Questions: Example #1: Find -3/4(-7/9). Write in simplest form. Example #2: Find -3 1/5(1 1/14). Write in simplest form. Partner Practice Partner B: -0.64(-1/4)

Transcript text: Example \#1: Find $-\frac{3}{4}\left(-\frac{7}{9}\right)$. Write in simplest form. Example \#2: Find $-3 \frac{1}{5}\left(1 \frac{1}{14}\right)$. Write in simplest form. Partner Practice Partner $B:-0.64\left(-\frac{1}{4}\right)$

Solution

Solution Steps

Step 1: Multiply the fractions

To solve $-\frac{3}{4}\left(-\frac{7}{9}\right)$, multiply the numerators and denominators: \[ -\frac{3}{4} \times -\frac{7}{9} = \frac{3 \times 7}{4 \times 9} = \frac{21}{36}. \]

Step 2: Simplify the fraction

Simplify $\frac{21}{36}$ by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3: \[ \frac{21 \div 3}{36 \div 3} = \frac{7}{12}. \]

Final Answer

\[ \boxed{\frac{7}{12}} \]

Step 1: Convert mixed numbers to improper fractions

Convert $-3 \frac{1}{5}$ and $1 \frac{1}{14}$ to improper fractions: \[ -3 \frac{1}{5} = -\frac{16}{5}, \quad 1 \frac{1}{14} = \frac{15}{14}. \]

Step 2: Multiply the fractions

Multiply the improper fractions: \[ -\frac{16}{5} \times \frac{15}{14} = -\frac{16 \times 15}{5 \times 14} = -\frac{240}{70}. \]

Step 3: Simplify the fraction

Simplify $-\frac{240}{70}$ by dividing the numerator and denominator by their GCD, which is 10: \[ -\frac{240 \div 10}{70 \div 10} = -\frac{24}{7}. \]

Final Answer

\[ \boxed{-\frac{24}{7}} \]

Step 1: Multiply the decimal and fraction

To solve $-0.64\left(-\frac{1}{4}\right)$, multiply the decimal and fraction: \[ -0.64 \times -\frac{1}{4} = 0.64 \times \frac{1}{4} = \frac{0.64}{4}. \]

Step 2: Simplify the result

Divide $0.64$ by $4$: \[ \frac{0.64}{4} = 0.16. \]

Final Answer

\[ \boxed{0.16} \]

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