Question

1. \\(\frac{29}{2} - \frac{37}{2}\\) \\(\boxed{-4}\\) 17) \\(\frac{3}{5} - \frac{1}{9}\\) \\(\frac{27}{45} - \frac{5}{45} = \frac{27 - 5}{45}\\) write the mixed number as an improper fraction or write the improper fraction as a mixed number. 18) \\(12\frac{2}{3}\\) 19) \\(\frac{13}{3}\\) evaluate each expression.

Explanation:

Problem 16: $\boldsymbol{\frac{29}{2} - \frac{37}{2}}$

Step1: Subtract numerators (same denominator)

Since the denominators are the same, we subtract the numerators: $\frac{29 - 37}{2}$

Step2: Simplify the numerator

Calculate $29 - 37 = -8$, so we have $\frac{-8}{2}$

Step3: Divide to simplify

Divide $-8$ by $2$: $\frac{-8}{2} = -4$

Step1: Find a common denominator

The least common denominator of 5 and 9 is 45. Rewrite the fractions: $\frac{3 \times 9}{5 \times 9} - \frac{1 \times 5}{9 \times 5} = \frac{27}{45} - \frac{5}{45}$

Step2: Subtract numerators

Subtract the numerators: $\frac{27 - 5}{45} = \frac{22}{45}$

Step1: Use the mixed number to improper fraction formula

The formula for converting a mixed number $a\frac{b}{c}$ to an improper fraction is $\frac{a \times c + b}{c}$. Here, $a = 12$, $b = 2$, $c = 3$.

Step2: Calculate the numerator

Calculate $12 \times 3 + 2 = 36 + 2 = 38$

Step3: Write the improper fraction

The improper fraction is $\frac{38}{3}$

Answer:

$-4$

Problem 17: $\boldsymbol{\frac{3}{5} - \frac{1}{9}}$