# Video: Arranging Fractions with Different Denominator in Word Problems

Liam was playing in the park. He collected four twigs that measured 2/3 ft, 8/15 ft, 1/5 ft, and 7/9 ft. Determine which of the twigs is the longest.

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### Video Transcript

Liam was playing in the park. He collected four twigs that measured two-thirds foot, eight fifteenths foot, one-fifth foot, and seven-ninths foot. Determine which of the twigs is the longest.

We have four fractions: two-thirds, eight fifteenths, one-fifth, and seven-ninths. Let’s imagine these fractions on a number line. All of them fall somewhere between zero and one. Let’s see if we can decide if these fractions are more or less than one-half. Two-thirds is more than one-half. What about eight fifteenths? 15 divided by two is seven and a half. Eight is more than seven and a half. And that means eight fifteenths is larger than one-half.

One-fifth is less than one-half. Five divided by two is two and a half. Our numerator is one. And that means one-fifth is less than one-half. And then, we have seven-ninths. Nine divided by two is four and a half. Seven is larger than four and a half. And that means seven-ninths is larger than one-half. Since we’re looking for the longest stick, we can eliminate one-fifth because one-fifth is less than half a foot.

But we still have three fractions to compare. And to compare these accurately, we need to find a common denominator. 45 is the least common multiple of three, 15, and nine. Three times 15 equals 45. And if we multiplied the denominator by 15, we need to multiply the numerator by 15. Two times 15 equals 30. 15 times three equals 45. And that means we need to multiply eight times three, which is 24. Nine times five equals 45. And seven times five equals 35.

Once we have a common denominator, we can see which of these fractions is largest. It’s the one with the largest numerator. 35 over 45 is the largest fraction. And that’s the fraction seven-ninths.

The twig that was seven-ninths foot is the longest.