McGraw Hill Math Grade 6 Lesson 7.3 Answer Key Multiplying Fractions and Mixed Numbers: Reducing

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 7.3 Multiplying Fractions and Mixed Numbers: Reducing will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 7.3 Multiplying Fractions and Mixed Numbers: Reducing

Exercises Multiply, Reduce

Question 1.
1\(\frac{1}{2}\) × \(\frac{4}{5}\)
Answer:
1\(\frac{1}{2}\) × \(\frac{4}{5}\) = \(\frac{6}{5}\)

Explanation:
1\(\frac{1}{2}\) × \(\frac{4}{5}\)
= {[(1 × 2) + 1] ÷ 2} × \(\frac{4}{5}\)
= [(2 + 1) ÷ 2] × \(\frac{4}{5}\)
= \(\frac{3}{2}\) × \(\frac{4}{5}\)
= \(\frac{3}{1}\) × \(\frac{2}{5}\)
= \(\frac{6}{5}\)

Question 2.
\(\frac{2}{9}\) × 4\(\frac{1}{4}\)
Answer:
\(\frac{2}{9}\) × 4\(\frac{1}{4}\) = \(\frac{17}{18}\)

Explanation:
\(\frac{2}{9}\) × 4\(\frac{1}{4}\)
= \(\frac{2}{9}\) ×{[(4 × 4) + 1] ÷ 4}
= \(\frac{2}{9}\) × [(16 + 1) ÷ 4]
= \(\frac{2}{9}\) × \(\frac{17}{4}\)
= \(\frac{1}{9}\) × \(\frac{17}{2}\)
= \(\frac{17}{18}\)

Question 3.
\(\frac{3}{4}\) × 2\(\frac{1}{7}\)
Answer:
\(\frac{3}{4}\) × 2\(\frac{1}{7}\) = \(\frac{45}{28}\)

Explanation:
\(\frac{3}{4}\) × 2\(\frac{1}{7}\)
= \(\frac{3}{4}\) × {[(2 × 7) + 1] ÷ 7}
= \(\frac{3}{4}\) × [(14 + 1) ÷ 7]
= \(\frac{3}{4}\) × \(\frac{15}{7}\)
= \(\frac{45}{28}\)

Question 4.
5\(\frac{1}{3}\) × \(\frac{1}{2}\)
Answer:
5\(\frac{1}{3}\) × \(\frac{1}{2}\) = \(\frac{8}{3}\)

Explanation:
5\(\frac{1}{3}\) × \(\frac{1}{2}\)
= {[(5 × 3) + 1] ÷ 3} × \(\frac{1}{2}\)
= [(15 + 1) ÷ 3] × \(\frac{1}{2}\)
= \(\frac{16}{3}\) × \(\frac{1}{2}\)
= \(\frac{8}{3}\) × \(\frac{1}{1}\)
= \(\frac{8}{3}\)

Question 5.
\(\frac{8}{9}\) × 3\(\frac{1}{5}\)
Answer:
\(\frac{8}{9}\) × 3\(\frac{1}{5}\) = \(\frac{128}{45}\)

Explanation:
\(\frac{8}{9}\) × 3\(\frac{1}{5}\)
= \(\frac{8}{9}\) × {[(3 × 5) + 1] ÷ 5}
= \(\frac{8}{9}\) × [(15 + 1) ÷ 5]
= \(\frac{8}{9}\) × \(\frac{16}{5}\)
= \(\frac{128}{45}\)

Question 6.
1\(\frac{2}{3}\) × \(\frac{2}{7}\)
Answer:
1\(\frac{2}{3}\) × \(\frac{2}{7}\) = \(\frac{10}{21}\)

Explanation:
1\(\frac{2}{3}\) × \(\frac{2}{7}\)
= {[(1 × 3) + 2] ÷ 3} × \(\frac{2}{7}\)
= [(3 + 2) ÷ 3] × \(\frac{2}{7}\)
= \(\frac{5}{3}\) × \(\frac{2}{7}\)
= \(\frac{10}{21}\)

