In other words, 1/5 and 2/5 does not need to be written as 1/5 + 2/5 = ? It can be written as 1+2/5 = ?. The denominator is the same, so it can be written only once. Both numerators then go on top.

Whether you have it written 1/5 + 2/5 or 1+2/5, you answer should be the same: 3! After all, 1 + 2 = 3.

So, using the same example, our denominator is 5. That’s it! That’s the bottom number of our fraction. That’s half the answer already!

What was your numerator? 3. The denominator? 5. Therefore, 1/5 + 2/5, or 1+2/5, equals 3/5.

Write out the multiples. The multiples of 3 are 3, 6, 9, 12, 15, 18. . . and so on. The multiples of 4? 4, 8, 12, 16, 20, etc. What’s the lowest number seen in both of the sets? 12! That’s your lowest common denominator, or LCD. Prime factorization. If you know what factors are, you can do prime factorization. That’s finding out what numbers can make your denominators. For 3, the factors are 3 and 1. For 4, the factors are 2 and 2. Then, you multiply them together. 3 x 2 x 2 = 12. Your LCD! Multiply the numbers together for small numbers. In some cases, like this one, you could just multiply the numbers together – 3 x 4 = 12. However, if your denominators are big, don’t do this! You don’t want to multiply 56 x 44 and have to work with 2,464 as your answer!

So our 2/3 turns into 2/3 x 4 and 3/4 turns into 3/4 x 3. That means we now have 2/12 and 3/12. But we’re not done yet! You’ll notice that the denominators, in this instance, are multiplied by each other. This works in this situation, but not all situations. Sometimes, instead of multiplying the two denominators together, you can multiply both denominators by different numbers to get one small number. And then in other cases, sometimes you only have to multiply one denominator to make it equal to the denominator of the other fraction in the equation.

We had 2/3x4 and 3/4x3 as our first step – to add the second step, it’s really 2 x 4/3 x 4 and 3 x 3/4 x 3. That means our new numbers are 8/12 and 9/12. Perfect!

For this example, (8+9)/12 = 17/12. To turn this into a mixed fraction, simply subtract the denominator from the numerator and see what’s left over. In this case, 17/12 = 1 5/12

For the example for this section, let’s work with 13/12 and 17/8.

Let’s figure out the multiples of our example, 12 and 8. What’s the smallest number these two go into? 24. 8, 16, 24 and 12, 24 – bingo!

So 13 x 2/12 x 2 = 26/24. And 17 x 3/8 x 3 = 51/24. We’re well on our way to solving the problem!

26/24 + 51/24 = 77/24. There’s your one fraction! That top number is mighty big, though. . . .

For this example, 24 goes into 77 three times. That is, 24 x 3 = 72. But there’s 5 leftover! So what’s your final answer? 3 5/24. That’s it!

e. g. ½ + ¾ + ⅝

Multiply ¹ to the denominator/s of the other fractions. Multiply 1 to 4 and 8. [32]

Multiply 3 with 2 and 8. [48] Lastly, multiply 5 with 4 and 2. [40]

32+48+40=120

2×4×8=64

120/64 = 1 56/64 = 1 ⅞