How to Calculate Fractions Manually
Fractions represent a part of a whole. The top number is called the Numerator (how many parts you have), and the bottom number is the Denominator (how many parts make up the whole). While multiplying fractions is straightforward, adding and subtracting them requires a few extra steps.
Adding and Subtracting Fractions
You cannot add or subtract fractions unless their bottom numbers (denominators) are exactly the same.
- Step 1: Find the Least Common Multiple (LCM) of the two denominators. This becomes your Common Denominator.
- Step 2: Multiply the top and bottom of each fraction by the number needed to reach that common denominator.
- Step 3: Add or subtract the top numbers (numerators). Never add the bottom numbers!
- Step 4: Simplify the final fraction if possible.
Multiplying Fractions
Multiplying is the easiest fraction operation. You do not need a common denominator.
Example: 1/2 × 3/4 = (1×3) / (2×4) = 3/8
Dividing Fractions (Keep-Change-Flip)
To divide fractions, mathematicians use a rule commonly taught as "Keep, Change, Flip."
- Keep: Leave the first fraction exactly as it is.
- Change: Change the division sign (÷) to a multiplication sign (×).
- Flip: Flip the second fraction upside down (this is called finding the reciprocal).
- Now, simply multiply straight across!
Dealing with Mixed Numbers
If you are calculating Mixed Numbers (like 2 ½), you must always convert them into Improper Fractions first. To do this, multiply the whole number by the denominator, and add the numerator. The denominator stays the same.
Example: 2 ½ = (2 × 2) + 1 = 5/2