Question 7.
5\(\frac{1}{4}\) × \(\frac{2}{3}\)
Answer:
5\(\frac{1}{4}\) × \(\frac{2}{3}\) = \(\frac{7}{2}\)

Explanation:
5\(\frac{1}{4}\) × \(\frac{2}{3}\)
= {[(5 × 4) + 1] ÷ 4} × \(\frac{2}{3}\)
= [(20 + 1) ÷ 4] × \(\frac{2}{3}\)
= \(\frac{21}{4}\) × \(\frac{2}{3}\)
= \(\frac{21}{2}\) × \(\frac{1}{3}\)
= \(\frac{7}{2}\) × \(\frac{1}{1}\)
= \(\frac{7}{2}\)

Question 8.
7\(\frac{1}{8}\) × \(\frac{1}{4}\)
Answer:
7\(\frac{1}{8}\) × \(\frac{1}{4}\) = \(\frac{57}{32}\)

Explanation:
7\(\frac{1}{8}\) × \(\frac{1}{4}\)
= {[(7 × 8) + 1] ÷ 8} × \(\frac{1}{4}\)
= [(56 + 1) ÷ 8] × \(\frac{1}{4}\)
= \(\frac{57}{8}\) × \(\frac{1}{4}\)
= \(\frac{57}{32}\)

Question 9.
1\(\frac{1}{2}\) × \(\frac{8}{9}\)
Answer:
1\(\frac{1}{2}\) × \(\frac{8}{9}\) = \(\frac{4}{3}\)

Explanation:
1\(\frac{1}{2}\) × \(\frac{8}{9}\)
= {[(1 × 2) + 1] ÷ 2 × \(\frac{8}{9}\)
= [(2 + 1) ÷ 2]× \(\frac{8}{9}\)
= \(\frac{3}{2}\) × \(\frac{8}{9}\)
= \(\frac{3}{1}\) × \(\frac{4}{9}\)
= \(\frac{1}{1}\) × \(\frac{4}{3}\)
= \(\frac{4}{3}\)

Question 10.
\(\frac{3}{7}\) × 5\(\frac{1}{7}\)
Answer:
\(\frac{3}{7}\) × 5\(\frac{1}{7}\) = \(\frac{108}{49}\)

Explanation:
\(\frac{3}{7}\) × 5\(\frac{1}{7}\)
= \(\frac{3}{7}\) × {[(5 × 7) + 1] ÷ 7}
= \(\frac{3}{7}\) × [(35 + 1) ÷ 7
= \(\frac{3}{7}\) × \(\frac{36}{7}\)
= \(\frac{108}{49}\)

Question 11.
\(\frac{1}{3}\) × 5\(\frac{2}{3}\)
Answer:
\(\frac{1}{3}\) × 5\(\frac{2}{3}\) = \(\frac{17}{9}\)

Explanation:
\(\frac{1}{3}\) × 5\(\frac{2}{3}\)
= \(\frac{1}{3}\) × {[(5 × 3) + 2] ÷ 3}
= \(\frac{1}{3}\) × [(15 + 2) ÷ 3]
= \(\frac{1}{3}\) × \(\frac{17}{3}\)
= \(\frac{17}{9}\)

Question 12.
\(\frac{5}{6}\) × 1\(\frac{1}{5}\)
Answer:
\(\frac{5}{6}\) × 1\(\frac{1}{5}\) = 1.

Explanation:
\(\frac{5}{6}\) × 1\(\frac{1}{5}\)
= \(\frac{5}{6}\) × {[(1 × 5) + 1] ÷ 5}
= \(\frac{5}{6}\) × [(5 + 1) ÷ 5]
= \(\frac{5}{6}\) × \(\frac{6}{5}\)
= 1.

