Reducing fractions after multiplication involves simplifying the resulting fraction to its lowest terms. This is achieved by finding the highest common factor (HCF) of the numerator and the denominator and then dividing both by that HCF. Here’s a detailed explanation:
Steps to Reduce Fractions After Multiplication
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Multiply the Numerators: Multiply all the numerators (the top numbers) of the fractions together.
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Multiply the Denominators: Multiply all the denominators (the bottom numbers) of the fractions together.
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Form the New Fraction: Create a new fraction with the product of the numerators as the new numerator and the product of the denominators as the new denominator.
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Find the Highest Common Factor (HCF): According to reference information, the key to reducing fractions is using the concept of the highest common factor (HCF). The HCF is the largest number that divides both the numerator and the denominator without leaving a remainder.
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Divide by the HCF: Divide both the numerator and the denominator by their HCF. This step simplifies the fraction to its lowest terms.
Example
Let's say you want to multiply and reduce the following fractions:
(2/4) * (3/6)
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Multiply Numerators: 2 * 3 = 6
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Multiply Denominators: 4 * 6 = 24
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New Fraction: 6/24
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Find HCF: The highest common factor of 6 and 24 is 6.
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Divide by HCF:
- Numerator: 6 / 6 = 1
- Denominator: 24 / 6 = 4
Therefore, the reduced fraction is 1/4.
Why Reduce?
Reducing fractions makes them easier to understand and work with. A simplified fraction represents the same value as the original but in its simplest form.
- Easier Calculations: Reduced fractions often involve smaller numbers, making subsequent calculations easier.
- Clearer Understanding: Simplified fractions are easier to visualize and compare.
Summary
To effectively reduce fractions after multiplying, calculate the product of the numerators and denominators, then find the HCF of the resulting numerator and denominator, and finally, divide both by the HCF to obtain the simplified fraction.
