Question

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\div 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

Since numerator (25) > denominator (3), it's improper.

Step2: Divide numerator by denominator

$25 \div 3 = 8$ with remainder 1.

Step3: Rewrite as mixed number

Mixed number: $8\frac{1}{3}$ (quotient $\frac{\text{remainder}}{\text{denominator}}$)

Step1: Identify fraction type

Numerator (19) > denominator (6), so improper.

Step2: Divide numerator by denominator

$19 \div 6 = 3$ with remainder 1.

Step3: Rewrite as mixed number

Mixed number: $3\frac{1}{6}$

Step1: Identify fraction type

It has a whole number and a fraction, so mixed.

Step2: Convert to improper fraction

Formula: $(\text{whole} \times \text{denominator}) + \text{numerator}$ over denominator.
$(4 \times 7) + 3 = 28 + 3 = 31$. So $\frac{31}{7}$.

Answer:

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

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