bottom line first as these are positive numbers so slightly easier to work with
a) 2
Solve what you can. So 23 x ? = 46. Then re-arrange the formula. ? = 46/23 = 2
b) 4
Remember BIDMAS. Solve 5-2 first = 3. So 3 to power of 2 is 3×3 = 9.
13 = ? + 9. Re-arrange to give 4
c) 9
2 + 6 = 8
72 ÷ ? = 8. Re-arrange to give 9
2&3&7
Easier to think of product of 42 first which would be 3&7&2 . Thinking was to get to 21 and then double it using the “2”
54
72/1 x 3/4
Cross cancel to give 18/1 x 3/1. It is far easier to work through these questions if you have 1 as your denominator. The objective is to ensure you cross cancel to make the equation easier to work out
63
Its easier to work through this by doing your 7 times table. You get 56,63 and 70
The only one that is a multiple of 3 is 63
a) 34,200
Add 3 zeros on. Or , move the decimal 3 places to the right as its also good to think of it this way
b) 1,940
Write the numbers out. Its far easier to look at numbers and work things out than at words
2,040 – 100
42,498
Simple Operations Question
704
Similar to a prior question. Try a simpler example to see what happens. 25X4=100. So , substituting this into the question means 100/2=50
The divide by 2 is halving the prior number of 4 because in the question, 100 is halved to 50. Applying this approach, gave us 704 because we take 352 x 2
a) 972
Simple operations question. But a trick here is for students to “sense check”/ estimate their answer. So perhaps round 27 up to 30 and 36 down to 30 just to make sure you are “very broadly” in the right ballpark. This would give you 900. So its just to ensure you haven’t for example left out the zero when you are doing the second line of the Multiplication calculation. Or any other major error
b) 486
Students should see that 18 is half 36. So the calculation is not 27/18 but in your workings, should be 972/2
c) 9.72
Simply add the number of digits after the decimal place in the question. This is 2. Then move the decimal from (972. ) in your answer to 9.72
a) 3/7
The way to look at this is how you would approach a simpler question: Lets say….10+6 = 16. So 16-6=10
Therefore, the same approach says that 3/7ths is the answer. Proven, you can do the following:
25/42 – 1/6 = 25/42 – 7/42 = 18/42 = 3/7
b) 11/12
Same test using Example numbers. 3X7=21. Therefore, 21/3 = 7 .
The examples given above are simply that. Its easier to think of the same principles using examples and then substitute in the real question numbers rather than think of the question as a tricky fractions question and try and work it out.
i) 10 miles
ii) S to B to F to E to D to T
The thing to note here is that the map is not drawn to scale so extra attention has to be paid to the miles between different points
iii) 40 minutes
Time = Distance/ Speed. So substituting into the formula, Time = 10/15 which = 2/3 of 1 Hour (10/15 x 60). So thats 40 minutes
iv) 8 minutes
The revised route is S-B-C-T. So an extra 2 miles
This means 12/15 of 1 hour so 12/15 x 60 = 48 minutes
Difference being 8 minutes
Completed blanks in the following order
81-25=56
14×4=56
They are the same. (NOTE: This is a nice trick to remember). Follow the example guideline.
(552+448)x(552-448) = 1000 x 104 = 104,000
(8.5+7.5)x(8.5-7.5) = 16 x 1 = 16
(19/37+18/37)x(19/37-18/37) = 37/37 x 1/37 = 1/37
(25001+24999)x(25001-24999) = 50,000 x 2 = 100,000
NOTE: The above is a great approach to remember for future questions.
i) 1 burger £0.99
1 chips £1.20
1 coffee £0.65
Total £2.84
Do your workings neatly by aligning the columns for each digit
ii) Change £5.00
– £2.84
= £2.16
4 coins therefore being £2 coin, 10p, 5p, 1p
iii) 3 Sausages £1.35 (£0.45 x 3)
Meat Pie £2.20
Drink can £0.35
Total £3.90
iv) £50 – £44.40 = £5.60 spent
2 Meat Pies £4.40 (£2.20 x 2). Leaving £1.20 to spend
1 Coffee £0.65
1 Tea £0.55
Total £5.60
The above is by some trial and error. It is worth adding in the larger ticket items first. ie the Meat Pies. Then understanding where that leaves you. The answer should then be clear as being 1 coffee and 1 tea
78
13 x 6.
5 large
13 small
Total 18 crates needed.
Question requires breaking down the words and going statement by statement
L = 12 cartons
S = 4 cartons
(5 x 12) + (20 x 4) = 140 capacity
To store 110, you would use all the large crates first:
- 5 large used = 60 cartons. So 110-60 = 50 left to find crates for
- 50/4 = 12.5. So you need 13 crates of which the 13th will have 2 cartons in there. The other 12 will be full with 4 each. So 48
i) 10cm
ii) 2 inches
iii) 295cm
i) Calculate number of cm per inch. So 30cm/12.5inches = 2.5cm per inch.
4 x 2.5 = 10cm
ii) Work backwards now that you know its 2.5cm per inch
5cm/2.5cm per inch = 2 inches
iii) cm in 9ft 10 inches
9ft = 30cm (per foot) * 9 = 270cm
10 inches = 2.5 x 10 = 25cm
Total 295cm
£0
Step 1: 10% of £20 = £2
Step 2: 20% of £10 = £2
If not sure on % of an amount, use the following approach. Remember, “of” in maths means multiply
So 10/100 x 20/1. Remember to cross cancel to make the fraction easier to calculate
47.6
0.392
Standard Operations questions but just moving the decimals. Number of zeros in first qtn is 1, move 1 place to right. Number of zeros in second question being 2, move 2 places to left.
Multiply, move decimal to right. Divide, move decimal to left
34
With word questions like this, just start off with one sentence at a time:
- 2/5 get off at stop 1 = 35/5 *2 = 14 passengers get off. So this leaves 21. 7 get on so this gives 28
- 28 remaining and 1/4 get off. So this is 7. Leaving 21. 13 get on so this gives 34
Many students do get confused because of the number of words and phases to this journey. However, just methodically do one sentence at a time
£1.20
Can be done a few ways. Easiest way is to think of HCF of 750g and 1kg. This is 250g. Then to work out 250g cost and from there, x by 4
7 x 48 = 336
Standard Multiplication question…in words
85
Standard Operations Question