# ADDING AND SUBTRACTING FRACTIONS WORD PROBLEMS

Problem 1 :

Find the total width of 3 boards that 1 3/4 inches wide, 7/8 inch wide1/2 inches wide.

Solution :

To find the total width of 3 boards :

= 1 3/4 + 7/8 + 1 1/2

= 7/4 + 7/8 + 3/2

= (7/4 × 2/2) + 7/8 + (3/2 × 4/4)

= 14/8 + 7/8 + 12/8

= 33/8

= 4  1/8

So, the total width of 3 boards is 4 1/8 inches.

Problem 2 :

A 7.15H tire is 6 5/8 inches wide and a 7.15C tire is 4 3/4 inches wide. What is the difference in their widths ?

Solution :

7.15H tire is 6 5/8 inches wide.

= 53/8

7.15C tire is 4 3/4 inches wide.

=19/4

To difference in their widths :

= 53/8 - (19/4 × 2/2)

= 53/8 - 38/8

= 15/8

= 1 7/8

So, the difference in their widths is 1 7/8 inches.

Problem 3 :

A patient is given 1 1/2 teaspoons of medicine in the morning and teaspoons at night. How many teaspoons total does the patient receive daily ?

Solution :

The teaspoons of medicine in the morning = 1 1/2

The teaspoons of medicine in the night = 2 1/4

= 3/2 + 9/4

= (3/2 × 2/2) + 9/4

= 6/4 + 9/4

= 15/4

= 3 3/4

The patient receive daily the teaspoons is 3 3/4.

Problem 4 :

3 1/3 feet are cut off a board that is 12 1/4 feet long. How long is the remaining part of the board ?

Solution :

Feet are cut off a board = 3 1/3

Length of the feet = 12 1/4

= 49/4 – 10/3

= (49/4 × 3/3) – (10/3 × 4/4)

= 147/12 – 40/12

= 107/12

= 8 11/12

So, length of the remaining part of the board is 8 11/12 feet.

Problem 5 :

3/8 of the corn in the U.S. is grown in Iowa. 1/4 of it is grown in Nebraska. How much of the corn supply is grown in the two states ?

Solution :

The U.S. is grown in Iowa = 3/8

The U.S. is grown in Nebraska = 1/4

= 3/8 + (1/4 × 2/2)

= 3/8 + 2/8

= 5/8

So, the corn supply is grown in the two states is 5/8.

Problem 6 :

A runner jogs 7 1/5 miles east, 5 1/4 miles south, and 8 2/3 miles west. How far has she covered ?

Solution :

East miles = 7 1/5

South miles = 5 1/4

West miles = 8 2/3

= 7 1/5 + 5 1/4 + 8 2/3

= 36/5 + 21/4 + 26/3

= (36/5 × 12/12) + (21/4 × 15/15) + (26/3 × 20/20)

= 432/60 + 315/60 + 520/60

= 1267/60

= 21 7/60

So, far has she loaaed is 21 7/60 miles.

Problem 7 :

If 3 1/2 ounce of cough syrup is used from a 9 1/4 ounce bottle, how much is left ?

Solution :

Ounce of cough syrup = 3 1/2

Cough syrup used the bottle = 9 1/4

Cough syrup left the bottle = 9 1/4 – 3 1/2

= 37/4 – 7/2

= 37/4 - (7/2 × 2/2)

= 37/4 – 14/4

= 23/4

= 5 3/4

So, cough syrup left the bottle is 5 3/4 ounces.

Problem 8 :

I set a goal to drink 64 ounces of water a day. If I drink 10 1/3 ounces in the morning, 15 1/2 ounces at noon, and 20 5/6 ounces at dinner, how much more ounces of water do I have to drink to reach my goal for the day ?

Solution :

I set a goal to drink 64 ounces of water a day.

Quantity of water drinking in the morning = 10  1/3

Quantity of water drinking in the noon = 15  1/2

Quantity of water drinking in the dinner = 20  5/6

= 64 – 10 1/3 – 15 1/2 - 20 5/6

= 64 – 31/3 – 31/2 -125/6

= (64/1 × 6/6) – (31/3 × 2/2) – (31/2 × 3/3) -125/6

= 104/6 – 62/6 – 93/6 – 125/6

= (104 – 62 – 93 – 125)/6

= 52/3

= 17   1/3

So, i have to drink to reach my goal for the day is 17 1/3.

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