# 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$$\frac{1}{2}$$ × $$\frac{4}{5}$$
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$$\frac{1}{4}$$
$$\frac{2}{9}$$ × 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$$\frac{1}{7}$$
$$\frac{3}{4}$$ × 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$$\frac{1}{3}$$ × $$\frac{1}{2}$$
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$$\frac{1}{5}$$
$$\frac{8}{9}$$ × 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$$\frac{2}{3}$$ × $$\frac{2}{7}$$
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$$\frac{1}{4}$$ × $$\frac{2}{3}$$
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$$\frac{1}{8}$$ × $$\frac{1}{4}$$
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$$\frac{1}{2}$$ × $$\frac{8}{9}$$
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$$\frac{1}{7}$$
$$\frac{3}{7}$$ × 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$$\frac{2}{3}$$
$$\frac{1}{3}$$ × 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$$\frac{1}{5}$$
$$\frac{5}{6}$$ × 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$$\frac{1}{3}$$
$$\frac{3}{4}$$ × 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$$\frac{1}{4}$$ × $$\frac{3}{7}$$
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$$\frac{2}{11}$$ × $$\frac{22}{23}$$
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$$\frac{2}{3}$$
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$$\frac{1}{4}$$
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$$\frac{2}{3}$$
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$$\frac{3}{4}$$
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$$\frac{1}{3}$$
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$$\frac{2}{3}$$
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$$\frac{2}{3}$$
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$$\frac{1}{2}$$
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$$\frac{1}{7}$$
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$$\frac{1}{3}$$
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$$\frac{1}{3}$$
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$$\frac{1}{16}$$
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$$\frac{1}{8}$$
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$$\frac{3}{5}$$
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$$\frac{7}{8}$$
5$$\frac{1}{2}$$ × 1$$\frac{7}{8}$$ = $$\frac{165}{16}$$
5$$\frac{1}{2}$$ × 1$$\frac{7}{8}$$
= $$\frac{11}{2}$$ × $$\frac{15}{8}$$
= $$\frac{165}{16}$$