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# 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.

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