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Comparing Fractions Using Models: Same Numerator
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In this video, we will learn how to use models to compare proper fractions with the same numerator and explain how the size of the denominator affects the size of the fraction.
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Would you rather have two-thirds of a doughnut or two-quarters of a doughnut?
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Both of these fractions have the same numerator.
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The numerator is the number on the top of a fraction.
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If you had two-thirds of this doughnut, you would have two pieces.
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And if you had two-quarters, you would also have two pieces.
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So maybe you think that having two-thirds would be the same as having two-quarters.
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But when we’re thinking about the size of a fraction, we need to look at the denominator.
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This is the number at the bottom of the fraction.
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The denominator tells us the size of the fraction.
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If we’re thinking about thirds, that means the whole amount has been divided into three equal parts.
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And when we think about quarters, the whole amount has been divided into four equal parts.
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So when we compare two fractions with the same numerator, we need to compare the denominators as well to tell us the size of the fraction.
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If we were to take our doughnut and divide it into three equal parts, each part would be a third.
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And if we were to take our doughnut and divide it into four equal parts, each part would be a quarter.
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By using these fraction strips, we can see that one-third is bigger than one-quarter.
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So if one-third is greater than one-quarter, two-thirds are greater than two-quarters.
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I would rather have two-thirds of a doughnut than two-quarters because two-thirds is worth more.
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The bigger the denominator, the smaller the part becomes.
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We could also say that the smaller the denominator, the bigger the part becomes.
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Would you rather have five-sevenths or five twelfths of a hot dog?
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Again, both of these fractions have the same numerator, but this doesn’t mean they have the same value.
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To work out the value of each fraction, we need to look at the denominator.
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Five-sevenths is equal to five out of seven equal parts.
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And five twelfths is equal to five out of 12 equal parts.
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Which would give you the most hot dog, five-sevenths or five twelfths?
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Let’s model five-sevenths using a fraction strip.
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The whole amount has been divided into seven equal parts.
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Each part is worth one-seventh.
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Five of these parts have been shaded blue to show five-sevenths.
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If we take the whole amount or a fraction strip and divide it into 12 equal parts, each part is a twelfth.
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Five of these equal parts have been shaded green to show five twelfths.
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If we compare our two models, we can see that five-sevenths is worth more than five twelfths.
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The bigger the denominator, the smaller the parts become.
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So I would rather have five-sevenths of the hot dog.
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So we’ve learned that when we compare fractions with the same numerator, the size of the denominator affects the size of the fraction.
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Let’s practice what we’ve learned about fractions with the same numerator now by answering some questions.
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Compare the fractions.
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Which symbol is missing?
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Four-fifths is equal to four-sevenths, four-fifths is greater than four-sevenths, or four-fifths is less than four-sevenths.
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In this question, we have to compare the two fractions we’ve been shown, four-fifths and four-sevenths.
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And we have to choose the correct symbol to compare.
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Is four-fifths equal to four-sevenths?
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We could think that these fractions are equal because they both have the same numerator or the number on top of the fraction, four-fifths and four-sevenths.
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Maybe you can already tell from our fraction strips that these fractions are not equal.
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They’re both different sizes.
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So these fractions are not equal.
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The missing symbol is not “equal to.”
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Is four-fifths greater than four-sevenths?
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To find out, we need to compare the denominator.
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If we take our whole amount or fraction strip and divide it into five equal parts, each part is worth a fifth.
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And if we take our fraction strip and divide it into seven equal parts, each part is worth a seventh.
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And we can see that one-fifth is bigger than one-seventh.
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The more equal parts we divide the whole amount into, the smaller the parts become.
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So the bigger the denominator, the smaller the size of the fraction.
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So if one-fifth is greater than one-seventh, four-fifths are greater than four-sevenths.
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The missing symbol is “greater than.”
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When we’re comparing two fractions with the same numerator, the denominator tells us the size of the fraction.
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Four-fifths is greater than four-sevenths.
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Compare the fractions.
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Which symbol is missing?
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Three-quarters, three-eighths.
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Is the missing symbol equal to, less than, or greater than?
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In this question, we have to compare the two fractions shown, three-quarters and three-eighths.
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And we have to select the correct symbol to compare these fractions.
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Is three-quarters equal to three-eighths?
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Both of these fractions do have the same numerator, three-quarters and three-eighths.
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So you might be mistaken into thinking these fractions are equal.
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But we need to look at the denominator of each fraction because the denominator affects the size of the fraction.
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And our two models help us to see this.
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If we take the whole amount and split it into four equal parts, each part would be one-quarter.
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And if we take the whole amount and split it into eight equal parts, each part is worth one-eighth.
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We can see that one-eighth is smaller than a quarter.
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The more equal parts we divide our whole into, the smaller each part becomes.
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So if one-eighth is less than one-quarter, three-eighths is also less than three-quarters.
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Three-quarters is worth more than three-eighths.
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So the missing symbol is “greater than.”
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Three-quarters is greater than three-eighths.
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When we’re comparing two fractions with the same numerator, we also need to compare the denominators because the size of the denominator affects the size of the fraction.
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The missing symbol is “greater than.”
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What have we learned in this video?
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We have learned how to use models to compare fractions with the same numerator.
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We also learned that the size of the denominator affects the size of the fraction.