How to Multiply a Fraction by a Mixed Number Using the Area Model


Hi, I'm Rachel, and today we're going to be going over how to multiply a fraction by a mixed number using the area model. So let's say our fraction is three over five, and we want to multiply it by a mixed number, so let's say that mixed number is 10 and we'll do two over seven. Okay? So, first let's convert this mixed number into a fraction. Now, when you're converting mixed numbers into a fraction, always remember to multiply by the denominator, and then add the numerator. So what does that mean? That means we multiply 10 times seven to get 70, and then we add the numerator, 70 plus two is 72. Then we put it all over the denominator. We keep the denominator the same. So we've got 72, that's 10 times seven plus two, all over seven, the denominator stays the same. Now we have three times five. Okay, it looks like we may not, we might not be able to reduce anything, so we're just going to have to multiply it out. Now 72 times three, I'll do it up here so you guys see what I'm doing, two times three is six, seven times three is 21, so that's 216 all over five times seven, which is 35, and there is our improper fraction. If you want to turn it into a mixed number, you can divide 35 into 216 and get your answer from there, but this is usually an acceptable answer as is. I'm Rachel, and thank you for learning with me today.

Rachel Kaplove has worked as a professional private tutor since 2005. Specializing in Math and Science, she tutors students from the second grade level to advanced high school honors levels.