Multiplying Fractions and Mixed Numbers

Student: I remember that a fraction is a number that is less than one!

Mentor: That's right, but -1 is less than one. Is it a fraction?

Student: No, so a fraction is between 0 and 1. And it has a numerator and a denominator, to tell you how many parts of the whole it represents.

Mentor: That's very good. Can anyone think of an example of this?

Student: 4/7, where 1 has been divided into 7 parts, and you have 4 of them.

Mentor: Great example! Now does anyone remember what a mixed number is?

Student: I think it is a number that has both a whole number and a fraction in it. Like one and five eighths, written 1 5/8.

Mentor: You know this well!

Mentor: Now do you recall how to multiply fractions?

Student: It's like multiplying regular numbers only you have to multiply both numerators to get the numerator of the answer. Then you multiply both denominators to get the denominator of the answer.

Mentor: Good, let's try an example. What is 3/4 * 5/7?

Student: 3 * 5 = 15, and 4 * 7 = 28. 15/28 can't be reduced, so that's our answer!

Mentor: Great job! Now who can tell me how to multiply mixed numbers?

Student: Its the same as multiplying with fractions, only you have to make the mixed number an improper fraction first.

Mentor: That's a great way to do it! Let's try an example: 2/3 * 1 3/4 = what?

Student: 1 3/4 = 7/4, so we just need to solve 2/3 * 7/4. 2 * 7 = 14, and 3 * 4 = 12. 14/12 can be reduced to 7/6. Then we can change it back to a mixed number to get the answer: 1 1/6!

Mentor: Exactly. Can you think of another way to do it?

Student: Could you multiply the integer by the number, then the fractional part and add the two answers together?

Mentor: Again, another excellent method! Let's try it out. What is 2/3 * 1 3/4?

Student: 1 * 2/3 = 2/3. 2/3 * 3/4 is... 2 * 3 = 6, and 3 * 4 = 12, so that's 6/12. 2/3 is the same as 4/6, and 6/12 is the same as 3/6. 4/6 + 3/6 = 7/6, which is the same as 1 1/6. I know I did it right because I got the same answer!

Mentor: Exactly. That's a good strategy to check your work. You can use either of these methods depending on which is simplest at the time.