Topic 7 Adding and Subtracting Fractions and Mixed Numbers

Adding Fractions

100

5/11 + 4/11

9/11

200

6/7 + 1/2

LCD=14, 12/14 + 7/14= 19/14 simplified= 1 5/14

300

3/8 + 5/6

1 and 5/24

400

3/12 + 4/5

1 and 1/20

500

John walked 3/4 of a mile to the store. Then he walked 3/8 of a mile to his grandmother's house. How far did John walk in all?

1 and 1/8 miles

Subtracting Fractions

100

11/15 - 6/15=

5/15 simplify divide by 5= 1/3

200

5/6 - 1/6=

4/6 simplify divide by 2= 2/3

300

3/4 - 1/4=

2/4 simplified = 1/2

400

Joel made some muffins. He gave 1/4 of the muffins to the neighbor and took 3/8 of the muffins to school. What fraction of the muffins is left?

3/8

500

Carl has 3 lengths of cable. The first is 5/6 yard long, the second is 1/4 yard long, and the third is 2/3 yard long. If he uses 1 yard of cable, how much will he have left over?

3/4 of a yard

Adding Mixed Numbers

100

2 3/4 + 4 1/4=

6 4/4= simplified = 7

200

5 1/8 + 6 3/8=

11 4/8 simplify divide by 4= 11 1/2

300

4 1/3 + 6 4/5=

LCD: 15= 4 5/15 + 6 12/15= 8 17/15= 11 2/15

400

5 5/12 + 2 1/6=

LCD: 12= 5 5/12 + 2 2/12= 7 7/12

500

9 3/5 + 4 7/15=

LCD: 15 = 9 9/15 + 4 7/15= 13 16/15= 14 1/15

Subtracting Mixed Number

100

10 3/4 - 8 1/4=

2 2/4 simplify divide by 2= 2 1/2

200

3 20/21 - 2 6/21=

1 14/21 simplify divide by 7= 1 2/3

300

A standard bowling lane is 41 1/2 inches wide. The width of a bowling lane and one gutter is 50 13/16 inches. What is the width of the gutter?

LCD: 16: 50 13/16 - 41 8/16= 9 5/16inches

400

5 1/8 - 2 3/4=

LCD: 8= 5 1/8 - 2 6/8= 41/8 - 22/8= 19/8 simplify= 2 3/8

500

20 1/4 - 19 1/2=

LCD: 4= 20 1/4 - 19 2/4= 81/4 - 78/4 = 3/4

Estimatiing and LCD

100

Find the LCD of 9, 12, 24.

9= 9, 18, 27, 36, 45, 54, 63, 72, 81 12: 12, 24, 36, 48, 60, 72 24: 24, 48, 72, 96,120 LCD: 72

200

What is the LCD of 1/3 and 3/5?

3: 3, 6, 9, 12, 15, 20 5: 5, 10, 15, 20, 25 LCD: 15

300

What is the least common denominator used to add 7/10 + 7/12?

10: 10, 20, 30, 40, 50, 60, 70 12: 12, 24, 36, 48, 60 LCD: 60

400

What is 5 15/32 rounded to the nearest whole number? (estimate)

5, half of 32 is 16. Therefore the numerator is larger than the denominator so you leave the number the same

500

Estimate 6 1/2 - 4 2/3=

7 - 5= 2