Video: Ordering Given Fractions with Unlike Denominators in Ascending Order

Order 7/10, 6/4, 4/5, 5/2 from least to greatest.


Video Transcript

Order seven tenths, six-fourths, four-fifths, and five-halves from least to greatest.

Least to greatest means we’re going to order them left or right from the smallest number to the largest number. Our only issue is that we have fractions. And they have different denominators. So it’s gonna be a little bit difficult to compare them. So we need to find a common denominator between all four of these fractions.

So what would be the smallest number that 10, four, five, and two can all go into? That would be 20. So let’s begin with the seven tenths. Seven tenths is equal to something over 20. So how could we go from 10 to 20? We multiply by two. So that means we need to multiply the numerator by two. And seven times two is 14. So seven tenths, we can rewrite it as fourteen twentieths.

Now let’s look at six-fourths. Six-fourths is equal to something over 20. To get from four to 20, we multiply by five. So we take six times five to get 30. So six-fourths is equal to thirty twentieths.

Now let’s look at the four-fifths. Four-fifths is equal to something over 20. To go from five to 20, we multiply by four. And four times four is 16. So we have sixteen twentieths.

Now let’s look at five-halves, the last one. Repeating our process to get from two to 20, we multiply by 10. And five times 10 is 50. So we have fifty twentieths. So from least to greatest is how we will arrange these fractions.

So looking at our fractions, which one has the smallest numerator? That would be the fourteen twentieths. So fourteen twentieths would be our smallest fraction. So why are we only looking at the numerators? Because all of the denominators are the same. So we’re not really comparing this.

So fourteen twentieths is the smallest. Now the next smallest would be the sixteen twentieths. And then we would have the thirty twentieths. And then finally the largest would be the fifty twentieths.

Now we need to put these numbers back in the original form just as the question had them. So the fourteen twentieths was equal to the seven tenths. And the sixteen twentieths is equal to the four-fifths. So that comes next. And now the thirty twentieths is equal to the six-fourths. And then lastly the fifty twentieths is equal to five-halves. So ordering these fractions from least to greatest, we get seven tenths, four-fifths, six-fourths, and five-halves.

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