Question

d 52. what is the product?
$3 \frac{1}{4} \times 2 \frac{3}{4} = ?$
a. 6
b. $6 \frac{3}{16}$
c. $8 \frac{3}{16}$
d. $8 \frac{15}{16}$
10.6 3. what is the area of the rectangle?
$8 \frac{1}{2}$ ft
$4 \frac{1}{3}$ ft
a. $25 \frac{2}{3}$ square feet
b. $32 \frac{1}{6}$ square feet
c. $34 \frac{5}{6}$ square feet
d. $36 \frac{5}{6}$ square feet

1. which expressions have a product that is less than the first factor? choose all that apply.

a. $2 \times \frac{3}{4}$
b. $7 \times \frac{2}{8}$
c. $16 \times \frac{5}{4}$
d. $5 \times \frac{10}{9}$

Explanation:

For Question 2:

Step1: Convert to improper fractions

$3\frac{1}{4}=\frac{13}{4}$, $2\frac{3}{4}=\frac{11}{4}$

Step2: Multiply the fractions

$\frac{13}{4} \times \frac{11}{4} = \frac{143}{16}$

Step3: Convert to mixed number

$\frac{143}{16}=8\frac{15}{16}$

Step1: Convert to improper fractions

$8\frac{1}{2}=\frac{17}{2}$, $4\frac{1}{3}=\frac{13}{3}$

Step2: Multiply for area

$\text{Area} = \frac{17}{2} \times \frac{13}{3} = \frac{221}{6}$

Step3: Convert to mixed number

$\frac{221}{6}=36\frac{5}{6}$

Step1: Rule for product < first factor

A product is less than the first factor when multiplying by a positive fraction less than 1.

Step2: Analyze each option

• A. $\frac{3}{4}<1$, so $2 \times \frac{3}{4}<2$
• B. $\frac{2}{8}=\frac{1}{4}<1$, so $7 \times \frac{2}{8}<7$
• C. $\frac{5}{4}>1$, so $16 \times \frac{5}{4}>16$
• D. $\frac{10}{9}>1$, so $5 \times \frac{10}{9}>5$

Answer:

D. $8\frac{15}{16}$

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For Question 3: