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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.

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

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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.

What is the definition of Adding and Subtracting Like Fractions

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).

Exactly the same as you do when multiplying fractions with different denominators. -- Multiply numerators . . . the product is the numeratore of the answer. -- Multiply denominators . . . the product is the denominator of the answer.

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

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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.

It's the same thing as adding or subtracting normal fractions - just make sure both fractions have the same denominators (by either multiplying the denominators or simplifying the fraction - whichever the question needs).

It depends what you are doing with the fractions. If you are multiplying or dividing fraction, the denominators do not need to be the same and the calculation can be carried out immediately. If you are adding or subtracting fractions, the denominators must be the same; if you have different denominators, the fractions must first be changed into equivalent fractions with the same denominator. When the denominators are the same (or have been made the same as equivalent fractions from being different) the calculation can be carried out.

When adding or subtracting fractions their denominators must be the same

You cannot add or subtract fractions with different denominators. If the denominators are different then you need to work with equivalent fractions.

If the denominators are the same, subtract the numerators. If the denominators are different, convert them to equivalent fractions with a common denominator and subtract the numerators.

When adding or subtracting fractions with different denominators and when reducing fractions to their lowest terms

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.

What is the definition of Adding and Subtracting Like Fractions

When adding or subtracting fractions with different denominators their lowest common denominator must be found first by using the LCM of their denominators

A common denominator is needed when adding or subtracting fractions of different denominators.

Because you can't add or subtract fractions that have different denominators. Making them like fractions, by multiplying so the denominators are the same, you can add and/or subtract them.