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Video: Subtracting Fractions with Unlike Denominators

Kathryn Kingham

How much more is 7/8 of a gallon than 3/4 of a gallon?

02:17

Video Transcript

How much more is seven-eighths of a gallon than three-fourths of a gallon?

In this question, we need to compare seven-eighths to three-fourths, but we have a problem. Before we can find out how much more seven-eighths is to three-fourths, we have to find a common denominator. Right now, we’re working with a denominator of eight and a denominator of four.

Because I know that eight is a multiple of four, I leave the seven-eighths exactly as it is. And now I need to try and convert three-fourths into some number over eight. To change the denominator from a four to an eight, we will multiply the denominator by two.

But remember, when we’re working with fractions, if we multiply the denominator by two, we also have to multiply the numerator by two. Three times two is six. Now we’re comparing seven-eighths to six-eighths, and our problems are solved.

We can copy down the same question using six-eighths instead of three-fourths. Now our question asks how much more is seven-eighths of a gallon than six-eighths of a gallon. We can visualize it like this, a rectangle divided into eight equal parts. In the seven-eighths, seven of the eight pieces will be shaded. In the six-eighths, six of the eight pieces will be shaded.

We see that seven-eighths is one out of eight more than six-eighths. Seven-eighths of a gallon is one-eighth of a gallon more than six-eighths.