What is the reciprocal of 36 divided 3/4
The Correct Answer and Explanation is:
To find the reciprocal of 36 ÷ (3/4), let’s first simplify the expression and then find the reciprocal.
Step 1: Simplify the Expression
We need to evaluate 36 ÷ (3/4). When you divide by a fraction, it’s equivalent to multiplying by the reciprocal of that fraction. So:36÷(34)=36×(43)36 \div \left( \frac{3}{4} \right) = 36 \times \left( \frac{4}{3} \right)36÷(43)=36×(34)
Now, multiply 36 by 4/3:36×43=36×43=1443=4836 \times \frac{4}{3} = \frac{36 \times 4}{3} = \frac{144}{3} = 4836×34=336×4=3144=48
Thus, 36 ÷ (3/4) = 48.
Step 2: Find the Reciprocal
The reciprocal of a number is simply 1 divided by that number. So, the reciprocal of 48 is:148\frac{1}{48}481
Explanation
To recap, the reciprocal of 36 ÷ (3/4) involves two steps:
- First, we rewrite the division of the fraction as multiplication by the reciprocal of 3/4.
- Then, we simplify the multiplication to get 48.
- Finally, the reciprocal of 48 is 1/48.
This process demonstrates how working with fractions and their reciprocals is a key skill in math. By remembering that division by a fraction is the same as multiplication by its reciprocal, you can simplify many mathematical operations.
