Question

13)

1. $\frac{3}{10} cdot -\frac{7}{6}$

find each quotient.

1. $\frac{-3}{2} div \frac{1}{4}$

Explanation:

Problem 15: Multiply the fractions $\boldsymbol{\frac{3}{10} \cdot -\frac{7}{6}}$

Step 1: Multiply numerators and denominators

To multiply two fractions, we multiply the numerators together and the denominators together. For $\frac{3}{10} \cdot -\frac{7}{6}$, the numerators are $3$ and $-7$, and the denominators are $10$ and $6$. So we have:
$$\frac{3 \times (-7)}{10 \times 6}$$

Step 2: Simplify the fraction

First, calculate the product in the numerator and the denominator:
$$\frac{-21}{60}$$
Then, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$.
$$\frac{-21 \div 3}{60 \div 3} = \frac{-7}{20}$$

Step 1: Recall the division rule for fractions

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{4}$ is $4$. So we rewrite the division as multiplication:
$$\frac{-3}{2} \times 4$$

Step 2: Multiply the numerator and simplify

Multiply the numerator $-3$ by $4$:
$$\frac{-3 \times 4}{2}$$
Simplify the numerator:
$$\frac{-12}{2}$$
Then divide $-12$ by $2$:
$$-6$$

Answer:

$\boldsymbol{-\frac{7}{20}}$

Problem 17: Divide the fractions $\boldsymbol{\frac{-3}{2} \div \frac{1}{4}}$