McGraw Hill Math

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 4 Lesson 4 Strategies for Multiplying Decimals are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 4 Lesson 4 Strategies for Multiplying Decimals

Solve.

Estimate and multiply to complete the table. You can use the grids to help.

Question 1.
0.2 × 0.2 =
Estimate: 0.04
Product: 0.04
Answer:
0.2
×0.2
0.04
By multiplying 0.2 with 0.2 we get 0.04
Estimate: 0.04
Product: 0.04

Question 2.
0.4 × 0.7 =
Estimate:
Product:
Answer:
0.4
×0.7
0.28
By multiplying 0.4 with 0.7 we get 0.28
Estimate: 0.3
Product: 0.28

Question 3.
0.3 × 0.8 =
Estimate:
Product:
Answer:
0.3
×0.8
0.24
By multiplying 0.3 with 0.8 we get 0.24
Estimate: 0.20
Product: 0.24

Question 4.
0.6 × 0.5 =
Estimate:
Product:
Answer:
0.6
×0.5
0.30
By multiplying 0.6 with 0.5 we get 0.30
Estimate: 0.3
Product: 0.30

Question 5.
0.9 × 0.8 =
Estimate:
Product:
Answer:
0.9
×0.8
0.72
By multiplying 0.9 with 0.8 we get 0.72
Estimate: 0.7
Product: 0.72

Question 6.
0.2 × 0.02 =
Estimate:
Product:
Answer:
0.2
×0.02
0.004
By multiplying 0.2 with 0.02 we get 0.04
Estimate: 0.004
Product: 0.004

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]
= \(\frac{11}{2}\) × \(\frac{15}{8}\)
= \(\frac{165}{16}\)

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 7.2 Multiplying Fractions: Reciprocals will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 7.2 Multiplying Fractions: Reciprocals

Exercises Multiply

Question 1.
\(\frac{1}{2}\) × \(\frac{1}{2}\)
Answer:
Multiplying \(\frac{1}{2}\) by \(\frac{1}{2}\), we get the product \(\frac{1}{4}\)

Explanation:
\(\frac{1}{2}\) × \(\frac{1}{2}\)
= \(\frac{1}{4}\)

Question 2.
\(\frac{2}{3}\) × \(\frac{6}{7}\)
Answer:
Multiplying \(\frac{2}{3}\) by \(\frac{6}{7}\), we get the product \(\frac{4}{7}\)

Explanation:
\(\frac{2}{3}\) × \(\frac{6}{7}\)
= \(\frac{2}{1}\) × \(\frac{2}{7}\)
= \(\frac{4}{7}\)

Question 3.
\(\frac{5}{9}\) × \(\frac{3}{11}\)
Answer:
Multiplying \(\frac{5}{9}\) by \(\frac{3}{11}\) , we get the product \(\frac{5}{33}\)

Explanation:
\(\frac{5}{9}\) × \(\frac{3}{11}\)
= \(\frac{5}{3}\) × \(\frac{1}{11}\)
= \(\frac{5}{33}\)

Question 4.
\(\frac{10}{13}\) × \(\frac{1}{3}\)
Answer:
Multiplying \(\frac{10}{13}\) by \(\frac{1}{3}\) , we get the product \(\frac{10}{39}\)

Explanation:
\(\frac{10}{13}\) × \(\frac{1}{3}\)
= \(\frac{10}{39}\)

Question 5.
\(\frac{3}{11}\) × \(\frac{11}{3}\)
Answer:
Multiplying \(\frac{3}{11}\) by \(\frac{11}{3}\) , we get the product 1.

Explanation:
\(\frac{3}{11}\) × \(\frac{11}{3}\)
= 1.

