Work out 20/35 × 14/30. Give your answer in the simplest form.
Understand the Problem
The question is asking us to multiply two fractions, 20/35 and 14/30, and provide the answer in its simplest form. The high-level approach involves multiplying the numerators together and the denominators together, and then simplifying the resulting fraction.
Answer
The answer is \( \frac{4}{15} \).
Answer for screen readers
The answer in its simplest form is ( \frac{4}{15} ).
Steps to Solve
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Multiply the Numerators To multiply the two fractions, we first multiply the numerators: $$ 20 \times 14 = 280 $$
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Multiply the Denominators Next, we multiply the denominators: $$ 35 \times 30 = 1050 $$
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Set Up the New Fraction Now we can set up our new fraction: $$ \frac{280}{1050} $$
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Simplify the Fraction To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 280 and 1050 is 70.
Now divide both the numerator and denominator by 70: $$ \frac{280 \div 70}{1050 \div 70} = \frac{4}{15} $$
The answer in its simplest form is ( \frac{4}{15} ).
More Information
When multiplying fractions, the process involves multiplying the numerators to create the new numerator and multiplying the denominators to create the new denominator. After obtaining the result, simplifying is necessary to represent the fraction in its simplest form.
Tips
- Forgetting to Simplify: A common error is not simplifying the final fraction, which can lead to an incomplete or incorrect answer.
- Incorrectly Calculating GCD: Making mistakes while finding the greatest common divisor can lead to improper simplification. It's vital to double-check GCD calculations.
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