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Q: When adding fractions with the same denominator why do you only add numerators?

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When adding like fractions, only the numerators are added.

No only when adding or subtracting fractions a common denominator is needed

Adding and subtracting fractions can ONLY be done if the denominators are the same; then the calculation is done by adding or subtracting the numerators. Multiplying (and dividing) fractions does not require the denominators to be the same. To divide by a fraction the divisor is inverted (the original numerator becomes the new denominator and the original denominator becomes the new numerator) and then the fractions are multiplied. Multiplying fractions is achieved by multiplying the numerators together AND multiplying the denominators together. A whole number is the same as a fraction with the whole number as the numerator and a denominator of 1, so when multiplying by a whole number the denominator is multiplied by 1 (leaving it the same) and the is multiplication is effectively just multiplying the numerator by the whole number.

Only fractions with the same denominator can be added directly. Addition of such fractions can be achieved by adding their numerators to form the numerator of the sum, with the common denominator of the added fractions constituting the denominator of the sum. In this instance, 2/3 = 6/9, and 4/9 + 6/9 = 10/9.

It stays the same. Only the numerators change.

No, You only need a common denominator when adding or subtracting fractions.

No. To multiple fractions multiple the numerators together and multiply the denominators together and simplify (by dividing both numerator and denominator of the result by common factors until the only common factor is 1). The denominators only need to be the same when adding or subtracting fractions.

Unless you are using a calculator that adds them for you, it is much harder to add fractions with uncommon denominators. Having the same denominator allows you to only have to add the numerators for your answer.

Fractions can only be added or subtracted if the denominators are the same. If the denominators are different, then the fractions need to be made into equivalent fractions with the same denominator. The new denominator can be found simply by multiplying the denominators together, but this can lead to some large fractions with which to work. A better new denominator is the lowest common multiple of (all the) denominators. (Once the new denominator is found, the fractions' new numerators are found by multiplying their current numerator by the new denominator divided by their current denominator to make their equivalent fractions with the new denominator.) Once all the fractions are converted into equivalent fractions with the new denominator then the fractions can be added or subtracted, with the result being simplified (if possible).

No, you only need a common denominator when adding or subtracting fractions.

No. Only if you're adding or subtracting and then only if the denominators are different.

The instructions are quite simple, but this is for similar denominators: 1. Line them up. 2. Add the numerators. 3. Put your sum over the same denominator as the other fractions. 4. *ONLY IF THE NUMERATOR IS LARGER THEN THE DENOMINATOR* Turn the improper fraction into a mixed number. However, if the problem states it wants it as an improper fraction, which normally it won't, leave it as it is.

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