Question 6.
\(\frac{7}{3}\) × \(\frac{3}{11}\)
Answer:
Multiplying \(\frac{7}{3}\) by \(\frac{3}{11}\), we get the product \(\frac{7}{11}\)

Explanation:
\(\frac{7}{3}\) × \(\frac{3}{11}\)
= \(\frac{7}{1}\) × \(\frac{1}{11}\)
= \(\frac{7}{11}\)

Question 7.
\(\frac{4}{5}\) × \(\frac{7}{8}\)
Answer:
Multiplying \(\frac{4}{5}\) by \(\frac{7}{8}\), we get the product \(\frac{7}{10}\)

Explanation:
\(\frac{4}{5}\) × \(\frac{7}{8}\)
= \(\frac{1}{5}\) × \(\frac{7}{2}\)
= \(\frac{7}{10}\)

Question 8.
\(\frac{3}{4}\) × \(\frac{4}{3}\)
Answer:
Multiplying \(\frac{3}{4}\) by \(\frac{4}{3}\) , we get the product 1.

Explanation:
\(\frac{3}{4}\) × \(\frac{4}{3}\)
= 1.

Question 9.
\(\frac{17}{27}\) × \(\frac{5}{3}\)
Answer:
Multiplying \(\frac{17}{27}\) by \(\frac{5}{3}\), we get the product \(\frac{85}{81}\)

Explanation:
\(\frac{17}{27}\) × \(\frac{5}{3}\)
= \(\frac{85}{81}\)

Question 10.
\(\frac{6}{10}\) × \(\frac{6}{11}\)
Answer:
Multiplying \(\frac{6}{10}\) by \(\frac{6}{11}\), we get the product \(\frac{18}{55}\)

Explanation:
\(\frac{6}{10}\) × \(\frac{6}{11}\)
= \(\frac{6}{5}\) × \(\frac{3}{11}\)
= \(\frac{18}{55}\)

Question 11.
\(\frac{13}{14}\) × \(\frac{2}{3}\)
Answer:
Multiplying \(\frac{13}{14}\) by \(\frac{2}{3}\), we get the product \(\frac{13}{21}\)

Explanation:
\(\frac{13}{14}\) × \(\frac{2}{3}\)
= \(\frac{13}{7}\) × \(\frac{1}{3}\)
= \(\frac{13}{21}\)

Question 12.
\(\frac{4}{5}\) × \(\frac{4}{5}\)
Answer:
Multiplying \(\frac{4}{5}\) by \(\frac{4}{5}\), we get the product \(\frac{16}{25}\)

Explanation:
\(\frac{4}{5}\) × \(\frac{4}{5}\)
= \(\frac{16}{25}\)

Question 13.
\(\frac{133}{145}\) × \(\frac{145}{133}\)
Answer:
Multiplying \(\frac{133}{145}\) by \(\frac{145}{133}\), we get the product 1.

Explanation:
\(\frac{133}{145}\) × \(\frac{145}{133}\)
= 1.

Question 14.
\(\frac{8}{19}\) × \(\frac{5}{7}\)
Answer:
Multiplying \(\frac{8}{19}\) by \(\frac{5}{7}\), we get the product \(\frac{40}{133}\)

Explanation:
\(\frac{8}{19}\) × \(\frac{5}{7}\)
= \(\frac{40}{133}\)

Question 15.
\(\frac{11}{13}\) × \(\frac{9}{14}\)
Answer:
Multiplying \(\frac{11}{13}\) by \(\frac{9}{14}\), we get the product \(\frac{99}{182}\)

Explanation:
\(\frac{11}{13}\) × \(\frac{9}{14}\)
= \(\frac{99}{182}\)

Question 16.
\(\frac{32}{33}\) × \(\frac{1}{2}\)
Answer:
Multiplying \(\frac{32}{33}\) by \(\frac{1}{2}\), we get the product \(\frac{16}{33}\)

Explanation:
\(\frac{32}{33}\) × \(\frac{1}{2}\)
= \(\frac{16}{33}\) × \(\frac{1}{1}\)
= \(\frac{16}{33}\)

Question 17.
\(\frac{1}{5}\) × \(\frac{1}{7}\)
Answer:
Multiplying \(\frac{1}{5}\) by \(\frac{1}{7}\), we get the product \(\frac{1}{35}\)

Explanation:
\(\frac{1}{5}\) × \(\frac{1}{7}\)
= \(\frac{1}{35}\)

Question 18.
\(\frac{5}{6}\) × \(\frac{5}{9}\)
Answer:
Multiplying \(\frac{5}{6}\) by \(\frac{5}{9}\), we get the product \(\frac{25}{54}\)

