Question

1. in the following exercises, convert the improper fraa) $\frac{3}{2} =$b) $\frac{11}{4} =$d) $\frac{5}{3} =$e) $\frac{28}{9} =$g) $\frac{13}{5} =$h) $\frac{47}{15} =$2. in the following exercisesa) $1\frac{2}{3}$d) $2\frac{5}{6}$

Explanation:

Step1: Divide numerator by denominator

For $\frac{3}{2}$: $3 \div 2 = 1$ remainder $1$

Step2: Write as mixed number

$1 + \frac{1}{2} = 1\frac{1}{2}$

Step1: Divide numerator by denominator

For $\frac{11}{4}$: $11 \div 4 = 2$ remainder $3$

Step2: Write as mixed number

$2 + \frac{3}{4} = 2\frac{3}{4}$

Step1: Divide numerator by denominator

For $\frac{5}{3}$: $5 \div 3 = 1$ remainder $2$

Step2: Write as mixed number

$1 + \frac{2}{3} = 1\frac{2}{3}$

Step1: Divide numerator by denominator

For $\frac{28}{9}$: $28 \div 9 = 3$ remainder $1$

Step2: Write as mixed number

$3 + \frac{1}{9} = 3\frac{1}{9}$

Step1: Divide numerator by denominator

For $\frac{13}{5}$: $13 \div 5 = 2$ remainder $3$

Step2: Write as mixed number

$2 + \frac{3}{5} = 2\frac{3}{5}$

Step1: Divide numerator by denominator

For $\frac{47}{15}$: $47 \div 15 = 3$ remainder $2$

Step2: Write as mixed number

$3 + \frac{2}{15} = 3\frac{2}{15}$

Step1: Convert mixed to improper fraction

For $1\frac{2}{3}$: $1\times3 + 2 = 5$, so $\frac{5}{3}$

Step1: Convert mixed to improper fraction

For $2\frac{5}{6}$: $2\times6 + 5 = 17$, so $\frac{17}{6}$

Answer:

1. a) $1\frac{1}{2}$
2. b) $2\frac{3}{4}$
3. d) $1\frac{2}{3}$
4. e) $3\frac{1}{9}$
5. g) $2\frac{3}{5}$
6. h) $3\frac{2}{15}$
7. a) $\frac{5}{3}$
8. d) $\frac{17}{6}$