Fraction questions can look tricky at first, but they become easier with practice and know-how. Once you understand the fundamentals of what fractions are, you'll be breezing through fraction problems like a knife through butter. You will have to start with Step 1 and learn how to perform basic addition and subtraction, and then move on to more complex calculations.
Method 1 of 4: Adding and Subtracting Fractions
1Find the lowest common denominator (bottom number). For both adding and subtracting fractions, you'll start with the same process. Figure out the lowest common fraction that both denominators can go into.
- For example, if you have 1/4 and 1/6, the lowest common denominator is 12. (4x3=12, 6x2=12)
2Multiply fractions to match the lowest common denominator. Remember that when you're doing this, you're not actually changing the number, just the terms in which it's expressed. Think of it like a pizza - 1/2 of a pizza and 2/4 of a pizza are the same amount.
- Figure out how many times your current denominator goes into the lowest common denominator. For 1/4, 4 multiplied by 3 is 12. For 1/6, 6 multiplied by 2 is 12.
- Multiply the fraction's numerator and denominator by that number. For 1/4, you would multiply both 1 and 4 by 3, coming up with 3/12. 1/6 multiplied by 2 becomes 2/12. Now your problem looks like 3/12 + 2/12 or 3/12 - 2/12.
3Add or subtract the two numerators (top number) but NOT the denominators. The reason is because you are trying to say how many of that type of fraction you have, total. If you added the denominators as well, you would be changing what type of fractions they are.
- For 3/12 + 2/12, your final answer is 5/12. For 3/12 - 2/12, it's 1/12
Method 2 of 4: Converting Mixed Numbers into Improper Fractions
1Convert mixed numbers into improper fractions. Improper fractions are those whose numerators are larger than their denominators. (For example, 17/5.) If you are multiplying and dividing, you must convert mixed numbers into improper fractions before you begin the rest of your calculations.
- Say you have the mixed number 3 2/5 (three and two-fifths).
2Take the whole (non-fraction) number and multiply it by the denominator.
- In our example, that means 3 x 5, which is 15.
3Add that answer to the numerator.
- For our example, we add 15 + 2 to get 17
4Put that amount over the original denominator and you will have an improper fraction.
- In our case, we get 17/5.
Method 3 of 4: Multiplying Fractions
1Make sure you're working with two fractions. These instructions work only if you have two fractions. If you have any mixed numbers involved, convert them to improper fractions first..
2Multiply numerator x numerator, then multiply denominator x denominator.
- So say I had 1/2 x 3/4, I would multiply 1 x 3 and 2 x 4. The answer is 3/8.
Method 4 of 4: Dividing Fractions
1Make sure you're working with two fractions. Again, this process will work ONLY if you have already converted any mixed numbers into improper fractions.
2Flip the second fraction upside down.
3Change the division sign into a multiplication sign.
- If you started with 8/15 ÷ 3/4 then it would become 8/15 x 4/3
4Multiply top x top and bottom x bottom.
- 8 x 4 is 32 and 15 x 3 is 45, so the final answer is 32/45.
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- Basic skills in the four operations (Multiplication, Division, Addition, and Subtraction) will help the process go quickly and easily.
- To take the reciprocal of a whole number, just put a 1 over it. For example, 5 becomes 1/5.
- You can multiply and divide mixed numbers without converting to improper fractions first. But to do so involves using the distributive property in a potentially intense and complicated way, so it's usually better to go the improper fractions route.
- Another way to say "flip the fraction over" is to say "find the reciprocal. You're still just reversing the numerator and denominator. Ex. 2/4 would be 4/2
- Convert mixed numbers into improper fractions before you begin.
- Check with your teacher to see if you must convert your improper fraction answers into mixed numbers.
- For example, 3 1/4 instead of 13/4.
- Check with your teacher regarding whether or not you must have your answers in lowest terms
- For example, 2/5 is in the lowest term, but 16/40 is not.
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