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Mental Arithmetic 4 (by Schofield & Sims) - Solution to Section 1 | Test 1B

August 02, 2025

Here is a detailed solutions to Mental Arithmetic 4 by Schofield & Sims, focusing on Section 1 | Test 1B. It is intended to support learners, educators, and parents by offering clear, step-by-step explanations for each question. The aim is to reinforce mental calculation strategies and help students assess their understanding through accurate and guided reasoning.

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This material, as provided by Ugwoke Charles, is not officially affiliated with or endorsed by Schofield & Sims. All questions, formats, and content referenced remain the intellectual property of their respective copyright holders. These solutions are offered strictly for educational and revision purposes. Readers are strongly encouraged to support the publisher by purchasing the original workbook.

 Solutions 

 Question 1: Write in digits the number twelve thousand and eight.

12 008

Question 2: How many groups of 9 are there in 6 sixes?

6 sixes means \(6 \times 6 = 36 \)
Divide 36 by 9
\( \frac{36}{9} = 4 \)
\( \therefore \) There are 4 groups of 9 in 6 sixes.
Answer = 4

Question 3: What is the difference in pence between \( £\frac{1}{5} \) and \( £\frac{1}{4} \)?

Convert the fractions of pounds to pence
£1 = 100pence
\( \frac{1}{5} \) pounds \( = \frac{1}{5} \times 100 = \frac{100}{5} = 20 \) pence
\( \frac{1}{4} \) pounds \( = \frac{1}{4} \times 100 = \frac{100}{4} = 25 \) pence
Difference in pence
25 pence \( - \) 20 pence \( = \) 5 pence
Answer = 5p

Question 4: How many tens are equal to 1070?

Divide 1070 by 10
\( \frac{1070}{10} = 107 \)
Answer = 107

Question 5: Find the total 0f 53p and £1.37

Convert £1.37 to pence
£1 = 100 pence
\(£1.37 = 1.37 \times 100 = 137 \) pence
Adding;
\( 53p + 137p = 190p \)

OR

Convert 53p to pounds
£1 = 100p
53p \( = £\frac{53}{100} = £0.53 \)
Adding;
\(£0.53 + £1.37 = £1.90 \)
Answer = 190p or £1.90

Question 6: By how many grams is \( \frac{1}{2} \) kg heavier than 280g?

Convert \( \frac{1}{2} \) kg to grams
1kg \( = \) 1000 g
\( \frac{1}{2} \) kg \( = \) \( (\frac{1}{2} \times 1000) \) grams \( = \frac{1000}{2} \) grams \( = 500 \) grams
Subtract 280g from 500g
500g \( - \) 280g \( = \) 220g
\( \therefore \) \( \frac{1}{2} \)kg is 220g heavier than 280g
Answer = 220g

Question 7: Find the cost of nine hairbands at 13p each.

To find the cost of nine hairbands at 13p each, you multiply:
\( 9 \times 13p = 117p \)
£1 = 100p
\( 117p = £\frac{117}{100} = £1.17 \)
Answer = 117p or £1.17

Question 8: How many millimetres are there in 10.7cm?

1cm = 10mm
10.7cm \( = 10.7 \times 10 \) mm \( = 107 \)mm
Answer = 107mm

Question 9: How much change from 50p after spending 17p and 16p?

First, add the two amounts spent:
\( 17p + 16p = 33p \)
Now subtract the total spent from 50p:
\( 50p − 33p = 17p \)
Answer = 17p

Question 10: Change to 24-hour clock times.
a. 9.35 a.m
b. 8.50 p.m.

a. 9:35 a.m.
Since it's a.m., the time stays the same but written in 24-hour format:
\( 9:35 \) a.m.\( = \) 09:35
b. 8:50 p.m.
For p.m. times (after 12 noon), add 12 hours:
\( 8:50 + 12 = 20:50 \)
\( \therefore 8:50 \) p.m. in 24-hour format is 20:50
Answer =
a. 09:35
b. 20:50

Question 11: Find the smallest number which will divide by both 6 and 8 without a remainder.

Break each number into its prime factors:
\( 6 = 2 \times 3 \)
\( 8 = 2 \times 2 \times 2 = 2^3 \)
Take the highest power of each prime number that appears:
For 2: Highest power is \( 2^3 \)
For 3: Highest power is \( 3^1 \)
Multiply the powers:
LCM \( = 2^3 \times 3 = 8 \times 3 = 24 \)
Answer = 24

Question 12: What sum of money when multiplied by 7 equals £1.12?

Convert £1.12 to Pence
Since £1 = 100p, we have:
£1.12 \( = 1 \times 100 + 12 = 112 \) pence
Let the Unknown Sum Be \( x \) Pence
\( 7x = 112 \)
\( x = \frac{112}{7} = 16 \)
Answer = 16p or £0.16
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