How do you find a common denominator for adding fractions?

How do you find a common denominator for adding fractions?

• A. Add the numerators.
• B. Subtract the denominators.
• C. Multiply the denominators together.
• D. Take the reciprocal of one fraction.

Answer: (C)

When adding fractions, you need a common denominator so the parts share the same base. A straightforward way is to multiply the two denominators to create that common denominator, then adjust the numerators by the same factors. For example, with 1/3 and 1/4, multiply the denominators to get 12. Convert each fraction to twelfths: 1/3 becomes 4/12 and 1/4 becomes 3/12. Add them to get 7/12. This demonstrates why multiplying the denominators provides a valid common denominator. Note that you can’t just add numerators when the bottoms are different, subtracting denominators isn’t meaningful here, and taking a reciprocal doesn’t help with addition. (There are sometimes smaller common denominators by using the least common multiple, but multiplying the denominators is a clear way to obtain a common denominator.)

When adding fractions, you need a common denominator so the parts share the same base. A straightforward way is to multiply the two denominators to create that common denominator, then adjust the numerators by the same factors. For example, with 1/3 and 1/4, multiply the denominators to get 12. Convert each fraction to twelfths: 1/3 becomes 4/12 and 1/4 becomes 3/12. Add them to get 7/12. This demonstrates why multiplying the denominators provides a valid common denominator. Note that you can’t just add numerators when the bottoms are different, subtracting denominators isn’t meaningful here, and taking a reciprocal doesn’t help with addition. (There are sometimes smaller common denominators by using the least common multiple, but multiplying the denominators is a clear way to obtain a common denominator.)