Chapter 6 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
Are 3/6 and 12/24 equivalent? Explain.
Multiply numerator and denominator of 3/6 by the same factor 4; the represented amount is unchanged.
Insert <, >, or =: 1/3 ___ 2/5.
Rename fractions using common denominator 15 and compare equal-size parts.
Write 26/5 as a mixed number in simplest form.
26 ÷ 5 gives 5 full wholes and 1 remaining parts of size 1/5. Simplify the fractional part to obtain 5 1/5.
Write 47/10 as a mixed number in simplest form.
47 ÷ 10 gives 4 full wholes and 7 remaining parts of size 1/10. Simplify the fractional part to obtain 4 7/10.
Write 4 2/3 as an improper fraction.
Each whole has 3 parts. 4 wholes and 2 more parts make 14 parts.
4 identical pies are shared equally among 8 children. What fraction of one pie does each child get?
Divide 4 equal wholes into 8 shares: each gets 4/8 of a pie, equivalent to 1/2.
Are 1/2 and 2/4 equivalent? Explain.
Multiply numerator and denominator of 1/2 by the same factor 2; the represented amount is unchanged.
Insert <, >, or =: 2/10 ___ 7/10.
Rename fractions using common denominator 10 and compare equal-size parts.
Write 23/4 as a mixed number in simplest form.
23 ÷ 4 gives 5 full wholes and 3 remaining parts of size 1/4. Simplify the fractional part to obtain 5 3/4.
Write 22/10 as a mixed number in simplest form.
22 ÷ 10 gives 2 full wholes and 2 remaining parts of size 1/10. Simplify the fractional part to obtain 2 1/5.
Write 2 1/12 as an improper fraction.
Each whole has 12 parts. 2 wholes and 1 more parts make 25 parts.
3 identical pies are shared equally among 6 children. What fraction of one pie does each child get?
Divide 3 equal wholes into 6 shares: each gets 3/6 of a pie, equivalent to 1/2.
Are 1/5 and 2/10 equivalent? Explain.
Multiply numerator and denominator of 1/5 by the same factor 2; the represented amount is unchanged.
Insert <, >, or =: 1/8 ___ 7/8.
Rename fractions using common denominator 8 and compare equal-size parts.
Write 13/4 as a mixed number in simplest form.
13 ÷ 4 gives 3 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 3 1/4.
Write 49/12 as a mixed number in simplest form.
49 ÷ 12 gives 4 full wholes and 1 remaining parts of size 1/12. Simplify the fractional part to obtain 4 1/12.
Write 1 3/12 as an improper fraction.
Each whole has 12 parts. 1 wholes and 3 more parts make 15 parts.
9 identical pies are shared equally among 9 children. What fraction of one pie does each child get?
Divide 9 equal wholes into 9 shares: each gets 9/9 of a pie, equivalent to 1.
Are 3/10 and 15/50 equivalent? Explain.
Multiply numerator and denominator of 3/10 by the same factor 5; the represented amount is unchanged.
Insert <, >, or =: 9/10 ___ 1/4.
Rename fractions using common denominator 20 and compare equal-size parts.
Write 19/10 as a mixed number in simplest form.
19 ÷ 10 gives 1 full wholes and 9 remaining parts of size 1/10. Simplify the fractional part to obtain 1 9/10.
Write 16/3 as a mixed number in simplest form.
16 ÷ 3 gives 5 full wholes and 1 remaining parts of size 1/3. Simplify the fractional part to obtain 5 1/3.
Write 1 2/6 as an improper fraction.
Each whole has 6 parts. 1 wholes and 2 more parts make 8 parts.
3 identical pies are shared equally among 5 children. What fraction of one pie does each child get?
Divide 3 equal wholes into 5 shares: each gets 3/5 of a pie, equivalent to 3/5.
Are 4/12 and 20/60 equivalent? Explain.
Multiply numerator and denominator of 4/12 by the same factor 5; the represented amount is unchanged.
Insert <, >, or =: 2/4 ___ 6/8.
Rename fractions using common denominator 8 and compare equal-size parts.
Write 14/4 as a mixed number in simplest form.
14 ÷ 4 gives 3 full wholes and 2 remaining parts of size 1/4. Simplify the fractional part to obtain 3 1/2.
A student claims 2/3 equals 3/4 because the numerator and denominator each increase by 1. Explain the error.
Equivalent fractions multiply numerator and denominator by the same nonzero factor. 2/3 = 8/12 while 3/4 = 9/12.
Two students each shade 2/5 of a rectangle, but one rectangle has twice the area of the other. Are the shaded areas necessarily equal? Explain.
Both shade 2/5 of their own reference whole. Because one whole has twice the area, that shaded region also has twice the area.
Someone calls 7/4 seven whole numbers. Express 7/4 as a mixed number and explain.
Four fourths make one whole; three fourths remain.
A student says 11/3 = 3 1/3. Use groups of thirds to correct the mixed number.
Eleven thirds contain three groups of three thirds with two thirds left.
A student converts 2 3/5 to 5/13. Explain the mistake and provide the correct improper fraction.
Two wholes contain ten fifths, plus three fifths gives thirteen fifths.