Explanation:
\(\frac{5}{6}\) × \(\frac{5}{9}\)
= \(\frac{25}{54}\)

Question 19.
\(\frac{2}{3}\) × \(\frac{33}{34}\)
Answer:
Multiplying \(\frac{2}{3}\) by \(\frac{33}{34}\), we get the product \(\frac{11}{17}\)

Explanation:
\(\frac{2}{3}\) × \(\frac{33}{34}\)
= \(\frac{1}{1}\) × \(\frac{11}{17}\)
= \(\frac{11}{17}\)

Question 20.
\(\frac{45}{47}\) × \(\frac{47}{45}\)
Answer:
Multiplying \(\frac{45}{47}\) by \(\frac{47}{45}\), we get the product 1.

Explanation:
\(\frac{45}{47}\) × \(\frac{47}{45}\)
= 1.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 7.1 Multiplying Fractions and Whole Numbers will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 7.1 Multiplying Fractions and Whole Numbers

Exercises Estimate

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

Explanation:
5 × \(\frac{3}{4}\)
= \(\frac{15}{4}\)
= 3\(\frac{3}{4}\)

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

Explanation:
4 × \(\frac{2}{7}\)
= \(\frac{8}{7}\)
= 1\(\frac{1}{7}\)

Question 3.
21 × \(\frac{5}{8}\)
Answer:
21 × \(\frac{5}{8}\) = 13\(\frac{1}{8}\)

Explanation:
21 × \(\frac{5}{8}\)
= \(\frac{105}{8}\)
= 13\(\frac{1}{8}\)

Question 4.
11 × \(\frac{2}{9}\)
Answer:
11 × \(\frac{2}{9}\) = 2\(\frac{4}{9}\)

Explanation:
11 × \(\frac{2}{9}\)
= \(\frac{22}{9}\)
= 2\(\frac{4}{9}\)

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

Explanation:
4 × \(\frac{3}{11}\)
= \(\frac{12}{11}\)
= 1\(\frac{1}{11}\)

Question 6.
13 × \(\frac{13}{14}\)
Answer:
13 × \(\frac{13}{14}\) = 12\(\frac{1}{14}\)

Explanation:
13 × \(\frac{13}{14}\)
= \(\frac{169}{14}\)
= 12\(\frac{1}{14}\)

Question 7.
21 × \(\frac{10}{23}\)
Answer:
21 × \(\frac{10}{23}\) = 9 \(\frac{3}{23}\)

Explanation:
21 × \(\frac{10}{23}\)
= \(\frac{210}{23}\)
= 9 \(\frac{3}{23}\)

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

Explanation:
7 × \(\frac{2}{3}\)
= \(\frac{14}{3}\)
= 4 \(\frac{2}{3}\)

Question 9.
12 × \(\frac{7}{19}\)
Answer:
12 × \(\frac{7}{19}\) = 4\(\frac{8}{19}\)

Explanation:
12 × \(\frac{7}{19}\)
= \(\frac{84}{19}\)
= 4\(\frac{8}{19}\)

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

Explanation:
14 × \(\frac{3}{5}\)
=\(\frac{42}{5}\)
= 8\(\frac{2}{5}\)

Question 11.
14 × \(\frac{11}{13}\)
Answer:
14 × \(\frac{11}{13}\) = 11\(\frac{11}{13}\)

Explanation:
14 × \(\frac{11}{13}\)
= \(\frac{154}{13}\)
= 11\(\frac{11}{13}\)

Question 12.
13 × \(\frac{4}{17}\)
Answer:
13 × \(\frac{4}{17}\) = 3\(\frac{1}{17}\)

Explanation:
13 × \(\frac{4}{17}\)
= \(\frac{52}{17}\)
= 3\(\frac{1}{17}\)

Question 13.
10 × \(\frac{9}{23}\)
Answer:
10 × \(\frac{9}{23}\) = 3\(\frac{21}{23}\)

Explanation:
10 × \(\frac{9}{23}\)
= \(\frac{90}{23}\)
= 3\(\frac{21}{23}\)

Question 14.
13 × \(\frac{21}{22}\)
Answer:
13 × \(\frac{21}{22}\) = 12\(\frac{9}{22}\)

Explanation:
13 × \(\frac{21}{22}\)
= \(\frac{273}{22}\)
= 12\(\frac{9}{22}\)

Question 15.
5 × \(\frac{14}{27}\)
Answer:
5 × \(\frac{14}{27}\) = 2\(\frac{16}{27}\)

Explanation:
5 × \(\frac{14}{27}\)
= \(\frac{70}{27}\)
= 2\(\frac{16}{27}\)

Question 16.
Chet found a pair of sunglasses that he would like to buy. They normally cost $43.00, but this week they are on sale for only \(\frac{7}{8}\) of the usual price. How much money will Chet need to buy the sunglasses?
Answer:
Amount of money Chet needs to buy the sunglasses = $37\(\frac{5}{8}\)

Explanation:
Cost of a pair of sunglasses usually = $43.00
Cost of a pair of sunglasses this week on sale for only of the usual price = \(\frac{7}{8}\)
Amount of money Chet needs to buy the sunglasses = Cost of a pair of sunglasses usually × Cost of a pair of sunglasses this week on sale for only of the usual price
= 43 × \(\frac{7}{8}\)
= \(\frac{301}{8}\)
= $37\(\frac{5}{8}\)

Question 17.
Ashlee is riding her bike to the beach. If the beach is 17 miles from her home, and she has already traveled \(\frac{3}{5}\) of the way, how much farther does she have to cycle?
Answer:
Number of miles more she needs to cycle = 10\(\frac{1}{5}\)

Explanation:
Number of miles from her home the beach = 17.
Number of miles already travelled of the way = \(\frac{3}{5}\)
Number of miles more she needs to cycle = Number of miles from her home the beach × Number of miles already travelled of the way
= 17 × \(\frac{3}{5}\)
= \(\frac{51}{5}\)
= 10\(\frac{1}{5}\)

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 4 Lesson 5 Relating Multiplication and Division of Decimals are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 4 Lesson 5 Relating Multiplication and Division of Decimals

Solve.

Solve each problem. Then list the related decimal multiplication and division facts.

Question 1.
2.4 ÷ 8 = 0.3
2.4 ÷ 0.3 = 8
0.3 × 8 = 2.4
8 × 0.3 = 2.4
Answer:
Given the expression is 2.4 ÷ 8 which is
2.4 ÷ 8 = 0.3,
2.4 ÷ 0.3 = 8,
0.3 × 8 = 2.4,
8 × 0.3 = 2.4

Question 2.
6 ÷ 0.2 = __________________
___________________________
Answer:
Given the expression is 6 ÷ 0.2 which is
6 ÷ 0.2 = 30,
30 ÷ 6 = 5,
30 × 0.2 = 6,
0.2 × 30 = 6.

Question 3.
2.2 ÷ 10 = __________________
___________________________
Answer:
Given the expression is 2.2 ÷ 10 which is
2.2 ÷ 10 = 0.22,
0.22 × 10 = 2.2,
10 × 0.22 = 2.2.

Question 4.
2 ÷ 0.1 = __________________
___________________________
Answer:
Given the expression is 2 ÷ 0.1 which is
2 ÷ 0.1 = 20,
20 × 0.1 = 2,
0.1 × 20 = 2.

Question 5.
8 ÷ 0.4 = __________________
___________________________
Answer:
Given the expression is 8 ÷ 0.4 which is
8 ÷ 0.4 = 20,
20 × 0.4 = 8,
0.4 × 20 = 8.

Question 6.
1.6 ÷ 5 = __________________
___________________________
Answer:
Given the expression is 1.6 ÷ 5 which is
1.6 ÷ 5 = 0.32,
0.32 × 5 = 1.6,
5 × 0.32 = 1.6.

Question 7.
When a whole number is divided by a decimal, is the quotient greater than or less than the dividend?
Answer:
The quotient is greater than the dividend

Explanation:
When a whole number is divided by a decimal, the quotient is greater than the dividend. For example, if we divide 25 by 0.5 which is
25 ÷ 0.5 = 50.