Question

add, subtract, multiply or divide the fractions. simplify the answers if possible.

1. $\frac{1}{2} + \frac{3}{4}$
2. $\frac{4}{5} - \frac{2}{3}$
3. $\frac{1}{6} \div \frac{1}{2}$
4. $\frac{2}{5} \cdot \frac{1}{3}$
5. $\frac{2}{6} - \frac{1}{9}$
6. $\frac{3}{5} \div \frac{1}{5}$

activity 2
give the reciprocal for each of the numbers.
model 8
answer: $\frac{1}{8}$

1. $\frac{1}{3}$
2. $\frac{4}{5}$
3. 9
4. $\frac{6}{8}$
5. 10
6. $\frac{2}{7}$

activity 3
fill in the missing part for each equation with reciprocals.

1. $\underline{\quad} \cdot \frac{4}{5} = 1$
2. $\frac{3}{2} \cdot \underline{\quad} = 1$
3. $5 \cdot \frac{1}{5} = \underline{\quad}$
4. $\frac{7}{8} \cdot \underline{\quad} = 1$
5. $\underline{\quad} \cdot \frac{1}{8} = 1$
6. $\frac{4}{3} \cdot \frac{3}{4} = \underline{\quad}$

activity 4 • distributed practice

1. list the first five multiples of 5 and 10. circle any common multiples.
2. what are the common factors of 8 and 12?

Explanation:

Activity 1

1. $\boldsymbol{\frac{1}{2} + \frac{3}{4}}$

Step1: Find common denominator

The common denominator of 2 and 4 is 4. Rewrite $\frac{1}{2}$ as $\frac{2}{4}$.
$\frac{1}{2} = \frac{2}{4}$

Step2: Add the fractions

Add the numerators: $\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}$ (or $1\frac{1}{4}$)

Step1: Find common denominator

Common denominator of 5 and 3 is 15. Rewrite fractions: $\frac{4}{5} = \frac{12}{15}$, $\frac{2}{3} = \frac{10}{15}$

Step2: Subtract the fractions

$\frac{12}{15} - \frac{10}{15} = \frac{12 - 10}{15} = \frac{2}{15}$

Step1: Multiply by reciprocal

Dividing by a fraction is multiplying by its reciprocal: $\frac{1}{6} \times \frac{2}{1}$

Step2: Multiply numerators and denominators

$\frac{1 \times 2}{6 \times 1} = \frac{2}{6} = \frac{1}{3}$ (simplify)

Answer:

$\frac{5}{4}$ (or $1\frac{1}{4}$)

2. $\boldsymbol{\frac{4}{5} - \frac{2}{3}}$