What is 20 divided by 3/4
The Correct Answer and Explanation is:
To solve the problem 20 ÷ (3/4), you need to divide 20 by the fraction 3/4. In mathematics, dividing by a fraction is equivalent to multiplying by its reciprocal.
Step-by-step Solution:
- Understand the operation:
- When you divide by a fraction, you multiply by its reciprocal. The reciprocal of 3/4 is 4/3.
- Rewrite the division as multiplication:
- The expression 20 ÷ (3/4) can be rewritten as:
[
20 \times \left( \frac{4}{3} \right)
]
- Convert 20 to a fraction:
- 20 is a whole number, and we can express it as a fraction by placing it over 1:
[
20 = \frac{20}{1}
]
So, the equation becomes:
[
\frac{20}{1} \times \frac{4}{3}
]
- Multiply the fractions:
- To multiply two fractions, multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{20 \times 4}{1 \times 3} = \frac{80}{3}
]
- Simplify the result:
- The result is 80/3, which is an improper fraction.
- Convert to a mixed number (optional):
- To express the improper fraction as a mixed number, divide 80 by 3:
[
80 ÷ 3 = 26 \text{ remainder } 2
]
So, 80/3 is equivalent to:
[
26 \frac{2}{3}
]
Final Answer:
- The result of 20 ÷ (3/4) is 80/3, or as a mixed number, 26 2/3.
Explanation:
Dividing by a fraction is a common mathematical operation, and understanding it helps simplify many problems. Dividing by a fraction like 3/4 essentially asks, “How many times does 3/4 fit into 20?” Instead of performing complex steps, we use the reciprocal (4/3) to make the operation easier. By multiplying 20 by 4/3, we convert the problem into a multiplication of whole numbers, which is a more straightforward process.