Explain how you can use equivalent fractions to find the quotient of 2

Question

3
÷ 4.

Answer 1

To find the quotient of the fraction \( \frac{2}{3} \div 4 \) using equivalent fractions, we can follow these steps:

1. Rewrite the whole number as a fraction: The number 4 can be rewritten as a fraction. Specifically, we can express 4 as \( \frac{4}{1} \).

2. Change the division to multiplication by the reciprocal: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{4}{1} \) is \( \frac{1}{4} \). So we can rewrite the expression as: \[ \frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} \]

3. Multiply the fractions: Now we multiply the numerators and the denominators: \[ \frac{2 \times 1}{3 \times 4} = \frac{2}{12} \]

4. Simplify the fraction: Next, we simplify \( \frac{2}{12} \) by finding the greatest common divisor (GCD) of 2 and 12, which is 2. We divide both the numerator and the denominator by 2: \[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]

Thus, the quotient of \( \frac{2}{3} \div 4 \) is \( \frac{1}{6} \).

In summary, by converting the whole number to a fraction and using multiplication by the reciprocal, we can effectively find the quotient using equivalent fractions.