Chapter 6 — cumulative chapter review
Semester 4A · Chapter 6 · 33 questions
This review integrates every chapter learning objective. Try questions before revealing answers.
Are 3/6 and 12/24 equivalent? Explain.
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Multiply numerator and denominator of 3/6 by the same factor 4; the represented amount is unchanged.
Insert <, >, or =: 1/3 ___ 2/5.
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Rename fractions using common denominator 15 and compare equal-size parts.
Write 26/5 as a mixed number in simplest form.
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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.
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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.
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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?
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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.
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Multiply numerator and denominator of 1/2 by the same factor 2; the represented amount is unchanged.
Insert <, >, or =: 2/10 ___ 7/10.
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Rename fractions using common denominator 10 and compare equal-size parts.
Write 23/4 as a mixed number in simplest form.
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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.
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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.
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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?
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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.
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Multiply numerator and denominator of 1/5 by the same factor 2; the represented amount is unchanged.
Insert <, >, or =: 1/8 ___ 7/8.
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Rename fractions using common denominator 8 and compare equal-size parts.
Write 13/4 as a mixed number in simplest form.
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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.
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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.
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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?
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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.
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Multiply numerator and denominator of 3/10 by the same factor 5; the represented amount is unchanged.
Insert <, >, or =: 9/10 ___ 1/4.
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Rename fractions using common denominator 20 and compare equal-size parts.
Write 19/10 as a mixed number in simplest form.
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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.
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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.
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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?
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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.
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Multiply numerator and denominator of 4/12 by the same factor 5; the represented amount is unchanged.
Insert <, >, or =: 2/4 ___ 6/8.
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Rename fractions using common denominator 8 and compare equal-size parts.
Write 14/4 as a mixed number in simplest form.
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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.
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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.
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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.
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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.
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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.
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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?
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Divide each pie into fourths: there are twelve fourths total, shared in groups of three fourths.