Chapter 8 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
What is 1/10 of 60 counters?
Partition 60 into 10 equal groups: 60 ÷ 10 = 6.
Calculate 1/4 × 8. Give the simplified result.
8 copies of 1/4 make 8/4 = 2.
Calculate 1/10 × 5. Give the simplified result.
5 copies of 1/10 make 5/10 = 1/2.
Find 6/8 of a set of 24 objects.
Divide into 8 equal groups of 3, then choose 6 groups for 18 objects.
Find 2/4 of a set of 20 objects.
Divide into 4 equal groups of 5, then choose 2 groups for 10 objects.
Find 4/5 of a set of 30 objects.
Divide into 5 equal groups of 6, then choose 4 groups for 24 objects.
A teacher has 70 cards. She gives 9/10 of them away. How many cards remain?
9/10 of 70 is 63; subtract from the original 70.
A shop starts with 36 items and sells 2/6. It then sells 1/4 of what remains. How many items remain?
First 12 sell, leaving 24. Taking 1/4 of that remainder removes 6, so 18 remain.
What is 1/6 of 48 counters?
Partition 48 into 6 equal groups: 48 ÷ 6 = 8.
Calculate 1/2 × 9. Give the simplified result.
9 copies of 1/2 make 9/2 = 4 1/2.
Calculate 4/8 × 8. Give the simplified result.
8 copies of 4/8 make 32/8 = 4.
Find 9/10 of a set of 40 objects.
Divide into 10 equal groups of 4, then choose 9 groups for 36 objects.
Find 2/5 of a set of 40 objects.
Divide into 5 equal groups of 8, then choose 2 groups for 16 objects.
Find 4/8 of a set of 64 objects.
Divide into 8 equal groups of 8, then choose 4 groups for 32 objects.
A teacher has 24 cards. She gives 4/8 of them away. How many cards remain?
4/8 of 24 is 12; subtract from the original 24.
A shop starts with 20 items and sells 3/4. It then sells 1/5 of what remains. How many items remain?
First 15 sell, leaving 5. Taking 1/5 of that remainder removes 1, so 4 remain.
What is 1/5 of 10 counters?
Partition 10 into 5 equal groups: 10 ÷ 5 = 2.
Calculate 5/8 × 6. Give the simplified result.
6 copies of 5/8 make 30/8 = 3 3/4.
Calculate 3/5 × 5. Give the simplified result.
5 copies of 3/5 make 15/5 = 3.
Find 2/4 of a set of 28 objects.
Divide into 4 equal groups of 7, then choose 2 groups for 14 objects.
Find 1/4 of a set of 32 objects.
Divide into 4 equal groups of 8, then choose 1 groups for 8 objects.
Find 3/8 of a set of 32 objects.
Divide into 8 equal groups of 4, then choose 3 groups for 12 objects.
A teacher has 40 cards. She gives 1/5 of them away. How many cards remain?
1/5 of 40 is 8; subtract from the original 40.
A shop starts with 30 items and sells 5/6. It then sells 1/5 of what remains. How many items remain?
First 25 sell, leaving 5. Taking 1/5 of that remainder removes 1, so 4 remain.
What is 1/6 of 42 counters?
Partition 42 into 6 equal groups: 42 ÷ 6 = 7.
Calculate 1/2 × 6. Give the simplified result.
6 copies of 1/2 make 6/2 = 3.
Calculate 3/6 × 4. Give the simplified result.
4 copies of 3/6 make 12/6 = 2.
A student finds one-fourth of 28 by multiplying 28 × 4. Explain and give the correct amount.
One fourth means dividing 28 into four equal groups; 28 ÷ 4 = 7.
A student says (2/5) × 3 equals 2/15 because the denominator should multiply by three. Correct and explain.
Three copies of two fifths give six fifths, or one and one fifth.
Calculate 1/6 × 4. Give the simplified result.
4 copies of 1/6 make 4/6 = 2/3.
How many buttons are in three-fifths of a set of 20 buttons? Explain the equal groups.
Twenty makes five groups of four; three groups contain twelve buttons.
A learner says 24 × 3/4 must be bigger than 24 because this is multiplication. Correct the claim.
Multiplying by a positive proper fraction takes part of the whole: three groups of six are eighteen.
Calculate 30 × 2/5 using division before multiplication. Explain why the order works.
Split 30 into five groups of six, then take two groups: 12.
A classroom has 40 cards and gives three-eighths away. How many cards remain?
Three-eighths of forty is fifteen, and forty minus fifteen is twenty-five.
A shop has 42 boxes and sells 1/3 of its stock on Monday and 1/2 of what remains on Tuesday. Did it sell 5/6 of its original stock? Explain.
