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Video: Subtracting Fractions with Unlike Denominators

Kathryn Kingham

Calculate 7/9 − 4/6.

02:46

Video Transcript

Calculate seven-ninths minus four-sixths.

We’ll need to follow the procedure for adding and subtracting fractions starting with step one: check for common denominators. Step one tells us that we need to check for a common denominator. We’re working with seven-ninths and four-sixths. Our denominators are not the same; they’re not common.

Before we move on to step two, we’ll need to look at six and nine and find a common denominator for them. I know that 18 is divisible by nine and six. I think that 18 would be a good common denominator here. To move from nine to 18, we would multiply by two; nine times two equals 18. But if we multiply the bottom half of our fraction, if we multiplied the denominator by two, we also need to multiply the numerator by that same number, which means we’ll need to multiply seven times two.

Another way to write the fraction seven-ninths is fourteen eighteenths. They are equal in value, just written differently. Six times three equals 18. And if I multiplied the denominator by three, I need to multiply the numerator by three which means I need to multiply four times three. Twelve eighteenths is an equivalent fraction for four-sixths.

Back to step one, we were checking for a common denominator. We’ve now found the common denominator and have converted these fractions so that we’re subtracting fourteen eighteenths minus twelve eighteenths. It means we can move on to step two.

Step two says add or subtract numerators. Well, our problem is a subtraction problem. That means we’ll subtract 14 minus 12. 14 minus 12 equals two, and the denominator doesn’t change. We leave that as 18.

Step three tells us to simplify this fraction, if we can. I noticed that two and 18 are both even numbers, which means they’re both divisible by two. I’ll need to divide the numerator and the denominator by two to simplify the fraction. The simplified fraction of two eighteenths is one-ninth.

Seven-ninths minus four-sixths equals one-ninth.