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Think of it this way: The denominators tell what kind of things are being added, whereas the numerators tell how many things are being added. Examples: (two/apple) + (three/apple) = (two+three)/(apple) = five/apple. ================================================ (two/apple) + (three/plum) is NOT equal to (two+three)/(apple+plum) ================================================ (one)/(pair) + (two)/(pair) = (one+two)/(pair) = (three)/(pair) ================================================= (one)/(pair) + (one)/(individual) + (two)/(individual) = ? ? ? ===> express (one)/(pair) as (two)/(individual), then: (two)/(individual) + (one)/(individual) + (two)/(individual) = (five)/(individual) or (2.5)/(pair)

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Q: Explain why when adding fractions the denominators are not added together?
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What is the definition of adding and subtracting fractions with unlike denominators?

What is the definition of Adding and Subtracting Like Fractions


Fractions Have The Same Denominators?

Not always but they need to have the same denominators when adding or subtracting them.


What way is subracting fractions with unlike denominators like adding fractions with unlike denominators?

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators.


How is multiplying fractions by a whole number is different from adding adding and subtracting fractions with like denominators?

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.


Can you multiply fractions that have a different demonminator?

Yes. When multiplying and dividing fractions your denominators do not have to be the same. The denominators only haveto be the same if you are subtracting or adding them.