Chapter 4, Problem 22MS

To determine

To simplify given expression $-\frac{12}{25}\cdot \left(-\frac{35}{42}\right)$ .

Answer to Problem 22MS

  $\frac{2}{5}$

Explanation of Solution

Given information: $-\frac{12}{25}\cdot \left(-\frac{35}{42}\right)$

Calculations: We have $-\frac{12}{25}\cdot \left(-\frac{35}{42}\right)$

Apply rule: $-a\cdot \left(-b\right)=a\cdot b$

  $-\frac{12}{25}\cdot \left(-\frac{35}{42}\right)=\frac{12}{25}\cdot \frac{35}{42}$

Simplify fraction $\frac{35}{42}$

  $\frac{35}{42}=\frac{5\times 7}{6\times 7}$

Cancel the common factor: 7

  $\frac{5\times \cancel{7}}{6\times \cancel{7}}=\frac{5}{6}$

So,

  $\frac{12}{25}\cdot \frac{35}{42}=\frac{12}{25}\cdot \frac{5}{6}$

Multiply fractions: $\frac{a}{b}\cdot \frac{c}{d}=\frac{a\cdot c}{b\cdot d}$

  $\frac{12\cdot 5}{25\cdot 6}$

Multiply the number: $12\cdot 5=60$

  $=\frac{60}{25\cdot 6}$

Multiply the number: $25\cdot 6=150$

  $=\frac{60}{150}$

Simplify fraction $\frac{60}{150}$

  $\frac{60}{150}=\frac{2\times 30}{5\times 30}$

Cross out common factor 30, we get

  $\frac{2\times 30}{5\times 30}=\frac{2}{5}$

Therefore, $-\frac{12}{25}\cdot \left(-\frac{35}{42}\right)=\frac{2}{5}.$