Question 13.
\(\frac{3}{4}\) × 5\(\frac{1}{3}\)
Answer:
\(\frac{3}{4}\) × 5\(\frac{1}{3}\) = 4.

Explanation:
\(\frac{3}{4}\) × 5\(\frac{1}{3}\)
= \(\frac{3}{4}\) ×{[(5 × 3) + 1] ÷ 3}
= \(\frac{3}{4}\) × [(15 + 1) ÷ 3]
= \(\frac{3}{4}\) × \(\frac{16}{3}\)
= \(\frac{1}{4}\) × \(\frac{16}{1}\)
= \(\frac{1}{1}\) × \(\frac{4}{1}\)
= \(\frac{4}{1}\)
= 4.

Question 14.
3\(\frac{1}{4}\) × \(\frac{3}{7}\)
Answer:
3\(\frac{1}{4}\) × \(\frac{3}{7}\) = \(\frac{39}{28}\)

Explanation:
3\(\frac{1}{4}\) × \(\frac{3}{7}\)
= {[(3 × 4) + 1] ÷ 4} × \(\frac{3}{7}\)
= [(12 + 1) ÷ 4] × \(\frac{3}{7}\)
= \(\frac{13}{4}\) × \(\frac{3}{7}\)
= \(\frac{39}{28}\)

Question 15.
5\(\frac{2}{11}\) × \(\frac{22}{23}\)
Answer:
5\(\frac{2}{11}\) × \(\frac{22}{23}\) = \(\frac{114}{23}\)

Explanation:
5\(\frac{2}{11}\) × \(\frac{22}{23}\)
= {[(5 × 11) + 2] ÷ 11}× \(\frac{22}{23}\)
= [(55 + 2) ÷ 11] × \(\frac{22}{23}\)
= \(\frac{57}{11}\) × \(\frac{22}{23}\)
= \(\frac{57}{1}\) × \(\frac{2}{23}\)
= \(\frac{114}{23}\)

Exercises Multiply, Reduce
Question 1.
1\(\frac{1}{4}\) × 2\(\frac{2}{3}\)
Answer:
1\(\frac{1}{4}\) × 2\(\frac{2}{3}\) = \(\frac{10}{3}\)

Explanation:
1\(\frac{1}{4}\) × 2\(\frac{2}{3}\)
= {[(1× 4) + 1] ÷ 4} × {[(2× 3) + 2] ÷ 3}
= [(4 + 1) ÷ 4] × [(6 + 2) ÷ 3]
= \(\frac{5}{4}\) × \(\frac{8}{3}\)
= \(\frac{5}{1}\) × \(\frac{2}{3}\)
= \(\frac{10}{3}\)

Question 2.
2\(\frac{1}{5}\) × 5\(\frac{1}{4}\)
Answer:
2\(\frac{1}{5}\) × 5\(\frac{1}{4}\) = \(\frac{231}{15}\)

Explanation:
2\(\frac{1}{5}\) × 5\(\frac{1}{4}\)
= {[(2× 5) + 1] ÷ 5} × {[(5× 4) + 1] ÷ 3}
= [(10 + 1) ÷ 5] × [(20 + 1) ÷ 3]
= \(\frac{11}{5}\) × \(\frac{21}{3}\)
= \(\frac{231}{15}\)

Question 3.
5\(\frac{1}{8}\) × 2\(\frac{2}{3}\)
Answer:
5\(\frac{1}{8}\) × 2\(\frac{2}{3}\) = \(\frac{41}{2}\)

Explanation:
5\(\frac{1}{8}\) × 2\(\frac{2}{3}\)
= {[(5 × 8) + 1] ÷ 8} × {[(2 × 3) + 2] ÷ 3}
= [(40 + 1) ÷ 8] × [(6 + 2) ÷ 3]
= \(\frac{41}{8}\) × \(\frac{12}{3}\)
= \(\frac{41}{2}\) × \(\frac{3}{3}\)
= \(\frac{41}{2}\) × \(\frac{1}{1}\)
= \(\frac{41}{2}\)

