5.08 Story problems with adding and subtracting fractions

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Do you remember how to add and subtract fractions?

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Sometimes a problem is given as a story or description, and might have the fractions given using words or a mix of words and numbers.

When faced with a story problem, start by determining what value we are trying to solve for - this will often be in the last sentence. After that, 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

Let's look at an example, and highlight the key terms: "Glen is walking along a hiking trail, and passes a campsite $5$5 sixths of a mile along. Later he reaches another campsite, a further $8$8 sixths of a mile along the trail. How far has Glen traveled in total when he reaches the second campsite?"

The keywords "in total" tells us that we want to find a sum of the two fractions.

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{4}{6}+\frac{3}{6}$46​+36​. 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{7}{12}$712​, 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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Question 1