Question

1. rewrite the following expressions as shown in the example: example: $\frac{2}{3}+\frac{2}{3}+\frac{2}{3}+\frac{2}{3}=\frac{4\times2}{3}=\frac{8}{3}$ a. $\frac{5}{3}+\frac{5}{3}+\frac{5}{3}$ b. $\frac{13}{5}+\frac{13}{5}$ c. $\frac{2}{4}+\frac{2}{4}+\frac{2}{4}$ 2. solve each problem in two different ways as modeled in the example: example: $\frac{2}{3}\times6=\frac{2\times6}{3}=\frac{12}{3}=4$ $\frac{2}{3}\times6=\frac{2\times\cancel{6}^2}{\cancel{3}^1}=4$ a. $\frac{3}{4}\times16$ $\frac{3}{4}\times16$ b. $\frac{4}{3}\times12$ $\frac{4}{3}\times12$ c. $40\times\frac{11}{10}$ $40\times\frac{11}{10}$ d. $\frac{7}{6}\times36$ $\frac{7}{6}\times36$ e. $24\times\frac{5}{8}$ $24\times\frac{5}{8}$

Explanation:

---

Problem 1

Part a:

Step1: Multiply count by numerator

$3 \times \frac{5}{3} = \frac{3 \times 5}{3}$

Step2: Simplify the fraction

$\frac{15}{3} = 5$

Part b:

Step1: Multiply count by numerator

$2 \times \frac{13}{5} = \frac{2 \times 13}{5}$

Step2: Calculate the numerator

$\frac{26}{5} = 5\frac{1}{5}$

Part c:

Step1: Multiply count by numerator

$3 \times \frac{9}{4} = \frac{3 \times 9}{4}$

Step2: Calculate the numerator

$\frac{27}{4} = 6\frac{3}{4}$
---

Problem 2

Part a:

Method 1: Multiply numerator first

$\frac{3 \times 16}{4} = \frac{48}{4} = 12$

Method 2: Simplify first

$\frac{3}{4} \times 16 = 3 \times \frac{16}{4} = 3 \times 4 = 12$

Part b:

Method 1: Multiply numerator first

$\frac{4 \times 12}{3} = \frac{48}{3} = 16$

Method 2: Simplify first

$\frac{4}{3} \times 12 = 4 \times \frac{12}{3} = 4 \times 4 = 16$

Part c:

Method 1: Multiply numerator first

$\frac{40 \times 11}{10} = \frac{440}{10} = 44$

Method 2: Simplify first

$40 \times \frac{11}{10} = \frac{40}{10} \times 11 = 4 \times 11 = 44$

Part d:

Method 1: Multiply numerator first

$\frac{7 \times 36}{6} = \frac{252}{6} = 42$

Method 2: Simplify first

$\frac{7}{6} \times 36 = 7 \times \frac{36}{6} = 7 \times 6 = 42$

Part e:

Method 1: Multiply numerator first

$\frac{24 \times 5}{8} = \frac{120}{8} = 15$

Method 2: Simplify first

$24 \times \frac{5}{8} = \frac{24}{8} \times 5 = 3 \times 5 = 15$

Answer:

1.
a. $5$
b. $\frac{26}{5}$ or $5\frac{1}{5}$
c. $\frac{27}{4}$ or $6\frac{3}{4}$

2.
a. $12$
b. $16$
c. $44$
d. $42$
e. $15$