Question

grade 5 fractions
find the product.

1. $1 \frac{2}{4} \times 3 \frac{5}{6} = $
2. $2 \frac{1}{2} \times 3 \frac{4}{5} = $
3. $3 \frac{3}{4} \times 3 \frac{2}{9} = $
4. $1 \frac{1}{2} \times 3 \frac{1}{2} = $
5. $3 \frac{2}{6} \times 3 \frac{2}{3} = $
6. $1 \frac{3}{4} \times 1 \frac{2}{4} = $
7. $1 \frac{5}{8} \times 2 \frac{6}{8} = $

Explanation:

Step1: Convert mixed numbers to improper fractions

For $1\frac{2}{4} \times 3\frac{5}{6}$:
$1\frac{2}{4} = \frac{1\times4 + 2}{4} = \frac{6}{4}$, $3\frac{5}{6} = \frac{3\times6 + 5}{6} = \frac{23}{6}$

Step2: Multiply numerators and denominators

$\frac{6}{4} \times \frac{23}{6} = \frac{6\times23}{4\times6} = \frac{23}{4} = 5\frac{3}{4}$

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Step1: Convert mixed numbers to improper fractions

For $2\frac{1}{2} \times 3\frac{4}{5}$:
$2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2}$, $3\frac{4}{5} = \frac{3\times5 + 4}{5} = \frac{19}{5}$

Step2: Multiply numerators and denominators

$\frac{5}{2} \times \frac{19}{5} = \frac{5\times19}{2\times5} = \frac{19}{2} = 9\frac{1}{2}$

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Step1: Convert mixed numbers to improper fractions

For $3\frac{3}{4} \times 3\frac{2}{9}$:
$3\frac{3}{4} = \frac{3\times4 + 3}{4} = \frac{15}{4}$, $3\frac{2}{9} = \frac{3\times9 + 2}{9} = \frac{29}{9}$

Step2: Multiply numerators and denominators

$\frac{15}{4} \times \frac{29}{9} = \frac{15\times29}{4\times9} = \frac{435}{36} = \frac{145}{12} = 12\frac{1}{12}$

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Step1: Convert mixed numbers to improper fractions

For $1\frac{1}{2} \times 3\frac{1}{2}$:
$1\frac{1}{2} = \frac{1\times2 + 1}{2} = \frac{3}{2}$, $3\frac{1}{2} = \frac{3\times2 + 1}{2} = \frac{7}{2}$

Step2: Multiply numerators and denominators

$\frac{3}{2} \times \frac{7}{2} = \frac{3\times7}{2\times2} = \frac{21}{4} = 5\frac{1}{4}$

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Step1: Simplify and convert mixed numbers

For $3\frac{2}{6} \times 3\frac{2}{3}$:
Simplify $3\frac{2}{6} = 3\frac{1}{3} = \frac{3\times3 + 1}{3} = \frac{10}{3}$, $3\frac{2}{3} = \frac{3\times3 + 2}{3} = \frac{11}{3}$

Step2: Multiply numerators and denominators

$\frac{10}{3} \times \frac{11}{3} = \frac{10\times11}{3\times3} = \frac{110}{9} = 12\frac{2}{9}$

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Step1: Convert mixed numbers to improper fractions

For $1\frac{3}{4} \times 1\frac{2}{4}$:
$1\frac{3}{4} = \frac{1\times4 + 3}{4} = \frac{7}{4}$, $1\frac{2}{4} = 1\frac{1}{2} = \frac{3}{2}$

Step2: Multiply numerators and denominators

$\frac{7}{4} \times \frac{3}{2} = \frac{7\times3}{4\times2} = \frac{21}{8} = 2\frac{5}{8}$

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Step1: Convert mixed numbers to improper fractions

For $1\frac{5}{8} \times 2\frac{6}{8}$:
$1\frac{5}{8} = \frac{1\times8 + 5}{8} = \frac{13}{8}$, $2\frac{6}{8} = 2\frac{3}{4} = \frac{2\times4 + 3}{4} = \frac{11}{4}$

Step2: Multiply numerators and denominators

$\frac{13}{8} \times \frac{11}{4} = \frac{13\times11}{8\times4} = \frac{143}{32} = 4\frac{15}{32}$

Answer:

1. $5\frac{3}{4}$
2. $9\frac{1}{2}$
3. $12\frac{1}{12}$
4. $5\frac{1}{4}$
5. $12\frac{2}{9}$
6. $2\frac{5}{8}$
7. $4\frac{15}{32}$