Video: Identifying the Appropriate Subtraction Sentence Using a Given Visual Fraction Model

Which of the following describes the given model? [A] 5/9 + 3/9 = 8/9 [B] 5/8 − 3/8 = 1/4 [C] 5/8 + 3/8 = 1 [D] 5/9 − 3/9 = 2/9 [E] 4/8 − 2/8 = 1/4.

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Video Transcript

Which of the following describes the given model?

Before we choose one of the equations, let’s think about what this model represents. We have a rectangle. How many pieces is this rectangle divided into? One, two, three, four, five, six, seven, eight. This whole is divided into eight parts.

One thing that we can do is look at our answer choices and remove any of them that aren’t divided into eight parts. Answer choice a says five-ninths plus three-ninths equals eight-ninths, but we’re not talking about ninths. So we can remove answer choice a. For the same reason, we can also remove answer choice d.

Okay, back to our model. In our model, pieces three four and five have an X through them. That X represents taking away. We represent take away mathematically by using subtraction. So we can eliminate answer choice c because it is an addition problem. We know that we’re dealing with subtraction. But in order to find the correct problem, we need to know what fraction did we start with.

Originally five out of the eight were shaded. Five-eighths were blue. Three-eighths were crossed out. And we use subtraction. So we say five-eighths minus three-eighths. And there were two-eighths blue-shaded pieces remaining. I notice that the answer choice e starts with four- eighths and not five-eighths.

And that leaves us with answer choice b: five-eighths minus three-eighths equals one-fourth. But wait! Two out of the eight were still shaded. Why does the answer choice say one-fourth? Two-eighths and one-fourth are equivalent fractions. If you divide two by two, you get one in the numerator. And if you divide eight by two, you get four.

Remember, when we’re working with fractions, we can divide the numerator and the denominator by the same number and we haven’t changed the value of that fraction. They are equivalent fractions. Five-eighths minus three-eighths equals one-fourth can be described with the given model.

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