Three equal pies are shared equally among four people. What fraction of a pie does each person get, and why?
Divide each pie into fourths: there are twelve fourths total, shared in groups of three fourths.
Practice examination solutions and scoring
Complete an equivalent fraction: 1/4 = ?/20.
The denominator was multiplied by 5, so the numerator must also be multiplied by 5.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Insert <, >, or =: 1/3 ___ 4/8.
Rename fractions using common denominator 24 and compare equal-size parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 21/6 as a mixed number in simplest form.
21 ÷ 6 gives 3 full wholes and 3 remaining parts of size 1/6. Simplify the fractional part to obtain 3 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 11/4 as a mixed number in simplest form.
11 ÷ 4 gives 2 full wholes and 3 remaining parts of size 1/4. Simplify the fractional part to obtain 2 3/4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 5 1/3 as an improper fraction.
Each whole has 3 parts. 5 wholes and 1 more parts make 16 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
10 identical pies are shared equally among 7 children. What fraction of one pie does each child get?
Divide 10 equal wholes into 7 shares: each gets 10/7 of a pie, equivalent to 10/7.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Insert <, >, or =: 2/4 ___ 1/4.
Rename fractions using common denominator 4 and compare equal-size parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 5/4 as a mixed number in simplest form.
5 ÷ 4 gives 1 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 1 1/4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 23/6 as a mixed number in simplest form.
23 ÷ 6 gives 3 full wholes and 5 remaining parts of size 1/6. Simplify the fractional part to obtain 3 5/6.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 5 1/2 as an improper fraction.
Each whole has 2 parts. 5 wholes and 1 more parts make 11 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
5 identical pies are shared equally among 9 children. What fraction of one pie does each child get?
Divide 5 equal wholes into 9 shares: each gets 5/9 of a pie, equivalent to 5/9.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Complete an equivalent fraction: 2/5 = ?/10.
The denominator was multiplied by 2, so the numerator must also be multiplied by 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 17/3 as a mixed number in simplest form.
17 ÷ 3 gives 5 full wholes and 2 remaining parts of size 1/3. Simplify the fractional part to obtain 5 2/3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 17/8 as a mixed number in simplest form.
17 ÷ 8 gives 2 full wholes and 1 remaining parts of size 1/8. Simplify the fractional part to obtain 2 1/8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 3 3/12 as an improper fraction.
Each whole has 12 parts. 3 wholes and 3 more parts make 39 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
7 identical pies are shared equally among 3 children. What fraction of one pie does each child get?
Divide 7 equal wholes into 3 shares: each gets 7/3 of a pie, equivalent to 7/3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Complete an equivalent fraction: 2/3 = ?/9.
The denominator was multiplied by 3, so the numerator must also be multiplied by 3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Order these fractions from least to greatest: 1/3, 4/5, 7/8.
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 9/2 as a mixed number in simplest form.
9 ÷ 2 gives 4 full wholes and 1 remaining parts of size 1/2. Simplify the fractional part to obtain 4 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 1 3/10 as an improper fraction.
Each whole has 10 parts. 1 wholes and 3 more parts make 13 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
7 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Divide 7 equal wholes into 4 shares: each gets 7/4 of a pie, equivalent to 7/4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Complete an equivalent fraction: 4/5 = ?/15.
The denominator was multiplied by 3, so the numerator must also be multiplied by 3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Insert <, >, or =: 1/3 ___ 3/6.
Rename fractions using common denominator 6 and compare equal-size parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 53/12 as a mixed number in simplest form.
53 ÷ 12 gives 4 full wholes and 5 remaining parts of size 1/12. Simplify the fractional part to obtain 4 5/12.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 2 1/2 as an improper fraction.
Each whole has 2 parts. 2 wholes and 1 more parts make 5 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
7 identical pies are shared equally among 5 children. What fraction of one pie does each child get?
Divide 7 equal wholes into 5 shares: each gets 7/5 of a pie, equivalent to 7/5.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Are 2/3 and 10/15 equivalent? Explain.
Multiply numerator and denominator of 2/3 by the same factor 5; the represented amount is unchanged.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Are 3/4 and 15/20 equivalent? Explain.
Multiply numerator and denominator of 3/4 by the same factor 5; the represented amount is unchanged.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Two students each shade 3/5 of a rectangle, but one rectangle has twice the area of the other. Are the shaded areas necessarily equal? Explain.
Both shade 3/5 of their own reference whole. Because one whole has twice the area, that shaded region also has twice the area.
Scoring (4 points): Award one point for a sound method and one for the correct result.
Write 42/12 as a mixed number in simplest form.
42 ÷ 12 gives 3 full wholes and 6 remaining parts of size 1/12. Simplify the fractional part to obtain 3 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 29/8 as a mixed number in simplest form.
29 ÷ 8 gives 3 full wholes and 5 remaining parts of size 1/8. Simplify the fractional part to obtain 3 5/8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Write 5 1/4 as an improper fraction.
Each whole has 4 parts. 5 wholes and 1 more parts make 21 parts.
Scoring (2 points): Award one point for a sound method and one for the correct result.
8 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Divide 8 equal wholes into 4 shares: each gets 8/4 of a pie, equivalent to 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.