Question

question 42 of 60
add.
$-\frac{1}{2}+\frac{5}{9}$
write your answer in simplest form.

question 43 of 60
subtract. write your answer as a fraction in simplest form.
$\frac{5}{12}-\frac{1}{12}$

question 44 of 60
subtract.
$\frac{5}{11}-\frac{2}{11}$

question 45 of 60
subtract.
$\frac{1}{2}-\frac{1}{10}$

question 46 of 60
add. write your answer as a mixed number in simplest form.
$3\frac{7}{11}+8\frac{10}{11}$

Explanation:

Question 42

Step1: Find a common denominator

The denominators are 2 and 9, so the common denominator is \( 2\times9 = 18 \).
Rewrite the fractions: \( -\frac{1}{2}=-\frac{1\times9}{2\times9}=-\frac{9}{18} \), \( \frac{5}{9}=\frac{5\times2}{9\times2}=\frac{10}{18} \)

Step2: Add the fractions

\( -\frac{9}{18}+\frac{10}{18}=\frac{-9 + 10}{18}=\frac{1}{18} \)

Step1: Subtract the numerators (same denominator)

Since the denominators are the same (12), subtract the numerators: \( \frac{5 - 1}{12} \)

Step2: Simplify

\( \frac{4}{12}=\frac{1}{3} \) (divide numerator and denominator by 4)

Step1: Subtract the numerators (same denominator)

Denominators are 11, so subtract numerators: \( \frac{5 - 2}{11} \)

Step2: Simplify

\( \frac{3}{11} \)

Answer:

\( \frac{1}{18} \)

Question 43