First ask, “What is the operation?” Identifying the operation will determine whether or not we need a common denominator. Remember, we need a common denominator to add or subtract, but not to multiply or divide.
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| What is the operation? The operation is subtraction. |
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| Do the fractions have a common denominator? No. |
65x−103 |
| Find the LCD of 6 and 10 |
The LCD is 30. |
| 6=2⋅3___________10=2⋅5LCD=2⋅3⋅5LCD=30 |
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| Rewrite each fraction as an equivalent fraction with the LCD. |
6⋅55x⋅5−10⋅33⋅3 |
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3025x−309 |
| Subtract the numerators and place the difference over the common denominators. |
3025x−9 |
| Simplify, if possible. There are no common factors. The fraction is simplified. |
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| What is the operation? Multiplication. |
65x⋅103 |
| To multiply fractions, multiply the numerators and multiply the denominators. |
6⋅105x⋅3 |
| Rewrite, showing common factors. Remove common factors. |
2⋅3⋅2⋅55x⋅3 |
| Simplify. |
4x |
| Notice, we needed an LCD to add 65x−103, but not to multiply 65x⋅103. |
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