**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) 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**

**120**

- Use BIDMAS
- 20 + (1 x 7) = 27
- (20 + 1) x 7 = 147
- 147-27

**74**

- (4+2) x 13 = 104
- 4 + (2×13) = 30
- Difference = 104 – 30

**70**

- Use BIDMAS. (7+3) x 11 = 10 x 11 = 110
- 7+ (3×11) = 40
- 110-40 = 70

Work backwards for this section….

Use BIDMAS

a) 5

b) 26

c) 112

Apply the rules of BIDMAS. Brackets, Indices, Division, Multiplication, Addition, Subtraction

**D**

- Use BIDMAS. Therefore…
- 32-8
- 24

**E**

- Apply the rules of BIDMAS
- 12-8+3
- 12-11
- 1

**5**

- Use BIDMAS. So Brackets, Indices, Division, Multiplication, Addition & Subtraction
- In that order
- First we do Multiplication. So 5 x 2 = 10
- Revised question becomes 21-10+6
- Then addition so 21-16
- Then subtraction
- So answer is 5

See below

**Ensure BIDMAS rules are applied**

**b)**

Remember the question is asking for the incorrect answer. In this case its b)

**a) 38**

BIDMAS. Do the multiplication first. 7×9 = 63. So, 63 – ? =25. Rearrange. -?=25-63. -?=-38.

**b) 9**

64/4 = 16. 16= ?+7

**c) 10**

36 = 16 + (2 x?). Rearrange. 36-16 = 2x?. 20/2 = ?

You can always substitute the numbers back into the equations to ensure your answer is correct

**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

**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

**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