Common denominators: 3/5 and 7/2 | Math | 4th grade | Khan Academy

Rewrite each fraction with a denominator of 10.

We have two fractions: 3 fifths and 7 halves, and we want to take their denominators of five and two and change them to be a common denominator of 10.

Let's start with 3 fifths. We can look at this visually here. We can use this rectangle to represent a whole. One whole, and to show three fifths of that whole, we're going to need to divide it into fifths or five equal pieces.

So let's do that. We'll try to make these as equal as possible. So we have three pieces, and then finally, there we go. These should represent five equal pieces, or fifths.

To show three fifths, we need to shade three of those five pieces. So one, two, three of those five pieces should be shaded in to show three fifths. But we've decided we don't want fifths anymore; now we want tenths.

We want a new denominator of 10. To change this fraction over here, to change this to be tenths, we need to split each of these fifths in half. We need to double the amount of pieces.

So we can do that here. Now, instead of fifths, or five equal pieces, we have tenths. We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

So we found a way to have tenths without changing the amount that's represented. The same amount is still shaded, but now we have tenths.

So our denominator doubled; we multiplied it by two. We have twice as many pieces. But look at what happened to our numerator. Instead of three pieces, now we have 1, 2, 3, 4, 5, 6 pieces.

It also doubled. It also was multiplied by two, because if we double all of the pieces, then the shaded ones will also double. Each of those pieces also split in two, so now there's twice as many shaded pieces.

So, 3 fifths can be rewritten as 6 tenths.

3 fifths is equal to 6/10. And again, we didn't change the fraction; we didn't change how much was shaded. 3 fifths and 6 tenths represent the same amount. We just changed the denominator and wrote it a different way.

So, 3 fifths can be rewritten in tenths as 6/10.

Now for 7 halves, we again want a denominator of 10. We could draw it out, or we could try to use this pattern we just noticed up here to figure out how to make halves turn into tenths.

To get from fifths to tenths, we had to double or multiply by two. To get from halves to tenths, we'd have to multiply each of our pieces times five.

Times five. Each of our halves would be split into five pieces. So we'd multiply 2 times 5 to get tenths.

Like the pattern showed us up here, if the denominator is multiplied by a number, we multiply the numerator by the same number. Because those shaded pieces would also be split five times.

So we'd multiply our 7 times 5 also. These should match; the numerator and denominator multiplied by the same number.

And 7 times 5 is 35.

So, 35 tenths is equal to 7 halves.

To change these two fractions to have a common denominator of 10, 3 fifths will become 6/10 and 7 halves will become 35/10.