Mental Arithmetic 4 (by Schofield & Sims) - Solution to Section 1 | Test 1B
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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Solutions
Question 1: Write in digits the number twelve thousand and eight.
Question 2: How many groups of 9 are there in 6 sixes?
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 \( £\frac{1}{4} \)?
£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?
\( \frac{1070}{10} = 107 \)
Answer = 107
Question 5: Find the total 0f 53p and £1.37
£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?
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.
\( 9 \times 13p = 117p \)
£1 = 100p
\( 117p = £\frac{117}{100} = £1.17 \)
Answer = 117p or £1.17
Question 8: How many millimetres are there in 10.7cm?
10.7cm \( = 10.7 \times 10 \) mm \( = 107 \)mm
Answer = 107mm
Question 9: How much change from 50p after spending 17p and 16p?
\( 17p + 16p = 33p \)
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.
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.
\( 6 = 2 \times 3 \)
\( 8 = 2 \times 2 \times 2 = 2^3 \)
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?
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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