How to Add Fractions

Fractions! The sound of the name sends chills up your spine. Nothing is more sinister or devious, the bane of every school child. People have awoken in the middle of the night screaming in terror, reliving their fifth grade teacher calling on them to add… FRACTIONS!

If you were as traumatized as I was with this mathematical terror, have no fear! I will show you the quick and easy steps on how to add fractions. In simple and easy steps, so you can face the fractural fear and put it back in the closet along with the monster under your bed.


Background Information

There are a few key terms you need to know, love, and understand to add fractions.

  • Numerator: When looking at a fraction 12/15 the numerator is the top number – 12.
  • Denominator: When looking at a fraction 12/15 the denominator is the bottom number – 15.
  • LCD: Lowest Common Denominator, this is important. In order to add fractions in the easiest possible manner, all of the fractions that you are adding need to have the SAME denominator. To find the LCD of 2/3 and 3/6, double the first fraction’s denominator (3 — to 6, which coincidentally is the same denominator as in the second fraction). REMEMBER, anytime you change the denominator, you MUST change the numerator. So, considering you doubled the denominator, double the numerator as well. 4/6.


Adding Two Fractions

  1. Let’s take our 2 fractions: 2/3 and 3/6. On paper it will look like 2/3 + 3/6. We need to find the LCD.
  2. To find the LCD, multiply both sides of 2/3 by 2.
  3. 2*2=4 and 2*3=6. This makes the fraction 4/6.
  4. The new problem now is 4/6 + 3/6.
  5. Since 6 is the LCD, we don’t need to add that, just the top portion.
  6. 4+3=7.
  7. Answer will be 7/6! We can convert this to a whole number. 6/6 is 1. The remainder portion goes into the fraction: 1 1/6!

Adding Three or More Fractions

  1. 3/4+5/8+9/15.
  2. What is the LCD? 4 and 8 cannot go into 15! We need to find a common denominator for all three numbers!
  3. The best way to find the LCD for all 3 numbers is simple. Look at the 2 smaller denominators. 4 and 8.
  4. 4*2 is 8, so change 3/4 into 6/8.
  5. Now we have 4/8+5/8+9/15.
  6. Add 4/8+5/8.
  7. Now we have 9/8+9/15.
  8. Find the LCD between 8 and 15. To do this, multiply 8 and 15. That is 120.
  9. Since we multiplied the 2 denominators, we need to adjust the numerators.
  10. 9*15 (for the 9/8 fraction) and 9*8 (for the 9/15 fraction).
  11. The resulting fraction will be 135/120 + 72/120 = 207/120.
  12. Now make it a whole number. 1 87/120.
  13. We can reduce the fraction some as well. 87 and 120 can be divided by 3.
  14. The final answer is 1 29/40!

Now you know how to add fractions! I hope this helps the nightmares stop!

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