Lesson Video: Subtracting Fractions from Mixed Numbers: No Regrouping | Nagwa Lesson Video: Subtracting Fractions from Mixed Numbers: No Regrouping | Nagwa

Lesson Video: Subtracting Fractions from Mixed Numbers: No Regrouping Mathematics • 5th Grade

In this video, we will learn how to add related fractions within one whole by finding a common denominator.

11:29

Video Transcript

Subtracting Proper Fractions Where Denominators Are Multiples

In this video, we’re going to learn how to subtract related fractions within one whole by finding a common denominator. How would we subtract a third from seven-ninths? When we’re subtracting fractions, both fractions need to have the same denominator. We can’t take thirds away from ninths. They’re not the same thing. Let’s use a model to help us represent this calculation. The denominator in our first fraction is a nine. This means we need to divide our whole amount into nine equal parts. One, two, three, four, five, six, seven, eight, nine. We divided the whole amount into nine equal parts. Each part is worth one-ninth.

The numerator, which is the top number in the fraction, is a seven. So we have to select seven-ninths. There we go. We’ve shaded seven-ninths. So how would we subtract one-third? Let’s draw a model to represent one-third. This bar represents one whole. And because the denominator of our fraction is a three, we need to divide our whole into three equal parts: one, two, three. Each part represents one-third. And because our numerator is a one, we need to shade one of our parts. These two models help us to see that one-third is equal to three-ninths. So to subtract one-third from seven-ninths, we just need to subtract three of our ninths. How many ninths do we have left? Four-ninths. So seven-ninths subtract one-third equals four-ninths. We used the model to help us work out that one-third is equal to three-ninths.

There’s another way to work out how many ninths are equal to one-third. To convert thirds into ninths, we can multiply by three, because three times three is nine. And whatever we do to the denominator, we need to do the same to the numerator to keep the fractions equal. And we know that one times three is three. Once we know that one-third is equal to three-ninths, we can subtract. Seven-ninths subtract three-ninths is four-ninths. If we have seven-ninths and we take three of them away, we’ll be left with four-ninths. Let’s have a go at answering a question now so we can put into practice what we’ve learned so far.

Using the given model, find five-eighths subtract one-quarter. Give your answer in its simplest form.

In this question, we have to find five-eighths subtract one-quarter, and we’ve been given a model to help. The first model represents five-eighths. The whole amount has been divided into eight equal parts, and five of those eight parts have been shaded. We have to subtract one-quarter from these five-eighths. Our second model represents one-quarter. The whole amount has been divided into four equal parts, and one of those four parts has been shaded.

By comparing these two models, we can see that one-quarter is equal to two-eighths. So to subtract a quarter from our five-eighths, we need to take away two-eighths. One, two. How many eighths do we have left? There are three. So five-eighths take away one-quarter is equal to five-eighths take away two-eighths. So if we have five-eighths and we take away two, we’ll have three-eighths left. And the question says we have to give our answer in its simplest form. We can’t simplify three-eighths. Five-eighths take away one-quarter equals three-eighths.

So far in this video, we’ve learned how to subtract fractions with different denominators using models. Let’s have a go at subtracting these fractions without a model.

What is five-sixths take away two-thirds?

Straightaway, we can see that the denominators in these two fractions are different. Before we can subtract two-thirds from five-sixths, we need to make both denominators the same. In other words, we need to make both of our fractions into an amount of sixths. We know six is a multiple of three. If we multiply three by two, we get six. And whatever we do to the denominator, we need to do the same to the numerator. So we need to multiply two by two. So two-thirds is equal to four-sixths. Now, both of our fractions have the same denominator. Now we’re ready to subtract.

We’ve got five-sixths, and we need to take away four. And we know that five take away four leaves us with one. Five-sixths take away four-sixths equals one-sixth. So to help us subtract five-sixths from two-thirds, we had to make both denominators the same. We know that six is a multiple of three. So we multiplied three by two to give us our denominator of six. Then we multiplied the numerator by two, which gave us four-sixths. Once the denominators are the same, we can subtract.

Let’s try answering some questions now where we need to subtract two fractions with different denominators without using a model.

Jackson has half of a chocolate bar and he eats one-sixth of it. How much of the chocolate bar is left over?

If Jackson has a half of a chocolate bar and he eats a sixth of it, to find out how much of the chocolate bar is left over, we need to subtract one-sixth from a half. Before we can subtract, both of the denominators need to be the same. Six is a multiple of two, so we could make both of the denominators a six. How many sixths are equal to one-half? How do we get from two to six? Two times three is six. We multiplied the denominator by three. Now we need to multiply the numerator by three, and we know that one times three is three. Now that we know a half is equal to three-sixths, we can subtract. Three-sixths subtract one-sixth equals two-sixths.

If we have three-sixths and we take one away, we’ll have two-sixths left. But we need to give our answer in its simplest form. Two-sixths is equal to one-third. If we divide two by two, we get one. And if we divide six by two, we get three. A half subtract one-sixth equals two-sixths or one-third.

Sophia’s bottle contains three-quarter liters of water. If she drinks one-eighth liters from her bottle, how much water in liters is left over?

We know that Sophia’s bottle contains three-quarter liters of water. If she drinks another eighth of a liter, how much water will she have left? We have to find three-quarters take away one-eighth. Before we can subtract, both of the denominators need to be the same. We know that eight is a multiple of four, so let’s see how many eighths are equal to three-quarters. Eight is the common denominator. How do we get from four to eight? We know that four times two is eight, so we need to multiply our numerator by two. And we know that three times two is six.

Now that we know that three-quarters is equal to six-eighths, we can subtract. If we’ve got six-eighths and we take away one of them, we’ll have five-eighths left. If Sophia’s bottle contains three-quarters of a liter of water and she drinks an eighth of a liter from her bottle, she will have five-eighths of a liter left over.

What have we learned in this video? We have learned how to subtract related fractions within one whole by finding a common denominator.

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