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

$\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}$

Step2: Add numerators

$\frac{2}{4}+\frac{3}{4}=\frac{2 + 3}{4}=\frac{5}{4}=1\frac{1}{4}$

Step1: Find common denominator (15)

$\frac{4}{5}=\frac{4\times3}{5\times3}=\frac{12}{15}$, $\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$

Step2: Subtract numerators

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

Step1: Multiply by reciprocal

$\frac{1}{6}\div\frac{1}{2}=\frac{1}{6}\times\frac{2}{1}$

Step2: Multiply numerators and denominators

$\frac{1\times2}{6\times1}=\frac{2}{6}=\frac{1}{3}$

Answer:

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

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