# 6.2.3 Adding and Subtracting Fractions

## Activity: Adding and Subtracting Fractions

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)

### Discussion

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

### Answer

(a) Both the given fractions are eighteenths, so they can be added together directly: . Don’t forget to reduce to , by dividing the numerator (top) and the denominator (bottom) by 6.

(b)

### 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?

### 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, and . Thus, the sum is .

(c)

### Discussion

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

### Answer

(c) Here, you can add the whole numbers first, , and then add the fractions, but first you must convert each fraction into twenty-fourths. So, the sum is .

(d)

### 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?

### 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: .

Think of our paper pizzas again:

(e)

### Discussion

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

### 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 . Don’t forget to reduce your answer!

6.2.2 Mixed Numbers on the Calculator