You have used models and algorithms to add and subtract decimals, paying special attention to the regrouping that was necessary to perform the computations. Now, you will extend the idea of regrouping to models and procedures used to add and subtract fractions, including mixed numbers.

Consider the following problem.

Use the animation below to see how Marley used fraction strips to solve this problem. Click the Next arrow to see Marley’s next steps.

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Pause and Reflect

How is regrouping when subtracting mixed numbers similar to regrouping when subtracting decimals?

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Check Your Answer

With decimals, you regroup to increase the place value so that you can subtract from the minuend. With mixed numbers, you regroup from the whole number to increase the numerator of the fractional part so that you can subtract from the minuend.

When adding decimals, you regroup when the sum of the two digits in a place value that is greater than 10. When would you need to regroup as you add mixed numbers?

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You would need to regroup when the value of the fractional part of the sum is greater than 1.

Practice

The table below shows the number of pounds of aluminum cans that Brad’s class collected each day last week. Use this information to answer questions 1 – 3.

1. How many pounds of aluminum cans did Brad’s class collect on Monday and Tuesday?

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   To solve this problem, you are combining the weight of cans collected on two days. What operation would you use when combining two quantities?
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2. How many more pounds of aluminum cans did Brad’s class collect on Wednesday than on Tuesday?

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   What operation does the phrase “how many more” suggest that you need to use?
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3. How many more pounds of aluminum cans did Brad’s class collect on Thursday than on Friday?

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   What operation does the phrase “how many more” suggest that you need to use?
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4. A rainbow trout is swimming in McKittrick Canyon in the Guadalupe Mountains 27 over 8 7 8 feet below the water level. The fish swims, and then jumps upward for a total of 31 over 2 1 2 feet. How far above the water level did the fish jump?

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   What sign would you use to represent 27 over 8 7 8 feet below the water level?
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