Adding rational numbers with different denominators requires finding a common denominator. This involves identifying the least common multiple (LCM) of the denominators. Once a common denominator is found, convert each fraction to an equivalent fraction with the common denominator. You can then add or subtract the numerators while keeping the denominator the same. Finally, simplify the resulting fraction if possible.
For example, to add $\frac{1}{3}$ and $\frac{1}{4}$, the LCM of 3 and 4 is 12. Convert $\frac{1}{3}$ to $\frac{4}{12}$ and $\frac{1}{4}$ to $\frac{3}{12}$. Then, add the numerators: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Numerator | A. The number below the fraction bar. |
| 2. Denominator | B. The smallest multiple that two or more numbers share. |
| 3. Least Common Multiple (LCM) | C. Fractions that represent the same value. |
| 4. Equivalent Fractions | D. The number above the fraction bar. |
| 5. Simplify | E. To reduce a fraction to its lowest terms. |
To add fractions with different denominators, you must first find a ________ ________. This is the ________ ________ ________ of the denominators. Once you have a common denominator, you can add the ________. Remember to ________ your answer if possible.
Explain in your own words why it is necessary to have a common denominator when adding or subtracting fractions. Give an example to support your explanation.
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