Question 4.
2\(\frac{3}{7}\) × 2\(\frac{3}{4}\)
Answer:
2\(\frac{3}{7}\) × 2\(\frac{3}{4}\) = \(\frac{187}{28}\)

Explanation:
2\(\frac{3}{7}\) × 2\(\frac{3}{4}\)
= {[(2 × 7) + 3] ÷ 7} × {[(2 × 4) + 3] ÷ 4}
= [(14 + 3) ÷ 7] × [(8 + 3) ÷ 4]
= \(\frac{17}{7}\) × \(\frac{11}{4}\)
= \(\frac{187}{28}\)

Question 5.
2\(\frac{1}{7}\) × 1\(\frac{1}{3}\)
Answer:
2\(\frac{1}{7}\) × 1\(\frac{1}{3}\) = \(\frac{20}{7}\)

Explanation:
2\(\frac{1}{7}\) × 1\(\frac{1}{3}\)
= {[(2 × 7) + 1] ÷ 7} × {[(1 × 3) + 1] ÷ 3}
= [(14 + 1) ÷ 7] × [(3 + 1) ÷ 3]
= \(\frac{15}{7}\) × \(\frac{4}{3}\)
= \(\frac{5}{7}\) × \(\frac{4}{1}\)
= \(\frac{20}{7}\)

Question 6.
2\(\frac{1}{2}\) × 3\(\frac{2}{3}\)
Answer:
2\(\frac{1}{2}\) × 3\(\frac{2}{3}\) = \(\frac{55}{6}\)

Explanation:
2\(\frac{1}{2}\) × 3\(\frac{2}{3}\)
= {[(2 × 2) + 1] ÷ 2} × {[(3 × 3) + 2] ÷ 3}
= [(4 + 1) ÷ 2] × [(9 + 2) ÷ 3]
= \(\frac{5}{2}\) × \(\frac{11}{3}\)
= \(\frac{55}{6}\)

Question 7.
3\(\frac{1}{3}\) × 1\(\frac{2}{3}\)
Answer:
3\(\frac{1}{3}\) × 1\(\frac{2}{3}\) = \(\frac{50}{9}\)

Explanation:
3\(\frac{1}{3}\) × 1\(\frac{2}{3}\)
= {[(3 × 3) + 1] ÷ 3} × {[(1 × 3) + 2] ÷ 3}
= [(9 + 1) ÷ 3] × [(3 + 2) ÷ 3]
= \(\frac{10}{3}\) × \(\frac{5}{3}\)
= \(\frac{50}{9}\)

Question 8.
3\(\frac{4}{5}\) × 1\(\frac{1}{2}\)
Answer:
3\(\frac{4}{5}\) × 1\(\frac{1}{2}\) = \(\frac{57}{10}\)

Explanation:
3\(\frac{4}{5}\) × 1\(\frac{1}{2}\)
= {[(3 × 5) + 4] ÷ 5} × {[(1 × 2) + 1] ÷ 2}
= [(15 + 4) ÷ 5] × [(2 + 1) ÷ 2]
= \(\frac{19}{5}\) × \(\frac{3}{2}\)
= \(\frac{57}{10}\)

Question 9.
3\(\frac{1}{2}\) × 2\(\frac{1}{7}\)
Answer:
3\(\frac{1}{2}\) × 2\(\frac{1}{7}\) = \(\frac{15}{2}\)

Explanation:
3\(\frac{1}{2}\) × 2\(\frac{1}{7}\)
= {[(3 × 2) + 1] ÷ 2} × {[(2 × 7) + 1] ÷ 7}
= [(6 + 1) ÷ 2] × [(14 + 1) ÷ 7]
= \(\frac{7}{2}\) × \(\frac{15}{7}\)
= \(\frac{1}{2}\) × \(\frac{15}{1}\)
= \(\frac{15}{2}\)

