Common denominators: 3/5 and 7/2

- Rewrite each fraction with a denominator of 10. So we have two fractions, three fifths and seven halves and we wanna take their denominators of five and two and change them to be a common denominator of 10. Lets start with three fifths and we can look at this visually. Here we can use this rectangle to represent a whole, one whole. To show three fifths of that whole, we're gonna need to divide it into fifths or five equal pieces. Lets do that. Try to make these as equal as possible. We have three pieces, and then finally, there we go. So, 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. 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. We can do that here. Now, instead of fifths, or five equal size pieces, we have tenths. We have one, two, three, four, five, six, seven, eight, nine, ten. 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. Our denominator doubled. We multiplied it be two, we have twice as many pieces. But look at what happened to our numerator, instead of three pieces, now we have one, two, three, four, five, six pieces. It also doubled. It also was multiplied by two, because if we double all of the pieces, well 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, three fifths can be rewritten as six tenths. Three fifths is equal to six tenths, and again, we didn't change the fraction. We didn't change how much was shaded. Three fifths and six tenths represented the same amount. We just changed the denominator and wrote it a different way. So, three fifths can be rewritten in tenths as six tenths. Now, for seven halves, we again want a denominator of 10. So, we can 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. Each of our halves would be split into five pieces. So, we multiply two times five 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. Those shaded pieces would also be split five times. We multiply our seven times five also. You should match the numerator and denominator are multiplied by the same number. Seven times five is 35. So 35 tenths is equal to seven halves. To change these two fractions to have a common denominator of 10, three fifths will become six tenths, and seven halves will become 35 tenths.