Question

1. solve each problem in two different ways as modeled in the example.

example: $\frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3} = 4$ $\frac{2}{3} \times 6 = \frac{2 \times \cancel{6}^2}{\cancel{3}_1} = 4$

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:

Part a: $\frac{3}{4} \times 16$

Way 1: Multiply first, then simplify

Multiply numerator by 16, simplify.
$\frac{3 \times 16}{4} = \frac{48}{4} = 12$

Way 2: Simplify first, then multiply

Cancel common factor 4 first.
$\frac{3 \times \cancel{16}^4}{\cancel{4}_1} = 3 \times 4 = 12$

Part b: $\frac{4}{3} \times 12$

Way 1: Multiply first, then simplify

Multiply numerator by 12, simplify.
$\frac{4 \times 12}{3} = \frac{48}{3} = 16$

Way 2: Simplify first, then multiply

Cancel common factor 3 first.
$\frac{4 \times \cancel{12}^4}{\cancel{3}_1} = 4 \times 4 = 16$

Part c: $40 \times \frac{11}{10}$

Way 1: Multiply first, then simplify

Multiply 40 by numerator, simplify.
$\frac{40 \times 11}{10} = \frac{440}{10} = 44$

Way 2: Simplify first, then multiply

Cancel common factor 10 first.
$\frac{\cancel{40}^4 \times 11}{\cancel{10}_1} = 4 \times 11 = 44$

Part d: $\frac{7}{6} \times 36$

Way 1: Multiply first, then simplify

Multiply numerator by 36, simplify.
$\frac{7 \times 36}{6} = \frac{252}{6} = 42$

Way 2: Simplify first, then multiply

Cancel common factor 6 first.
$\frac{7 \times \cancel{36}^6}{\cancel{6}_1} = 7 \times 6 = 42$

Part e: $24 \times \frac{5}{8}$

Way 1: Multiply first, then simplify

Multiply 24 by numerator, simplify.
$\frac{24 \times 5}{8} = \frac{120}{8} = 15$

Way 2: Simplify first, then multiply

Cancel common factor 8 first.
$\frac{\cancel{24}^3 \times 5}{\cancel{8}_1} = 3 \times 5 = 15$

Answer:

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