Question

skills practice 1
mixed + improper fractions
for each of the following fractions, give them the appropriate label and rewrite them in the alternate form. show your work.
\\(\frac{42}{5}\\) improper
42 ÷ 5 = 8 r2
\\(8\frac{2}{5}\\)
\\(\frac{25}{3}\\) ______
\\(\frac{19}{6}\\) ______
\\(4\frac{3}{7}\\) ______
\\(2\frac{1}{3}\\) ______
\\(\frac{11}{2}\\) ______
\\(5\frac{1}{2}\\) ______
\\(\frac{17}{3}\\) ______
\\(6\frac{4}{5}\\) ______

Explanation:

1. $\boldsymbol{\frac{25}{3}}$

Step1: Identify fraction type

$\frac{25}{3}$ is improper (numerator > denominator).

Step2: Convert to mixed number

Divide 25 by 3: $25 \div 3 = 8$ with remainder $1$.
Mixed number: $8\frac{1}{3}$.

Step1: Identify fraction type

$\frac{19}{6}$ is improper (numerator > denominator).

Step2: Convert to mixed number

Divide 19 by 6: $19 \div 6 = 3$ with remainder $1$.
Mixed number: $3\frac{1}{6}$.

Step1: Identify fraction type

$4\frac{3}{7}$ is a mixed number (has whole + fractional part).

Step2: Convert to improper fraction

Multiply whole number by denominator: $4 \times 7 = 28$.
Add numerator: $28 + 3 = 31$.
Improper fraction: $\frac{31}{7}$.

Answer:

Label: Improper; Alternate form: $8\frac{1}{3}$

2. $\boldsymbol{\frac{19}{6}}$