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### Course: Arithmetic > Unit 9

Lesson 2: Common denominators# Common denominators: 3/5 and 7/2

Learn how to rewrite fractions with different denominators as equivalent fractions with a common denominator. Watch how to visually represent this process and apply it to solve problems.

## Want to join the conversation?

- how can you find common denomenators in really huge fractions like 5/101 and 6/500(34 votes)
- It's the exact same process with finding the greatest common denominator and everything. Except, for the numbers
**101**AND**500**like you mentioned in your example fractions you might find yourself having to*multiply the two numbers together*in order to find the common denominator. So you would multiply:`101*500`

which ends up equaling`50500`

. That would be the common denominator.(59 votes)

- What are common fractions and least common fractions?(30 votes)
- And common fractions are the answers or multiple which is in both numbers(17 votes)

- what if the fraction is a mix number(21 votes)
- You turn it back into a improper fraction. For example, 2 1/3. You multiply the whole number and the denominator, which in this case would be 2 x 3. That equals 6. Then, add that on to the numerator. The numerator is 1, so you add 6+1. That equals 7, so that is the numerator of the improper fraction. The denominator always stays the same, so the improper fraction of 2 1/3 is 7/3.(20 votes)

- No, 3/5+2/6 = 3/5+1/3 = 9/15+5/15 = 14/15.

Have a blessed, wonderful day!(8 votes)

- so 7/2 would be 14/4?

(im asking this half way through the video btw)(9 votes) - what are benchmark fractions?(8 votes)
- A benchmark fraction is a fraction we can easily see in our head like 1/2(3 votes)

- Honestly what's the difference between a factor and a multiple?(6 votes)
- A factor is a number that leaves no remainder behind after it divides the specific number. On the contrary, multiple is a number reached by multiplying a given number by another. While factors of a number are are finite, multiples are infinite.(5 votes)

- What is the l c m of3/5,3/10,9/5(4 votes)
- The LCM of 3/5, 3/10, and 9/5 is 10.

To find the LCM, divide the numbers by a prime that evenly divides at least two of them. Once you can no longer perform any more divisions, multiply your prime factors with the remaining quotients.

5 -- 5 -- 10 (Divided by 5)

1 -- 1 -- 2 (Multiply the prime 5 by 1, 1 and 2 to find the LCM 10.)(3 votes)

- how can yo multiply 6/100 times 10(5 votes)

## Video transcript

- 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.