Fraction Multiplying and Dividing

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Student: I understand how to add and subtract fractions, but multiplying and dividing seems different. How is it done?

Mentor: We'll start with multiplying. It is a little bit more straight-forward. Simply multiply the numerator and multiply the denominator.

To solve 2/3 x 3/4

multiply the numerators 2 and 3 (which will be 6)

and then the denominators 3 and 4 (which will be 12)

so 2/3 x 3/4 = 6/12

Student: And I already learned that I can reduce that fraction to 1/2 by dividing both numbers by 6. How does it work when I divide numbers?

Mentor: Let's try it with the problem 2/7 divided by 2/5. There are several ways to look at this, but one way is to invert the fraction doing the dividing, and then multiply the numbers across. Invert means to turn upside down, so the steps of the problem look like this:

  • Step 1: 2/7 divided by 2/5
  • Step 2: inverting 2/5 makes it 2/7 x 5/2
  • Step 3: multiplying makes it 10/14
  • Step 4: reducing makes it 5/7

Student: OK, so 2/7 divided by 2/5 equals 5/7.

Mentor: That's right.

Now try this one: 1/3 divided by 6/7.

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