Question

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

1. $4 \times 6\frac{1}{4}$
2. $3\frac{1}{2} \times 2\frac{3}{4}$
3. $\frac{7}{8} \times 4\frac{1}{6}$
4. $\frac{11}{2}$
5. $8\frac{1}{10} \times \frac{2}{3}$
6. $4\frac{1}{12} \times 7$
7. $3\frac{4}{5} \times 7\frac{1}{2}$
8. $6$

Explanation:

Step1: Estimate product (Q5)

Round $6\frac{1}{4}$ to 6: $4\times6=24$

Step2: Calculate exact product (Q5)

Convert mixed number: $6\frac{1}{4}=\frac{25}{4}$
$4\times\frac{25}{4}=25$

Step3: Estimate product (Q6)

Round $3\frac{1}{2}$ to 4, $2\frac{3}{4}$ to 3: $4\times3=12$

Step4: Calculate exact product (Q6)

Convert mixed numbers: $3\frac{1}{2}=\frac{7}{2}$, $2\frac{3}{4}=\frac{11}{4}$
$\frac{7}{2}\times\frac{11}{4}=\frac{77}{8}=9\frac{5}{8}$

Step5: Estimate product (Q7)

Round $\frac{7}{8}$ to 1, $4\frac{1}{6}$ to 4: $1\times4=4$

Step6: Calculate exact product (Q7)

Convert mixed number: $4\frac{1}{6}=\frac{25}{6}$
$\frac{7}{8}\times\frac{25}{6}=\frac{175}{48}=3\frac{31}{48}$

Step7: Estimate product (Q10)

Round $4\frac{1}{12}$ to 4: $4\times7=28$

Step8: Calculate exact product (Q10)

Convert mixed number: $4\frac{1}{12}=\frac{49}{12}$
$\frac{49}{12}\times7=\frac{343}{12}=28\frac{7}{12}$

Answer:

1. Estimate: 24; Exact: $25$
2. Estimate: 12; Exact: $9\frac{5}{8}$
3. Estimate: 4; Exact: $3\frac{31}{48}$
4. Estimate: 28; Exact: $28\frac{7}{12}$