Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Lesson 2.1 Multiplying Fractions and Mixed Numbers and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 2 Lesson 2.1 Multiplying Fractions and Mixed Numbers Answers Key
Multiply fractions.
\(\frac{3}{8}\) × \(\frac{2}{3}\) = \(\frac{3 \times 2}{8 \times 3}\)
Multiply numerators together.
Multiply denominators together.
= \(\frac{6}{24}\) = \(\frac{1}{4}\) Simplify
Multiply mixed numbers.
2\(\frac{3}{4}\) × 3\(\frac{1}{3}\) = \(\frac{11}{4}\) × \(\frac{10}{3}\)
Rename each mixed number as an improper fraction.
Multiply. Write answers in simplest form.
Question 1.
a.
\(\frac{2}{5}\) × \(\frac{2}{3}\) =
Answer:
Simplest form of \(\frac{2}{5}\) × \(\frac{2}{3}\) is \(\frac{4}{15}\).
Explanation:
\(\frac{2}{5}\) × \(\frac{2}{3}\)
= \(\frac{4}{15}\).
b.
\(\frac{3}{4}\) × \(\frac{5}{6}\) =
Answer:
Simplest form of \(\frac{3}{4}\) × \(\frac{5}{6}\) is \(\frac{5}{8}\).
Explanation:
\(\frac{3}{4}\) × \(\frac{5}{6}\)
= \(\frac{15}{24}\)
= \(\frac{5}{8}\)
c.
\(\frac{7}{8}\) × \(\frac{5}{7}\) =
Answer:
Simplest form of \(\frac{7}{8}\) × \(\frac{5}{7}\) is \(\frac{5}{8}\).
Explanation:
\(\frac{7}{8}\) × \(\frac{5}{7}\)
= \(\frac{1}{8}\) × \(\frac{5}{1}\)
= \(\frac{5}{8}\)
d.
\(\frac{2}{5}\) × \(\frac{3}{4}\) =
Answer:
Simplest form of \(\frac{2}{5}\) × \(\frac{3}{4}\) is \(\frac{3}{10}\).
Explanation:
\(\frac{2}{5}\) × \(\frac{3}{4}\)
= \(\frac{1}{5}\) × \(\frac{3}{2}\)
= \(\frac{3}{10}\)
Question 2.
a.
\(\frac{7}{12}\) × \(\frac{3}{4}\) =
Answer:
Simplest form of \(\frac{7}{12}\) × \(\frac{3}{4}\) is \(\frac{7}{16}\).
Explanation:
\(\frac{7}{12}\) × \(\frac{3}{4}\)
= \(\frac{7}{4}\) × \(\frac{1}{4}\)
= \(\frac{7}{16}\)
b.
\(\frac{2}{3}\) × \(\frac{8}{9}\) =
Answer:
Simplest form of \(\frac{2}{3}\) × \(\frac{8}{9}\) is \(\frac{16}{27}\).
Explanation:
\(\frac{2}{3}\) × \(\frac{8}{9}\)
= \(\frac{16}{27}\)
c.
\(\frac{4}{5}\) × \(\frac{3}{8}\) =
Answer:
Simplest form of \(\frac{4}{5}\) × \(\frac{3}{8}\) is \(\frac{3}{10}\).
Explanation:
\(\frac{4}{5}\) × \(\frac{3}{8}\)
= \(\frac{1}{5}\) × \(\frac{3}{2}\)
= \(\frac{3}{10}\)
d.
\(\frac{3}{7}\) × \(\frac{3}{5}\) =
Answer:
Simplest form of \(\frac{3}{7}\) × \(\frac{3}{5}\) is \(\frac{9}{35}\).
Explanation:
\(\frac{3}{7}\) × \(\frac{3}{5}\)
= \(\frac{9}{35}\)
Question 3.
a.
\(\frac{1}{6}\) × \(\frac{2}{3}\) =
Answer:
Simplest form of \(\frac{1}{6}\) × \(\frac{2}{3}\) is \(\frac{1}{9}\).
Explanation:
\(\frac{1}{6}\) × \(\frac{2}{3}\)
= \(\frac{1}{3}\) × \(\frac{1}{3}\)
= \(\frac{1}{9}\)
b.
\(\frac{11}{12}\) × \(\frac{2}{3}\) =
Answer:
Simplest form of \(\frac{11}{12}\) × \(\frac{2}{3}\) is \(\frac{11}{18}\).
Explanation:
\(\frac{11}{12}\) × \(\frac{2}{3}\)
= \(\frac{11}{6}\) × \(\frac{1}{3}\)
= \(\frac{11}{18}\)
c.
\(\frac{2}{5}\) × \(\frac{2}{5}\) =
Answer:
Simplest form of \(\frac{2}{5}\) × \(\frac{2}{5}\) is \(\frac{4}{25}\).
