To work out fraction sums, you need to ensure the fractions have a common denominator, then add the numerators. Here's a step-by-step guide:
1. Find the Lowest Common Multiple (LCM)
The first step is to find the lowest common multiple (LCM) of the denominators. This LCM will become the new, common denominator for both fractions. The LCM is the smallest number that both denominators divide into evenly.
Example: If you want to add 1/4 and 1/6, the denominators are 4 and 6. The LCM of 4 and 6 is 12.
2. Rewrite the Fractions as Equivalent Fractions
Once you have the LCM, rewrite each fraction as an equivalent fraction with the LCM as the new denominator. To do this, determine what number you need to multiply the original denominator by to get the LCM. Then, multiply both the numerator and the denominator of the original fraction by that number.
Example (Continuing from above):
- For 1/4, you need to multiply the denominator (4) by 3 to get 12 (the LCM). So, multiply both the numerator and denominator by 3: (1 3) / (4 3) = 3/12
- For 1/6, you need to multiply the denominator (6) by 2 to get 12 (the LCM). So, multiply both the numerator and denominator by 2: (1 2) / (6 2) = 2/12
3. Add the Numerators
Now that both fractions have the same denominator, you can add the numerators. Keep the denominator the same.
Example (Continuing from above):
3/12 + 2/12 = (3 + 2) / 12 = 5/12
4. Simplify
Finally, simplify the resulting fraction if possible. Look for a common factor that divides both the numerator and the denominator. If there is one, divide both by that factor.
Example: In our example (5/12), 5 and 12 don't have any common factors other than 1, so the fraction is already in its simplest form. Therefore, the final answer is 5/12. However, if you had a fraction like 4/8, you could simplify it to 1/2 by dividing both the numerator and denominator by 4.
In Summary:
- Find the Lowest Common Multiple (LCM) of the denominators.
- Rewrite each fraction as an equivalent fraction with the LCM as the denominator.
- Add the numerators, keeping the denominator the same.
- Simplify the resulting fraction if possible.
