WORD PROBLEMS INVOLVING MIXED FRACTIONS

Problem 1 :

Renata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs 2  3/8 yards of fabric for her husband’s shirt and 1  1/8 yards of fabric for her son’s shirt. How much fabric does she need to make both shirts?

Solution :

Fabric needed for her husband’s shirt = 2  3/8 yards

Fabric needed for her son’s shirt = 1  1/8 yards

= 2  3/8 + 1  1/8

Adding whole parts, we get

= (2+1) + 3/8 + 1/8

= 3 + (3+1)/8

= 3 + 4/8

= 3  4/8

Mixed fractions is convert to the improper fractions.

= 28/8

= 3.5

So, 3.5 yards of fabric she needs to make both shirts.

Problem 2 :

Nishant is printing invitations on his computer. The paper is 8  1/2 inches wide, and he sets the print area to have a 1  1/2-inch border on each side. How wide is the print area on the sheet of paper?

Solution :

Required width = 8 1/2 - 1 1/2 - 1 1/2

= 17/2 - 3/2 - 3/2

= (17 - 3 - 3)/2

= 11/2

= 5.5

Problem 3 :

Draw a diagram and use it to explain how to add

1  5/8 + 2  7/8

Solution :

1  5/8 + 2  7/8 = (1 + 2) + 5/8 + 7/8

= 3 + 5/8 + 7/8

From the picture, we get

= (3 + 1) + 4/8

= 4 + 4/8

= 36/8

= 9/2

Problem 4 :

Add 4  5/12 + 3  7/8 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

Solution :

Method 1 :

= 2 (4  5/12 + 3  7/8)

= 2 (4 + 3) + (5/12 + 7/8)

= 2  [ 7 (5/12 + 7/8)]

= 2 [ 7  (10 + 21)/24 ]

= 2[ 7 + 31/24]

= 2[(168 + 31)/24]

= 2 [199/24]

= 199/12

= 16  7/12

Method 2 :

= 2 (4  5/12 + 3  7/8)

Converting the mixed fraction to improper fraction, we get

= 2 (53/12 + 31/8)

Least common multiple of 12 and 8 is 24.

= 2 [53(2) + 31(3)]/24

= 2 (106 + 93)/24

= 2 (199/24)

= 199/12

Converting the improper fraction to mixed fraction, we get

= 16  7/12

Problem 5 :

Pauline has 3  1/4 yards of fabric to make a jacket. The jacket uses 2  2/3 yards. How much fabric will she have left after making the jacket?

Solution :

Material needed to make the jacket = 3  1/4

Quantity of material needed = 2  2/3

Remaining quantity of fabric = 3  1/4 - 2  2/3

Mixed fractions is convert to the improper fractions.

= 13/4 - 8/3

= (13/4) × (3/3) - (8/3) × (4/4)

= 39/12 - 32/12

= 7/12

So, 7/12 fabric she have left after making the jacket.

Problem 6 :

Tessa bought a picture frame for her son’s graduation picture. The picture is 8 inches wide. The picture frame is 2  5/8 inches wide on each side. How wide will the framed picture be?

Solution :

Width of the picture = 8 inches

width of the frame on each side = 2  5/8

Along with frame, the required width = 8 + 2 + 5/8

= 10 + 5/8

= 10  5/8 inches

Problem 7 :

Edgar will have to pay $3.75 in tolls to drive to the city.

a) Explain how he can make change from a $10 bill before he leaves so that he has the exact amount he needs.

b) How is Edgar’s situation similar to how you subtract 10 – 3 3/4?

Solution :

Amount he has to pay = $3.75

a) The change = $10 - $3.75

= $6.25

So, the exact amount he needs = $6.25.

b) Given, 10 – 3 3/4

Mixed fractions is convert to the improper fractions.

= 10 – 15/4

= (40 - 15)/4

= 25/4

= 6.25

Both ways are similar.