6.2.3 Adding and Subtracting Fractions

Activity symbol Activity: Adding and Subtracting Fractions

Calculator symbol The calculator can be accessed on the left-hand side bar under the Toolkit.

In your math notebook, work out the following by hand. Then, check your results using the calculator.

(a) five divided by 18 plus seven divided by 18

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Discussion

Are both fractions out of the same number of parts? Can you relate this to the chocolate bar example?

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Answer

(a) Both the given fractions are eighteenths, so they can be added together directly: equation sequence five divided by 18 plus seven divided by 18 equals five plus seven divided by 18 equals 12 divided by 18 equals two divided by three. Don’t forget to reduce 12 divided by 18 to two divided by three, by dividing the numerator (top) and the denominator (bottom) by 6.

(b) five divided by six plus three divided by seven

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Discussion

Can you find equivalent fractions for each given fraction that all share the same denominator? What number can be divided by both 6 and 7?

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Answer

(b) This sum involves sixths and sevenths, which are different types of fraction. However, you can change both into forty-seconds, since both 6 and 7 evenly divide into 42. So, equation left hand side five divided by six equals right hand side 35 divided by 42 and equation left hand side three divided by seven equals right hand side 18 divided by 42. Thus, the sum is equation sequence five divided by six plus three divided by seven equals 35 divided by 42 plus 18 divided by 42 equals 53 divided by 42 equals.

(c)

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Discussion

Try adding the whole numbers first, then add the fractional parts together.

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Answer

(c) Here, you can add the whole numbers first, two plus three equals five, and then add the fractions, but first you must convert each fraction into twenty-fourths. So, the sum is equation sequence sum with, 3 , summands five plus two divided by three plus one divided by eight equals sum with, 3 , summands five plus 16 divided by 24 plus three divided by 24 equals.

(d) 15 divided by 16 minus five divided by 16

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Discussion

Imagine that you have an extra large pizza with 16 slices. After you eat one slice, what fraction of the pizza would be left? How much would be left after you eat 5 more slices?

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Answer

(d) Both the fractions are sixteenths. You can imagine subtracting five slices of pizza from 15 slices will leave 10 slices out of the original 16: equation sequence 15 divided by 16 minus five divided by 16 equals 10 divided by 16 equals five divided by eight.

Think of our paper pizzas again:

(e) 19 divided by 24 minus three divided by eight

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Discussion

This problem is very similar to the chocolate bar example. Try drawing a picture to help.

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Answer

(e) This calculation is similar to the chocolate bar example. The problem is that we need both fractions to be out of the same number of parts—remember the 24 pieces of chocolate? So, to solve it the same way, the calculation becomes equation sequence 19 divided by 24 minus three divided by eight equals 19 divided by 24 minus nine divided by 24 equals 10 divided by 24 equals five divided by 12. Don’t forget to reduce your answer!

6.2.2 Mixed Numbers on the Calculator

6.2.4 Adding and Subtracting Fractions Challenge