Mental Arithmetic 4 (by Schofield & Sims) - Solution to Section 1 | Test 1C
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Solutions
Question 1: In a box were 48 cards. How many cards were there in seven boxes?
\( 48 \times 7 = (50 - 2) \times 7 = 350 - 14 = 336 \)
Answer = 336 cards
Question 2: In the number \( \overset{x}{7} 4 \overset{y}{7} 9 \) how many times is the 7 marked x greater than the 7 marked y?
The second 7 (on the right) is marked \( y \) — it is in the tens place
7 in the thousands place (marked \( x \)) → value is 7000
7 in the tens place (marked \( y \)) → value is 70
Divide to find how many times greater the value of \( x \) is than \( y \):
\( \frac{7000}{70} = 100 \)
\( \therefore \) The 7 marked \( x \) is 100 times greater than the 7 marked \( y \).
Answer = 100
Question 3: The temperature was \( 4^o \)C and dropped by \( 7^o \)C. How many degrees warmer than \( -5 \) is the new temperature?
Starting temperature: \( 4^o \)C
Temperature dropped by \( 7^o \)C
We need to find how many degrees warmer than \( −5^o \)C the new temperature is.
Find the New Temperature
If the temperature dropped by \( 7^o \)C from \( 4^o \)C:
\( 4 − 7 = −3^o \)C
So, the new temperature is: \( -3^o \)C
How Many Degrees Warmer than \( −5^o \)C is \( −3^o \)C?
To find how much warmer:
\( − 3 − (−5) = − 3 + 5 = 2 \)
\( \therefore \) The new temperature is 2 degrees warmer than \( −5^o \)C.
Answer = \( 2^o \)C
Question 4: The rectangular card is cut into two equal parts along a diagonal. Find the area of each part.
A base \( = 8 \)cm
A height \( = 4 \)cm
Area of triangle \( = \frac{1}{2} \times base \times height \)
Substitute the Values
Area \( = \frac{1}{2} \times 8 \)cm \( \times 4 \)cm
\(= \frac{1}{2} \times 32 = \frac{32}{2} = 16 \) cm\(^2 \)
\( \therefore \) Each triangular part has an area of 16cm\( ^2 \) Answer = 16cm\( ^2 \)
Question 5: What are the next two numbers in this sequence?
\( \frac{1}{10}, 1, 10, \_\_, \_\_ \)
\( \frac{1}{10} \times 10 = \frac{10}{10} = 1 \)
\( 1 \times 10 = 10 \)
The next two terms will therefore be:
\( 10 \times 10 = 100 \)
\( 100 \times 10 = 1000 \)
Answer = 100, 1000
Question 6: Find the difference in cost between 12 items at 3p each and 12 items at 5p each.
12 items at 5p each
Find Total Cost for Each Group
First group (3p each):
\( 12 \times 3 \)p \( = 36 \)p
Second group (5p each):
\( 12 \times 5 \)p \( = 60 \)p
Find the Difference
\( 60 \)p \( − 36 \)p \( = 24 \)p
Answer = 24p
Question 7: A bus leaves its station at 8:40 a.m. and arrives at its destination at noon. How long does the journey take?
Departure time: 8:40 a.m.
Arrival time: 12:00 noon
Duration of journey:
From 8:40 a.m. to 9:00 a.m. \( = \) 20 minutes
From 9:00 a.m. to 12:00 noon \( = \) 3 hours
Adding:
3 hours \( + \) 20 minutes \( = \) 3 hours and 20 minutes
Answer = 3h 20min
Question 8: By how much is fabric B more expensive per metre than fabric A?
Fabric A = £3.96 per metre
Fabric B = £4.18 per metre
Subtracting:
£4.18 \( - \) £3.96 \( = \) £0.22
Answer = £0.22 or 22 pence
Question 9: The mass of cereal in a box is 425g. Find in kilograms and grams the mass of the cereal in 10 boxes.
Multiply to get total mass of 10 boxes of cereal
425g \( \times \) 10 \( = \) 4250g
Convert grams to kilograms and grams
1kg \( = \) 1000g
4250g \( = \) 4kg and 250g
Answer = 4kg and 250g
Question 10: The minute hand of a clock turns from pointing to number 2 the number 8. Through how many degrees has it turned?
A clock is a circle divided into 12 equal parts (for 12 hours).
Each number (or hour) on the clock is separated by:
\( \frac{360^o}{12} = 30^o \)
So, each number on the clock represents 30 degrees of rotation by the minute hand.
From 2 to 8 is 6 hours
\( 5 \times 30^o = 180^o \)
Answer \( = 180^o \)
Question 11: A cheesecake is cut into 12 equal pieces. What fraction of the cheesecake is seven pieces?
So if we have 7 out of 12 pieces, the fraction is:
\( \frac{7}{12} \)
Answer = \( \frac{7}{12} \)
Question 12: The diagram shows how Isla used her prize money.
b. The prize was £40. How much did she save?
From the shaded part, we can see that Isla spent 3 out of 8 parts.
a. What fracton did she spend?
She spent \( = \frac{3}{8} \)
b. The prize was £40. How much did she save?
If she spent \( \frac{3}{8} \) of her prize, then she saved:
\( 1 - \frac{3}{8} = \frac{8 - 3}{8} = \frac{5}{8} \)
Now calculate \( \frac{5}{8} \) of £40:
\( \frac{5}{8} \times \)£40 \( = \) £\( \frac{200}{8} = \)£25
Answer =
a. \( \frac{3}{8} \)
b. £25
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