Simplify 78/66

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How to reduce a fraction

Among different ways simplifying a fraction, we will show the two procedure below:

Method 1 - Divide by a Small Number When Possible

Start by dividing both the numerator and the denomiator of the fraction by the same number, and repeat this until it is impossible to divide. Begin dividing by small numbers like 2, 3, 5, 7. For example,

Simplify the fraction 42/98

• First divide both (numerator/denominator) by 2 to get 21/49.
• Dividing by 3 and 5 will not work, so,
• Divide both numerator and denominator by 7 to get 3/7. Note: 21 ÷ 7 = 3 and 49 ÷ 7 = 7

In the fraction 3/7, 3 is only divisible by itself, and 7 is not divisible by other numbers than itself and 1, so the fraction has been simplified as much as possible. No further reduction is possible, so 42/98 is equal to 3/7 when reduced to its lowest terms. This is a PROPER FRACTION once the absolute value of the top number or numerator (3) is smaller than the absolute value of the bottom number or denomintor (7).

Method 2 - Greatest Common Divisor

To reduce a fraction to lowest terms (also called its simplest form), just divide both the numerator and denominator by the GCD (Greatest Common Divisor).

For example, 3/4 is in lowest form, but 6/8 is not in lowest form (the GCD of 6 and 8 is 2) and 6/8 can be written as 3/4. You can do this because the value of a fraction will remain the same when both the numerator and denominator are divided by the same number.

Note: The Greatest Common Factor (GCF) for 6 and 8, notation gcf(6,8), is 2. Explanation:

• Factors of 6 are 1,2,3,6;
• Factors of 8 are 1,2,4,8.

So, it is ease see that the 'Greatest Common Factor' or 'Divisor' is 2 because it is the greatest number which divides evenly into all of them.

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