After Monday 2/3 remains; on Tuesday half of that is 1/3 of original, so 2/3 was sold altogether.
Practice examination solutions and scoring
What is 1/2 of 14 counters?
Partition 14 into 2 equal groups: 14 ÷ 2 = 7.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A shop starts with 12 items and sells 1/4. It then sells 1/3 of what remains. How many items remain?
First 3 sell, leaving 9. Taking 1/3 of that remainder removes 3, so 6 remain.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
A teacher has 40 cards. She gives 2/5 of them away. How many cards remain?
2/5 of 40 is 16; subtract from the original 40.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Find 3/4 of a set of 24 objects.
Divide into 4 equal groups of 6, then choose 3 groups for 18 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 2/4 of a set of 36 objects.
Divide into 4 equal groups of 9, then choose 2 groups for 18 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 1/2 of a set of 18 objects.
Divide into 2 equal groups of 9, then choose 1 groups for 9 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1/2 × 4. Give the simplified result.
4 copies of 1/2 make 4/2 = 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1/2 × 5. Give the simplified result.
5 copies of 1/2 make 5/2 = 2 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 7/8 × 5. Give the simplified result.
5 copies of 7/8 make 35/8 = 4 3/8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is 1/5 of 40 counters?
Partition 40 into 5 equal groups: 40 ÷ 5 = 8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A shop starts with 21 items and sells 1/3. It then sells 1/2 of what remains. How many items remain?
First 7 sell, leaving 14. Taking 1/2 of that remainder removes 7, so 7 remain.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
A teacher has 20 cards. She gives 8/10 of them away. How many cards remain?
8/10 of 20 is 16; subtract from the original 20.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Find 1/5 of a set of 15 objects.
Divide into 5 equal groups of 3, then choose 1 groups for 3 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 2/10 of a set of 60 objects.
Divide into 10 equal groups of 6, then choose 2 groups for 12 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 1/4 of a set of 16 objects.
Divide into 4 equal groups of 4, then choose 1 groups for 4 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1/2 × 7. Give the simplified result.
7 copies of 1/2 make 7/2 = 3 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 7/8 × 4. Give the simplified result.
4 copies of 7/8 make 28/8 = 3 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 4/6 × 8. Give the simplified result.
8 copies of 4/6 make 32/6 = 5 1/3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is 1/2 of 4 counters?
Partition 4 into 2 equal groups: 4 ÷ 2 = 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A shop starts with 64 items and sells 3/8. It then sells 1/2 of what remains. How many items remain?
First 24 sell, leaving 40. Taking 1/2 of that remainder removes 20, so 20 remain.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
A teacher has 12 cards. She gives 4/6 of them away. How many cards remain?
4/6 of 12 is 8; subtract from the original 12.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Find 9/10 of a set of 30 objects.
Divide into 10 equal groups of 3, then choose 9 groups for 27 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 1/3 of a set of 27 objects.
Divide into 3 equal groups of 9, then choose 1 groups for 9 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 3/4 of a set of 12 objects.
Divide into 4 equal groups of 3, then choose 3 groups for 9 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 3/4 of a set of 20 objects.
Divide into 4 equal groups of 5, then choose 3 groups for 15 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 3/6 × 3. Give the simplified result.
3 copies of 3/6 make 9/6 = 1 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 2/3 × 9. Give the simplified result.
9 copies of 2/3 make 18/3 = 6.
Scoring (2 points): Award one point for a sound method and one for the correct result.
What is 1/2 of 6 counters?
Partition 6 into 2 equal groups: 6 ÷ 2 = 3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1/2 × 2. Give the simplified result.
2 copies of 1/2 make 2/2 = 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 4/10 × 5. Give the simplified result.
5 copies of 4/10 make 20/10 = 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 2/4 of a set of 8 objects.
Divide into 4 equal groups of 2, then choose 2 groups for 4 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 1/4 of a set of 24 objects.
Divide into 4 equal groups of 6, then choose 1 groups for 6 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 1/2 of a set of 14 objects.
Divide into 2 equal groups of 7, then choose 1 groups for 7 objects.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A teacher has 12 cards. She gives 2/6 of them away. How many cards remain?
2/6 of 12 is 4; subtract from the original 12.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A shop has 33 boxes and sells 1/3 of its stock on Monday and 1/2 of what remains on Tuesday. Did it sell 5/6 of its original stock? Explain.
After Monday 2/3 remains; on Tuesday half of that is 1/3 of original, so 2/3 was sold altogether.
Scoring (4 points): Award one point for a sound method and one for the correct result.