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Video: Solving Word Problems Involving Subtraction of Fractions with Like Denominators

Bethani Gasparine

In Mr. Phillip’s class, 17/24 of the students finished their homework, whereas, in Mr. Joe’s class, 13/24 of the students finished their homework. How many more of the students finished their homework in Mr. Phillip’s class than Mr. Joe’s?

02:43

Video Transcript

In Mr. Phillip’s class, seventeen twenty-fourths of the students finish their homework, whereas in Mr. Joe’s class, thirteen twenty-fourths of the students finish their homework. How many more of the students finish their homework in Mr Phillip’s class than Mr. Joe’s? So we essentially wanna know the difference between the two classes. That way we’ll know how many more students actually finish their homework in Mr. Philip’s class compared to the lesser amount that finished their homework in Mr. Joe’s class. So we will take the number of students in Mr. Phillips that finished their homework and subtract the number of students who finished their homework in Mr. Joe’s.

So we have seventeen twenty-fourths minus thirteen twenty-fourths. Here we are subtracting like fractions. Like fractions are fractions with the same denominator. Here our denominators are twenty-four. So to subtract like fractions, we subtract the numerators and we keep our like denominators, twenty-four. So seventeen minus thirteen is equal to four. And then we keep our denominator of twenty-four. However, we’re not completely done, because four and twenty-four have a common factor. That means we can take out a four from both. In other words, we can divide the numerator and denominator both by four. Because four risen to four and four risen to twenty-four, which we call common factors.

Therefore, our answer is one-sixths. However, let’s go ahead and place this on a number line to have kind of visualize our answer. Looking at this number line, we see we have thirteen twenty-fourths on the left and seventeen twenty-fourths on the right. That’s because smaller numbers go to the left and larger numbers go to the right on a number line. So the difference between these two fractions is four spaces. Now we have to remember we’re looking at fractions, so that would be four twenty-fourths. And as we said before, four twenty-fourths reduces because they both, four and twenty-four, the numerator and denominator, both are divisible by four, which is their common factor. So our final answer is one-sixths.