Content

• Steps
• Advice

Have you ever come across such confusing problems? Fractions are a very difficult form of math, especially when you are just starting out. The problem can become even more complicated when the terms have a different denominator (number below). However, adding up fractions with different denominators is also relatively easy, so don't worry.

Steps

1. 

   Write down the original fractions. Restate the expression so that the terms are closer together and easier to see. You can see the examples below.
   • Example 1: 1/2 + 1/4
   • Example 2: 1/3 + 3/4
   • Example 3: 6/5 + 4/3

2. 

   
   
   Find the common denominator of two fractions. Find the common denominator of two fractions by "multiplying" the denominator of the two terms together.
   • Example 1: 2 x 4 = 8. Both fractions will have the same denominator of 8.
   • Example 2: 3 x 4 = 12. Both fractions will have the same denominator of 12.
   • Example 3: 5 x 3 = 15. Both fractions will have the same denominator of 15.

3. 

   
   
   Multiply two integers in the fraction first with the denominator of the second fraction. We are not altering the value of the fraction but only the way it is present fraction. Its value remains unchanged.
   • Example 1: 1/2 x 4/4 = 4/8.
   • Example 2: 1/3 x 4/4 = 4/12.
   • Example 3: 6/5 x 3/3 = 18/15.

4. 

   
   
   Multiply two integers in the fraction Monday with the denominator of the first fraction. Again, we are not altering the value of the fraction but only the way present fraction. Its value remains unchanged.
   • Example 1: 1/4 x 2/2 = 2/8.
   • Example 2: 3/4 x 3/3 = 9/12.
   • Example 3: 4/3 x 5/5 = 20/15.

5. 

   Restate the math with new fractions. We'll start adding fractions in the next step! In this step, you need to multiply each fraction by an integer 1.
   • Example 1: Instead of writing 1/2 + 1/4, we have 4/8 + 2/8
   • Example 2: Instead of writing 1/3 + 3/4, we get 4/12 + 9/12
   • Example 3: Instead of writing 6/5 + 4/3, we have 18/15 + 20/15

6. 

   Add the numerators together. The numerator is the number on the top of the fraction.
   • Example 1: 4 + 2 = 6. So the new numerator is 6.
   • Example 2: 4 + 9 = 13. So the new numerator is 13.
   • Example 3: 18 + 20 = 38. So the new numerator is 38.

7. 

   Bring the denominator you found in step 2 underneath the new numerator.
   • Example 1: 8 will be the new denominator of the fraction.
   • Example 2: 12 will be the new denominator of the fraction.
   • Example 3: 15 will be the new denominator of the fraction.

8. 

   Combine the new numerator and the new denominator.
   • Example 1: 6/8 is the answer to the problem 1/2 + 1/4 =?
   • Example 2: 13/12 is the answer to the problem 1/3 + 3/4 =?
   • Example 3: 38/15 is the answer to the problem 6/5 + 4/3 =?

9. 

   Return the fraction to its simplified and reduced form. To minimize a fraction by dividing both the numerator and the denominator of the fraction by their greatest common divisor.
   • Example 1: 6/8 can be simplified to 3/4.
   • Example 2: December 13 can be reduced to 1 1/12.
   • Example 3: 38/15 can be shortened to 2 8/15.
   advertisement

Advice

• You must multiply all the numbers in the fraction by the same number.
• Don't forget to shorten the fraction.
• Reduce the fraction to its simplified form by considering whether the above number is divisible by the lower number.
• Unless the request is made, you should always reduce the fraction to a simplified form in order to make it easier to calculate.
• To add up fractions their denominator "must" be the same, which is why the denominator is called "generic". Trying to solve a problem without converting terms to fractions with the same denominator is not a quick solution, but only leaves you with more steps.
• You can find the smallest common multiple to determine the lowest common denominator of fractions.