7.08 Story problems with adding and subtracting fractions

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Do you remember how to add and subtract fractions which don't have a common denominator?

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When a problem is given as a story or description, we first want to determine what value we are trying to solve for - this will often be in the last sentence. After that, we look back through the rest of the story to find:

• any numbers/values that we know
• a keyword that will tell us what operation to use

If the fractions in the question are given as mixed numbers, it is usually simplest to start by converting them to improper fractions and then do the addition or subtraction. You may wish to review this here.

Once we've found an answer, we can then use estimation to help us check whether the answer is reasonable. For example, let's look at adding the fractions $\frac{3}{5}+\frac{1}{2}$35​+12​. This is "a little more than one half" plus "one half", so we would expect the answer to be "a little more than one whole".

If we tried to solve the problem and got an answer of $\frac{4}{7}$47​, we could then compare this to the estimate and see that it is incorrect straight away - because it is "less than one whole".

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