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How to Add & Subtract Fractions with Denominators of 10, 100 & 1,000

Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we will see how to add and subtract fractions with denominators of 10, 100, and 1000. After learning how to do this, we will look at a couple of real life examples and apply the process of solving to these problems.

Steps to Solve

We're going to learn how to add and subtract fraction with denominators 10, 100, and 1000. The good news is that adding and subtracting fractions of these types is the exact same process as adding and subtracting fractions in general. As a matter of fact, the biggest difference is that finding a common denominator is easier, because 10, 100, and 1000 are multiples of each other.

Okay, first let's consider the steps involved when the fractions we are adding and subtracting have the same denominator. When this is the case, we simply keep the denominator as is, add or subtract the numerators as indicated, and then simplify the result if necessary.


addsubfrac1


For instance, if we were adding 4/10 and 3/10, we would keep the denominator as 10, add the numerators, and then simplify if necessary.


addsubfrac2


We see that 4/10 + 3/10 = 7/10. That's pretty easy, huh? Well, let's take a look at what we do when the denominators are not the same. When this is the case, we follow these steps to add or subtract the fractions.

  1. Find a common denominator by finding the smallest number both denominators divide into evenly.
  2. Manipulate both fractions so they have that common denominator.
  3. Now the fractions have common denominators, so you can add or subtract the numerators as indicated and simplify if necessary.

Now, as we said, when the denominators are 10, 100, or 1000, finding a common denominator in step one is actually pretty easy. Let's think about it. If the denominators are 10 and 100, then the smallest number both numbers divide into evenly is 100, so the common denominator would be 100. Similarly, we have the following.

  • Denominators 10 and 100 have common denominator 100.
  • Denominators 10 and 1000 have common denominator 1000.
  • Denominators 100 and 1000 have common denominator 1000.

Manipulating the fractions to get the common denominator isn't too hard either when dealing with these denominators. We simply multiply both the numerator and denominator by the number we need to multiply the denominator by to get the common denominator. For instance, suppose we are adding a / 10 + b / 100. We know the common denominator is 100. To make 10 into 100, we multiply by 10. Therefore, we manipulate a / 10 by multiplying the numerator and denominator by 10 to get 10a / 100. We don't have to do anything to b / 100, because we already have the common denominator of 100. This turns the problem into

(10a / 100) + (b / 100)

Well, that's easy! We simply add the numerators to get (10a + b) / 100.

In short, when we are adding and subtracting fractions with denominators 10, 100, and 1000, and the denominators are different, there are three possibilities.

1. The denominators are 10 and 100.


addsubfrac3


2. The denominators are 10 and 1000.


addsubfrac4


3. The denominators are 100 and 1000.


addsubfrac5


Solution

When adding or subtracting fractions with denominators 10, 100, and 1000, there are two cases. The first is when the fractions have a common denominator.


addsubfrac1


The second is when the fractions have different denominators. When this is the case, there are three possibilities.


addsubfrac6


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