15/20 ÷ 3/5
Understand the Problem
The question is asking us to perform the division of two fractions, specifically 15/20 divided by 3/5. To solve this, we will invert the second fraction and multiply it by the first fraction.
Answer
The answer is \( \frac{5}{4} \).
Answer for screen readers
The final answer is ( \frac{5}{4} ).
Steps to Solve
- Write the Division of Fractions To divide fractions, we can use the rule that states: $$ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} $$
Using that rule for this problem: $$ \frac{15}{20} \div \frac{3}{5} = \frac{15}{20} \times \frac{5}{3} $$
- Multiply the Numerators and Denominators Now, we need to multiply the numerators and the denominators together: $$ \text{Numerator: } 15 \times 5 = 75 $$ $$ \text{Denominator: } 20 \times 3 = 60 $$
So we have: $$ \frac{15}{20} \div \frac{3}{5} = \frac{75}{60} $$
- Simplify the Resulting Fraction To simplify the fraction $\frac{75}{60}$, we can find the greatest common divisor (GCD) of 75 and 60, which is 15.
Now, we divide both the numerator and the denominator by 15: $$ \frac{75 \div 15}{60 \div 15} = \frac{5}{4} $$
The final answer is ( \frac{5}{4} ).
More Information
The answer ( \frac{5}{4} ) is an improper fraction which can also be expressed as a mixed number, ( 1 \frac{1}{4} ), meaning it is greater than 1. This division of fractions shows the relationship between the parts involved, allowing one to see how many times one fraction fits into another.
Tips
- Forgetting to invert the second fraction when dividing, which would lead to an incorrect operation.
- Not simplifying the resulting fraction, leading to answers that are not in their simplest form.
AI-generated content may contain errors. Please verify critical information
