Video: Comparing Fractions with Negative Signs

Which of the following is true? [A] −3/5 = −7/9 [B] −3/5 > −7/9 [C] −3/5 < −7/9.

02:43

Video Transcript

Which of the following is true? Negative three-fifths is equal to negative seven-ninths. Negative three-fifths is greater than negative seven-ninths. Or, negative three-fifths is less than negative seven-ninths.

Here, we have two fractions we’re trying to compare. However, these fractions do not have a common denominator. Before we compare them, we’ll have to find a common denominator. I know that nine times five equals 45. And that means 45 could be used as a common denominator. To go from five to 45, we multiply by nine. And if we multiply by nine in the denominator, we have to multiply by nine in the numerator. Negative three times nine equals negative 27.

We’ll follow this same process for negative seven-ninths. Nine times five equals 45. And if we multiply by five in the denominator, we’ll need to multiply by five in the numerator. Negative seven times five equals negative 35. Now that we have a common denominator, we realize we’re comparing negative 27 over 45 and negative 35 over 45. Comparing negative numbers can sometimes be confusing. An easy way to make sure we’re comparing them correctly is to plot them on a number line.

We have zero and negative one. In our case, we could write negative one as negative 45 over 45. That’s the same thing as negative one. Negative 35 over 45 is closer to negative one than it is to zero. And negative 27 over 45 is about halfway between zero and negative one. We also want to remember the equivalent, negative seven-ninths and negative three-fifths. When we’re working with negative numbers, the value closest to zero is the largest. Negative 27 over 45, negative three-fifths, is closer to zero. And that means it’s larger than negative seven-ninths.

Negative three-fifths is larger than negative seven-ninths.

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