How to Multiply Fractions by Integers

Learn about multiplication of fractions and integers. We’ll multiply fractions with integers. We’re given two examples. The first one is 6×2/3. Now, 6 is the integer, 2/3 is the fraction. It’s fairly simple to do. If we want to multiply 6 with 2/3, this is the same as we multiply the numerators, 6×2 and we multiply the denominator which is 1, 1×3 is 3 which gives me 12/3. Now, 12÷3 we know is 4, so the answer is 4, relatively simple.

Let’s try the second one which is we are going to multiply -2 with 3 1/5. Before we can multiply this particular number, first we need to convert the mixed fraction into a regular improper fraction. We know the way we do that is we take the whole number, multiply it by the denominator, add to this the numerator and we place the denominator below. So, whole number in this case is 3 multiplied by the denominator which is 5, add to this the numerator which is 1 and the denominator comes back which is 5, so 15+1=16/5. So, this part is 16/5. So, rewriting the equation, this is 3 1/5 becomes this. So, rewriting the expression, it’s -2×16/5. Now that we have this, we know how to do this which is -2×16 and the denominator is 1×5 which is 2×16, so this becomes -32 and the denominator is 5 which is the answer.

Quickly recapping what we’ve learned. If we’re multiplying an integer with a fraction, we multiply the numerators together and the denominator of integer is one. So, 6×2/3 gives us 12/3 which is 4. If we are multiplying an integer with a mixed number, first we have got to convert the mixed number into an improper fraction and we do that using this method, so if we’re multiplying -2 with 16/5, numerator times numerator, denominator times denominator gives us the answer.