find each sum, difference, or product.
8. $\frac{2}{5}+\frac{1}{4}$
9. $\frac{5}{6}-\frac{1}{4}$
10. $2\frac{5}{8}+7\frac{1}{4}$
11. $14 - 3\frac{5}{8}$
12. $3\frac{2}{3}+4\frac{1}{2}$
13. $\frac{3}{8}×2$
14. $\frac{1}{4}×\frac{3}{5}$
15. $8×\frac{9}{10}$
16. $3\frac{1}{2}×2\frac{3}{5}$

Question

Accepted Answer

Let's solve each problem one by one:

### Problem 8: $\boldsymbol{\frac{2}{5} + \frac{1}{4}}$
## Step1: Find a common denominator (20)
$\frac{2}{5} = \frac{2	imes4}{5	imes4} = \frac{8}{20}$, $\frac{1}{4} = \frac{1	imes5}{4	imes5} = \frac{5}{20}$
## Step2: Add the fractions
$\frac{8}{20} + \frac{5}{20} = \frac{13}{20}$
# Answer: $\frac{13}{20}$

### Problem 9: $\boldsymbol{\frac{5}{6} - \frac{1}{4}}$
## Step1: Find a common denominator (12)
$\frac{5}{6} = \frac{5	imes2}{6	imes2} = \frac{10}{12}$, $\frac{1}{4} = \frac{1	imes3}{4	imes3} = \frac{3}{12}$
## Step2: Subtract the fractions
$\frac{10}{12} - \frac{3}{12} = \frac{7}{12}$
# Answer: $\frac{7}{12}$ (Note: The original answer of $\frac{4}{2}$ is incorrect)

### Problem 10: $\boldsymbol{2\frac{5}{8} + 7\frac{1}{4}}$
## Step1: Convert mixed numbers to improper fractions or find a common denominator for the fractions
$7\frac{1}{4} = 7\frac{2}{8}$, so $2\frac{5}{8} + 7\frac{2}{8}$
## Step2: Add the whole numbers and the fractions
$(2 + 7) + (\frac{5}{8} + \frac{2}{8}) = 9 + \frac{7}{8} = 9\frac{7}{8}$
# Answer: $9\frac{7}{8}$ (Note: The original answer of $9\frac{6}{12}$ is incorrect)

### Problem 11: $\boldsymbol{14 - 3\frac{5}{8}}$
## Step1: Convert 14 to a mixed number with denominator 8: $14 = 13\frac{8}{8}$
## Step2: Subtract the mixed numbers
$13\frac{8}{8} - 3\frac{5}{8} = (13 - 3) + (\frac{8}{8} - \frac{5}{8}) = 10 + \frac{3}{8} = 10\frac{3}{8}$
# Answer: $10\frac{3}{8}$

### Problem 12: $\boldsymbol{3\frac{2}{3} + 4\frac{1}{2}}$
## Step1: Find a common denominator (6) for the fractions
$3\frac{2}{3} = 3\frac{4}{6}$, $4\frac{1}{2} = 4\frac{3}{6}$
## Step2: Add the whole numbers and the fractions
$(3 + 4) + (\frac{4}{6} + \frac{3}{6}) = 7 + \frac{7}{6} = 7 + 1\frac{1}{6} = 8\frac{1}{6}$
# Answer: $8\frac{1}{6}$

### Problem 13: $\boldsymbol{\frac{3}{8} 	imes 2}$
## Step1: Write 2 as a fraction ($\frac{2}{1}$)
## Step2: Multiply the numerators and denominators
$\frac{3}{8} 	imes \frac{2}{1} = \frac{3	imes2}{8	imes1} = \frac{6}{8}$
## Step3: Simplify the fraction
$\frac{6}{8} = \frac{3}{4}$
# Answer: $\frac{3}{4}$

### Problem 14: $\boldsymbol{\frac{1}{4} 	imes \frac{3}{5}}$
## Step1: Multiply the numerators and denominators
$\frac{1	imes3}{4	imes5} = \frac{3}{20}$
# Answer: $\frac{3}{20}$

### Problem 15: $\boldsymbol{8 	imes \frac{9}{10}}$
## Step1: Multiply the numerator and 8
$\frac{8	imes9}{10} = \frac{72}{10}$
## Step2: Simplify the fraction
$\frac{72}{10} = \frac{36}{5} = 7\frac{1}{5}$
# Answer: $7\frac{1}{5}$ (or $\frac{36}{5}$)

### Problem 16: $\boldsymbol{3\frac{1}{2} 	imes 2\frac{3}{5}}$
## Step1: Convert mixed numbers to improper fractions
$3\frac{1}{2} = \frac{7}{2}$, $2\frac{3}{5} = \frac{13}{5}$
## Step2: Multiply the improper fractions
$\frac{7}{2} 	imes \frac{13}{5} = \frac{7	imes13}{2	imes5} = \frac{91}{10}$
## Step3: Convert back to a mixed number
$\frac{91}{10} = 9\frac{1}{10}$
# Answer: $9\frac{1}{10}$ (or $\frac{91}{10}$)

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QUESTION IMAGE

Question

Explanation:

Problem 8: $\boldsymbol{\frac{2}{5} + \frac{1}{4}}$

Step1: Find a common denominator (20)

Step2: Add the fractions

Answer:

Problem 9: $\boldsymbol{\frac{5}{6} - \frac{1}{4}}$

Step1: Find a common denominator (12)

Step2: Subtract the fractions