Question 10.
4\(\frac{3}{5}\) × 2\(\frac{1}{3}\)
Answer:
4\(\frac{3}{5}\) × 2\(\frac{1}{3}\) = \(\frac{91}{15}\)

Explanation:
4\(\frac{3}{5}\) × 2\(\frac{1}{3}\)
= {[(4 × 5) + 3] ÷ 5} × {[(2 × 3) + 1] ÷ 3}
= [(10 + 3) ÷ 5] × [(6 + 1) ÷ 3]
= \(\frac{13}{5}\) × \(\frac{7}{3}\)
= \(\frac{91}{15}\)

Question 11.
4\(\frac{1}{2}\) × 3\(\frac{1}{3}\)
Answer:
4\(\frac{1}{2}\) × 3\(\frac{1}{3}\) = 15.

Explanation:
4\(\frac{1}{2}\) × 3\(\frac{1}{3}\)
= {[(4 × 2) + 1] ÷ 2} × {[(3 × 3) + 1] ÷ 3}
= [(8 + 1) ÷ 2] × [(9 + 1) ÷ 3]
= \(\frac{9}{2}\) × \(\frac{10}{3}\)
= \(\frac{3}{2}\) × \(\frac{10}{1}\)
= \(\frac{3}{1}\) × \(\frac{5}{1}\)
= \(\frac{15}{1}\)
= 15.

Question 12.
5\(\frac{2}{3}\) × 2\(\frac{1}{16}\)
Answer:
5\(\frac{2}{3}\) × 2\(\frac{1}{16}\) = \(\frac{187}{16}\)

Explanation:
5\(\frac{2}{3}\) × 2\(\frac{1}{16}\)
= {[(5 × 3) + 2] ÷ 3} × {[(2 × 16) + 1] ÷ 16}
= [(15 + 2) ÷ 3] × [(32 + 1) ÷ 16]
= \(\frac{17}{3}\) × \(\frac{33}{16}\)
= \(\frac{17}{1}\) × \(\frac{11}{16}\)
= \(\frac{187}{16}\)

Question 13.
1\(\frac{1}{2}\) × 1\(\frac{1}{8}\)
Answer:
1\(\frac{1}{2}\) × 1\(\frac{1}{8}\) = \(\frac{27}{16}\)

Explanation:
1\(\frac{1}{2}\) × 1\(\frac{1}{8}\)
= {[(1 × 2) + 1] ÷ 2} × {[(1 × 8) + 1] ÷ 8}
= [(2 + 1) ÷ 2] × [(8 + 1) ÷ 8]
= \(\frac{3}{2}\) × \(\frac{9}{8}\)
= \(\frac{27}{16}\)

Question 14.
3\(\frac{1}{4}\) × 2\(\frac{3}{5}\)
Answer:
3\(\frac{1}{4}\) × 2\(\frac{3}{5}\) = \(\frac{169}{20}\)

Explanation:
3\(\frac{1}{4}\) × 2\(\frac{3}{5}\)
= {[(3 × 4) + 1] ÷ 4} × {[(2 × 5) + 3] ÷ 5}
= [(12 + 1) ÷ 4] × [(10 + 3) ÷ 5]
= \(\frac{13}{4}\) × \(\frac{13}{5}\)
= \(\frac{169}{20}\)

Question 15.
5\(\frac{1}{2}\) × 1\(\frac{7}{8}\)
Answer:
5\(\frac{1}{2}\) × 1\(\frac{7}{8}\) = \(\frac{165}{16}\)

Explanation:
5\(\frac{1}{2}\) × 1\(\frac{7}{8}\)
= {[(5 × 2) + 1] ÷ 2} × {[(1 × 8) + 7] ÷ 8}
= [(10 + 1) ÷ 2] × [(8 + 7) ÷ 8]
= \(\frac{11}{2}\) × \(\frac{15}{8}\)
= \(\frac{165}{16}\)

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