How to Multiply Mixed Numbers by Fractions

TenMarks teaches you how to multiply mixed numbers by fractions.

How to Multiply Mixed Numbers by Fractions Multiply Mixed Numbers by Fractions So, in this problem it states that Jeffrey is building a model that is 1/7 the size of a real sailboat. If the real sailboat measures 17 1/2 feet, how long will the model be when it is built? In this problem, we know the size of the real sailboat. So the size of the real sailboat is 17 1/2 feet long, right? We also know the length of the model. We know that the length of the model is 1/7 of the real – the model is 1/7 of the real sailboat. So, that means 1/7 of the real sailboat would be 1/7 x – because we know “of” means times, right, 1/7 times the real sailboat which is 17 1/2 feet. So now we have our problem 1/7 x 17 1/2. So now we need to go ahead and solve. So to solve, the first step that we’re going to do – give a little bit of room here. So the steps that we’re going to use to solve this is, the first thing is to rename the mixed number as an improper fraction. So we have our mixed number 17 1/2, so we have to take this mixed number and we need to rename it into an improper fraction. To do that, we have our mixed number 17 1/2, and to rename it, we’re going to take the whole number 17 and we’re going to multiply it by 2, by the denominator and then we’re going to add the numerator. So we’re going to take the 17, multiply it by the denominator, times 2, we’re going to add the numerator which is 1. Then, we’re going to put that over our denominator, which is 2. So, when I compute (17 x 2) + 1 is 35/2. So now we have our mixed number into an improper fraction. Our second step is we need to divide the numerator and the denominator by a common factor, if any, and then multiply by a common factor, and then multiply. So sometimes you have a common factor and sometimes you don’t, but you first check. So we have our problem, 1/7 x, now it’s 35/2. So remember we changed our mixed number to the improper fraction, so there it is. Now, let’s check if we have any common factors. Well, the 7 and 35, there is a common factor because 7 x 1 is 7 and 7 x 5 is 35. So here we have a common factor 7, so I can cancel this out. So 7 goes in the 7 one time and 7 goes into 35 five times. So I just divided it by a common factor. So now I have 1 x 5 over 1 x 2, which gives me 1 x 5 is 5 and 1 x 2 is 2, 5/2. So our last step, is we simplify. So I’m going to simplify 5/2. Well, I know that 2 goes into 5 two times, 2 x 2 is 4, 2 goes into 5 two times and there is 1 left over, so it’s 1/2. So when we simplified, we just took this improper fraction and we went ahead and renamed into a mixed number. So the model will then have to be 2 1/2 feet, so how long will the model be? 2 1/2 feet. Alright, some tips to remember. The steps to follow to multiply a mixed number by a fraction, is such. The first step is to rename the mixed number as an improper fraction, so just how we renamed 17 1/2 into our improper fraction 35/2. The second step is then to divide the numerators and the denominators by common factors and then multiply. So in our problem 7 was a common facto or 7 and 35, so we divided 7 by 7 and 35 by 7, and we got 5/2. And then our last step is to simplify. So we had our improper fraction and we simplified it into our mixed number.