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} \times 6 = \frac{2\times6}{3} = \frac{12}{3} = 4 \\) \\( \frac{2}{3} \times 6 = \frac{2\times\cancel{6}^2}{\cancel{3}^1} = 4 \\) a. \\( \frac{3}{4} \times 16 \\) \\( \frac{3}{4} \times 16 \\) b. \\( \frac{4}{3} \times 12 \\) \\( \frac{4}{3} \times 12 \\) c. \\( 40 \times \frac{11}{10} \\) \\( 40 \times \frac{11}{10} \\) d. \\( \frac{7}{6} \times 36 \\) \\( \frac{7}{6} \times 36 \\) e. \\( 24 \times \frac{5}{8} \\) \\( 24 \times \frac{5}{8} \\)

Explanation:

Problem 1

Step1: Multiply count by numerator

a. $3 \times 5 = 15$

Step2: Divide by denominator

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

Step1: Multiply count by numerator

b. $2 \times 13 = 26$

Step2: Divide by denominator

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

Step1: Multiply count by numerator

c. $3 \times 9 = 27$

Step2: Divide by denominator

$\frac{27}{4} = \frac{27}{4}$

Part a

Step1: Multiply numerator by integer

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

Step2: Simplify the fraction

$\frac{48}{4} = 12$

Step1: Cancel common factors first

$\frac{3 \times \cancel{16}^4}{\cancel{4}_1}$

Step2: Multiply remaining terms

$3 \times 4 = 12$

Part b

Step1: Multiply numerator by integer

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

Step2: Simplify the fraction

$\frac{48}{3} = 16$

Step1: Cancel common factors first

$\frac{4 \times \cancel{12}^4}{\cancel{3}_1}$

Step2: Multiply remaining terms

$4 \times 4 = 16$

Part c

Step1: Multiply integer by numerator

$\frac{40 \times 11}{10}$

Step2: Simplify the fraction

$\frac{440}{10} = 44$

Step1: Cancel common factors first

$\frac{\cancel{40}^4 \times 11}{\cancel{10}_1}$

Step2: Multiply remaining terms

$4 \times 11 = 44$

Part d

Step1: Multiply numerator by integer

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

Step2: Simplify the fraction

$\frac{252}{6} = 42$

Step1: Cancel common factors first

$\frac{7 \times \cancel{36}^6}{\cancel{6}_1}$

Step2: Multiply remaining terms

$7 \times 6 = 42$

Part e

Step1: Multiply integer by numerator

$\frac{24 \times 5}{8}$

Step2: Simplify the fraction

$\frac{120}{8} = 15$

Step1: Cancel common factors first

$\frac{\cancel{24}^3 \times 5}{\cancel{8}_1}$

Step2: Multiply remaining terms

$3 \times 5 = 15$

Answer:

a. $5$
b. $\frac{26}{5}$
c. $\frac{27}{4}$

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Problem 2