Question

in 5-12, estimate the product. then find each product.

1. $4×6\frac{1}{4}$
2. $3\frac{2}{3}×2\frac{3}{4}$
3. $\frac{7}{8}×4\frac{1}{6}$
4. $1\frac{1}{2}×2\frac{3}{4}$
5. $8\frac{1}{10}×\frac{2}{3}$
6. $4\frac{1}{12}×7$
7. $3\frac{4}{5}×7\frac{1}{2}$
8. $6\frac{2}{3}×4\frac{4}{5}$

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topic 8 | lesson 8-7

Explanation:

Problem 5:

Step1: Estimate the product

Round $6\frac{1}{4}$ to 6: $4 \times 6 = 24$

Step2: Convert mixed number to fraction

$6\frac{1}{4} = \frac{25}{4}$

Step3: Multiply the numbers

$4 \times \frac{25}{4} = 25$

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Problem 6:

Step1: Estimate the product

Round $3\frac{2}{3}$ to 4, $2\frac{3}{4}$ to 3: $4 \times 3 = 12$

Step2: Convert mixed numbers to fractions

$3\frac{2}{3} = \frac{11}{3}$, $2\frac{3}{4} = \frac{11}{4}$

Step3: Multiply the fractions

$\frac{11}{3} \times \frac{11}{4} = \frac{121}{12} = 10\frac{1}{12}$

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Problem 7:

Step1: Estimate the product

Round $\frac{7}{8}$ to 1, $4\frac{1}{6}$ to 4: $1 \times 4 = 4$

Step2: Convert mixed number to fraction

$4\frac{1}{6} = \frac{25}{6}$

Step3: Multiply the fractions

$\frac{7}{8} \times \frac{25}{6} = \frac{175}{48} = 3\frac{31}{48}$

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Problem 10:

Step1: Estimate the product

Round $4\frac{1}{12}$ to 4: $4 \times 7 = 28$

Step2: Convert mixed number to fraction

$4\frac{1}{12} = \frac{49}{12}$

Step3: Multiply the numbers

$\frac{49}{12} \times 7 = \frac{343}{12} = 28\frac{7}{12}$

Answer:

1. Estimate: 24, Exact product: $25$
2. Estimate: 12, Exact product: $10\frac{1}{12}$
3. Estimate: 4, Exact product: $3\frac{31}{48}$
4. Estimate: 28, Exact product: $28\frac{7}{12}$