To use equivalent fractions to find the quotient of \( \frac{2}{3} \) ÷ 4, follow these steps:
### Step 1: Understand the Operation
Division of fractions can be thought of as multiplying by the reciprocal. The reciprocal of a number a is simply \( \frac{1}{a} \).
### Step 2: Find the Reciprocal of the Divisor
The divisor here is the whole number 4. Its reciprocal is \( \frac{1}{4} \).
### Step 3: Multiply the Dividend by the Reciprocal of the Divisor
Instead of dividing \( \frac{2}{3} \) by 4, you can multiply \( \frac{2}{3} \) by \( \frac{1}{4} \).
### Step 4: Perform the Multiplication
Now, multiply the two fractions:
\[ \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} \]
This results in a new fraction:
\[ \frac{2}{12} \]
### Step 5: Simplify the Resulting Fraction
Finally, you need to simplify the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and the denominator and divide both by this number.
For \( \frac{2}{12} \), the greatest common factor is 2. So we divide both the numerator and the denominator by 2:
\[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]
### Conclusion
Therefore, the quotient of \( \frac{2}{3} \) ÷ 4 is \( \frac{1}{6} \). This is the simplest form of the fraction you obtain when \( \frac{2}{3} \) is divided by 4.