Explanation:
\(\frac{2}{5}\) × \(\frac{2}{5}\)
= \(\frac{4}{25}\)
d.
\(\frac{3}{4}\) × \(\frac{3}{7}\) =
Answer:
Simplest form of \(\frac{3}{4}\) × \(\frac{3}{7}\) is \(\frac{9}{28}\).
Explanation:
\(\frac{3}{4}\) × \(\frac{3}{7}\)
= \(\frac{9}{28}\)
Question 4.
a.
1\(\frac{1}{3}\) × 2\(\frac{1}{8}\) =
Answer:
Simplest form of 1\(\frac{1}{3}\) × 2\(\frac{1}{8}\) is \(\frac{17}{6}\).
Explanation:
1\(\frac{1}{3}\) × 2\(\frac{1}{8}\)
= {[(1 × 3) + 1] ÷ 3} × {[(2 × 8) + 1] ÷ 8}
= [(3 + 1) ÷ 3] × [(16 + 1) ÷ 8]
= \(\frac{4}{3}\) × \(\frac{17}{8}\)
= \(\frac{1}{3}\) × \(\frac{17}{2}\)
= \(\frac{17}{6}\)
b.
2\(\frac{1}{2}\) × 1\(\frac{3}{4}\) =
Answer:
Simplest form of 2\(\frac{1}{2}\) × 1\(\frac{3}{4}\) is \(\frac{35}{2}\) or 17\(\frac{1}{2}\).
Explanation:
2\(\frac{1}{2}\) × 1\(\frac{3}{4}\)
= {[(2 × 2) + 1] ÷ 2} × {[(1 × 4) + 3] ÷ 4}
= [(4 + 1) ÷ 2] × [(4 + 3) ÷ 4]
= \(\frac{5}{2}\) × \(\frac{7}{4}\)
= \(\frac{5}{1}\) × \(\frac{7}{2}\)
= \(\frac{35}{2}\) or 17\(\frac{1}{2}\)
c.
2\(\frac{5}{8}\) × 2\(\frac{3}{5}\) =
Answer:
Simplest form of 2\(\frac{5}{8}\) × 2\(\frac{3}{5}\) is \(\frac{273}{45}\) or 6\(\frac{3}{45}\).
Explanation:
2\(\frac{5}{8}\) × 2\(\frac{3}{5}\)
= {[(2 × 8) + 5] ÷ 8} × {[(2 × 5) + 3] ÷ 5}
= [(16 + 5) ÷ 8] × [(10 + 3) ÷ 5]
= \(\frac{21}{8}\) × \(\frac{13}{5}\)
= \(\frac{273}{45}\) or 6\(\frac{3}{45}\)
d.
1\(\frac{1}{2}\) × 2\(\frac{2}{3}\) =
Answer:
Simplest form of 1\(\frac{1}{2}\) × 2\(\frac{2}{3}\) is 4.
Explanation:
1\(\frac{1}{2}\) × 2\(\frac{2}{3}\)
= {[(1 × 2) + 1] ÷ 2} × {[(2 × 3) + 2] ÷ 3}
= [(2 + 1) ÷ 2] × [(6 + 2) ÷ 3]
= \(\frac{3}{2}\) × \(\frac{8}{3}\)
= \(\frac{1}{2}\) × \(\frac{8}{1}\)
= \(\frac{1}{1}\) × \(\frac{4}{1}\)
= \(\frac{4}{1}\)
= 4.
Question 5.
a.
3\(\frac{1}{5}\) × 5\(\frac{2}{3}\) =
Answer:
Simplest form of 3\(\frac{1}{5}\) × 5\(\frac{2}{3}\) is \(\frac{272}{15}\) or 18\(\frac{2}{15}\)
Explanation:
3\(\frac{1}{5}\) × 5\(\frac{2}{3}\)
= {[(3 × 5) + 1] ÷ 5} × {[(5 × 3) + 2] ÷ 3}
= [(15 + 1) ÷ 5] × [(15 + 2) ÷ 3]
= \(\frac{16}{5}\) × \(\frac{17}{3}\)
= \(\frac{272}{15}\) or 18\(\frac{2}{15}\)
b.
4\(\frac{1}{2}\) × 4\(\frac{1}{2}\) =
Answer:
Simplest form of 4\(\frac{1}{2}\) × 4\(\frac{1}{2}\) is \(\frac{81}{4}\) or 20\(\frac{1}{4}\).
Explanation:
4\(\frac{1}{2}\) × 4\(\frac{1}{2}\)
= {[(4 × 2) + 1] ÷ 2} × {[(4 × 2) + 1] ÷ 2}
= [(8 + 1) ÷ 2] × [(8 + 1) ÷ 2]
= \(\frac{9}{2}\) × \(\frac{9}{2}\)
= \(\frac{81}{4}\) or 20\(\frac{1}{4}\)
c.
