Question
Divide. Write your answer in simplest form \[ \frac{3}{14} \div \frac{7}{10} \]
Ask by Macdonald Graham. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{15}{49} \).
Solution
To divide the fractions, multiply by the reciprocal of the second fraction. That is,
(3/14) ÷ (7/10) = (3/14) × (10/7).
Multiply the numerators and the denominators:
= (3 × 10) / (14 × 7)
= 30 / 98.
Now simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
= (30 ÷ 2) / (98 ÷ 2)
= 15 / 49.
The answer in simplest form is 15/49.
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Simplify this solution Beyond the Answer
To divide fractions, you multiply by the reciprocal of the second fraction. So, we have: \[ \frac{3}{14} \div \frac{7}{10} = \frac{3}{14} \times \frac{10}{7} \] Now, multiply the numerators and the denominators: \[ = \frac{3 \times 10}{14 \times 7} = \frac{30}{98} \] Next, we simplify \(\frac{30}{98}\) by finding the greatest common divisor (GCD) of 30 and 98, which is 2: \[ \frac{30 \div 2}{98 \div 2} = \frac{15}{49} \] So, the answer in simplest form is: \[ \frac{15}{49} \]
