Lesson Video: Comparing Fractions Using Models: Same Denominator | Nagwa Lesson Video: Comparing Fractions Using Models: Same Denominator | Nagwa

# Lesson Video: Comparing Fractions Using Models: Same Denominator Mathematics

In this video, we will learn how to use models to compare proper fractions that have the same denominator and explain how the size of the numerator affects the size of the fraction.

09:28

### Video Transcript

Comparing Fractions Using Models: Same Denominator

In this video, we will learn how to use models to compare proper fractions that have the same denominator and explain how the size of the numerator affects the size of the fraction.

Each of these models shows an amount of fifth. We know this because each model has been divided into five equal parts: one, two, three, four, five. When we divide a shape or a number into five equal parts, we call each part a fifth. And we write this as one over five. Did you notice that the number at the bottom of the fraction is a five? We call this number the denominator.

The denominator tells us the number of equal parts. In this model, one of the parts has been shaded pink. This model represents one-fifth. We call the number at the top of the fraction the numerator. This tells us the number of selected parts. In this case, one out of five equal parts is shaded. So this model which has two out of five parts shaded shows two-fifths. The denominator stays the same, because we still have five equal parts, but the number of parts selected is two.

So this model shows three-fifths. Three parts have been shaded out of five. Three over five is three-fifths. And the last of our models shows four-fifths. Four parts out of five are selected. So we write this as four over five.

Which of our four fractions is worth the most? Which has the greatest value: one-fifth, two-fifths, three-fifths, or four-fifths? Two-fifths are worth more than one-fifth. Three-fifths are worth more than two-fifths. And four-fifths are worth more than three-fifths. So the fraction which is worth the most is four-fifths.

When we’re comparing fractions with the same denominator or the same number of equal parts, the fraction with the highest numerator is worth the most. Four-fifths are worth more than three-fifths. Four-fifths are worth more than two-fifths. And four-fifths are worth more than one-fifth.

In this video, we’re going to be comparing fractions with the same denominator. Let’s put into practice what we’ve learned so far by answering some questions.

Complete the following using less than, equal to, or greater than. Is four-sixths less than, equal to, or greater than five-sixths?

In this question. we’re being asked to compare two fractions: four-sixths and five-sixths. We have to use the symbol less than, equal to, or greater than. Both of our models show an amount of sixths. This is because the bar models have been divided into six equal parts. The denominator, or the number at the bottom of the fraction, is the same. Both models show an amount of sixths.

But the numerators, or the numbers on the top of the fractions, are different. The numerator on our first fraction is a four. And we can see that four out of the six equal parts have been shaded. The numerator in our second fraction is a five. This is because five out of the six equal parts are shaded.

We can tell by looking at the model and by comparing the numerators that four-sixths is less than five-sixths. Four equal parts is less than five equal parts. We completed the comparison using the symbol less than. Four-sixths is less than five-sixths.

Complete four-ninths what seven-ninths using less than, equal to, or greater than.

In this question, we’re being asked to compare two fractions. And both fractions have the same denominator. The denominator is the bottom number in the fraction. Both of these fractions are an amount of ninths.

Let’s model these fractions on a number line. Our number line has nine divisions. So the first division represents one-ninth. When we divide into nine equal parts, we call each part a ninth. Our next division represents two-ninths. And the next division is three-ninths. Did you notice that the denominator stays the same? And the numerator is increasing by one each time.

Next is four-ninths, five-ninths, six-ninths, seven-ninths, eight-ninths, and nine-ninths. Nine-ninths is equal to one or one whole. Now we’ve got our number line, we can compare our fractions four-ninths and seven-ninths. As we count along the number line, the number of parts increases. The numerator increases by one each time. Since four comes before seven on the number line or four-ninths comes before seven-ninths, we can say that four-ninths is less than seven-ninths. So the missing symbol is less than. Four-ninths is less than seven-ninths.

Complete five-ninths what four-ninths using the symbol less than, equal to, or greater than.

In this question, we’re being asked to compare two fractions: five-ninths and four-ninths. We can see that both fractions have the same denominator. That’s the number on the bottom of the fraction. It’s a nine. So this means nine equal parts.

Here’s a bar model. It’s been divided into nine equal parts. Each part is worth one-ninth. If we shade five of our nine equal parts, our model shows five-ninths. And if we shade four out of our nine equal parts, the model shows the fraction four-ninths. Since five is greater than four and both of our fractions are ninths, we can say that five-ninths is greater than four-ninths. The missing symbol is greater than. Five-ninths are greater than four-ninths.

What have we learned in this video? We’ve learned how to compare fractions with the same denominator using models. We also learned that the greater the numerator, the top number on the fraction, the bigger the fraction.

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