2\(\frac{1}{3}\) × 3\(\frac{1}{4}\) =
Answer:
Simplest form of 2\(\frac{1}{3}\) × 3\(\frac{1}{4}\) is \(\frac{91}{12}\) or 7\(\frac{7}{12}\).
Explanation:
2\(\frac{1}{3}\) × 3\(\frac{1}{4}\)
= {[(2 × 3) + 1] ÷ 3} × {[(3 × 4) + 1] ÷ 4}
= [(6 + 1) ÷ 3] × [(12 + 1) ÷ 4]
= \(\frac{7}{3}\) × \(\frac{13}{4}\)
= \(\frac{91}{12}\) or 7\(\frac{7}{12}\)
d.
2\(\frac{4}{5}\) × 3\(\frac{1}{8}\) =
Answer:
Simplest form of 2\(\frac{4}{5}\) × 3\(\frac{1}{8}\) is \(\frac{35}{4}\) or 8\(\frac{3}{4}\).
Explanation:
2\(\frac{4}{5}\) × 3\(\frac{1}{8}\)
= {[(2 × 5) + 4] ÷ 5} × {[(3 × 8) + 1] ÷ 8}
= [(10 + 4) ÷ 5] × [(24 + 1) ÷ 8]
= \(\frac{14}{5}\) × \(\frac{25}{8}\)
= \(\frac{7}{5}\) × \(\frac{25}{4}\)
= \(\frac{7}{1}\) × \(\frac{5}{4}\)
= \(\frac{35}{4}\) or 8\(\frac{3}{4}\)
Question 6.
a.
2\(\frac{2}{3}\) × 5\(\frac{1}{4}\) =
Answer:
Simplest form of 2\(\frac{2}{3}\) × 5\(\frac{1}{4}\) is 14.
Explanation:
2\(\frac{2}{3}\) × 5\(\frac{1}{4}\)
= {[(2 × 3) + 2] ÷ 3} × {[(5 × 4) + 1] ÷ 4}
= [(6 + 2) ÷ 3] × [(20 + 1) ÷ 4]
= \(\frac{8}{3}\) × \(\frac{21}{4}\)
= \(\frac{2}{3}\) × \(\frac{21}{1}\)
= \(\frac{2}{1}\) × \(\frac{7}{1}\)
= \(\frac{14}{1}\)
= 14.
b.
2\(\frac{1}{3}\) × 2\(\frac{1}{3}\) =
Answer:
Simplest form of 2\(\frac{1}{3}\) × 2\(\frac{1}{3}\) is \(\frac{49}{9}\) or 5\(\frac{4}{9}\).
Explanation:
2\(\frac{1}{3}\) × 2\(\frac{1}{3}\)
= {[(2 × 3) + 1] ÷ 3} × {[(2 × 3) + 1] ÷ 3}
= [(6 + 1) ÷ 3] × [(6 + 1) ÷ 3]
= \(\frac{7}{3}\) × \(\frac{7}{3}\)
= \(\frac{49}{9}\) or 5\(\frac{4}{9}\)
c.
3\(\frac{1}{4}\) × 1\(\frac{1}{8}\) =
Answer:
Simplest form of 3\(\frac{1}{4}\) × 1\(\frac{1}{8}\) is \(\frac{117}{32}\) or 3\(\frac{21}{32}\).
Explanation:
3\(\frac{1}{4}\) × 1\(\frac{1}{8}\)
= {[(3 × 4) + 1] ÷ 4} × {[(1 × 8) + 1] ÷ 8}
= [(12 + 1) ÷ 4] × [(8 + 1) ÷ 8]
= \(\frac{13}{4}\) × \(\frac{9}{8}\)
= \(\frac{117}{32}\) or 3\(\frac{21}{32}\)
d.
2\(\frac{7}{8}\) × 1\(\frac{1}{3}\) =
Answer:
Simplest form of 2\(\frac{7}{8}\) × 1\(\frac{1}{3}\) is \(\frac{23}{6}\) or 3\(\frac{5}{6}\).
Explanation:
2\(\frac{7}{8}\) × 1\(\frac{1}{3}\)
= {[(2 × 8) + 7] ÷ 8} × {[(1 × 3) + 1] ÷ 3}
= [(16 + 7) ÷ 8] × [(3 + 1) ÷ 3]
= \(\frac{23}{8}\) × \(\frac{4}{3}\)
= \(\frac{23}{2}\) × \(\frac{1}{3}\)
= \(\frac{23}{6}\) or 3\(\frac{5}{6}\)