SOLVING WORD PROBLEMS INVOLVING CONVERSION UNITS

Problem 1 :

Michael is planning a party for 30 people. He plans that each guest will drink 1 cup of juice. He has 2 1/2 gallons of juice. Does he have enough juice for the party ?

Solution :

Cups are a smaller measurement unit than gallons, so to convert, use multiplication.

Michael multiplies 2 1/2 by 16 to find the number of cups of juice he has.

2 1/2 × 16 = (2 + 1/2) × 16

= 2 × 16 + 1/2 × 16

= 32 + 8

= 40

There are 40 cups of juice.

40 > 30

So, Michael has enough juice for the party.

Problem 2 :

Juanita has 1 1/2 gallons of milk. How many cups of milk does she have ? Explain how you know.

Solution :

To find the total number of cubs :

1 1/2 × 16 = (1 + 1/2) × 16

= 1 × 16 + 1/2 × 16

= 16 + 8

= 24

So, Juanita has 24 cups of milk.

Problem 3 :

Benjamin has 3 gallons of punch. He adds another 1/2 gallon of juice to the punch. How many gallons of punch does he have now ? How many cups ? Explain your reasoning.

Solution :

Punch of the gallons = 3

He adds another gallon = 1/2

1 gallon is 16 cups.

(3 + 1/2 ) × 16

= 3 × 16 + 1/2 × 16

= 48 + 8

= 56

Problem 4 :

Ms. Monet, the art teacher at Giverny School, has 3 quarts of liquid glue and 24 empty glue bottles that each hold 1 cup, Does she have enough glue to fill all of the bottles ? Expalin.

Solution :

Liquid glue = 3 1/2

Empty glue = 24

Each hold 1 cup

Total glue = 7/2 × 4 = 14 cups

No, she doesn’t have enough glue.

Problem 5 :

Ms. Monet gave 1 cup of red paint to each of her 20 students. How many quarts of red paint did she give out ?

Solution :

Cup of red paint = 1

Number of students = 20

= 20 × 1

= 20 cups

1 quart = 4 cups

20 cups = 20/4 = 5 quarts

So, 5 quarts of red paint she give out.

Problem 6 :

Ms. Monet is combining 15 cups of green paint with 15 cups of white paint. She is pouring the paint mixture into empty quart bottles. How many quart bottles does she need ? Explain.

Solution :

Green paint cups = 15

White paint cups = 15

Total cups = 30

1 quart = 4 cups

30 cups = 30/4

= 7.5 (whole number)

= 8

So, 8 quart bottles she need.

Problem 7 :

Ryan and Layla measured the length of their hermit crabs. Ryan measured his crab to be 34 millimeters. Layla measured her crab to be 2.8 centimeters. Who has the longer crab ?

Solution :

It is easier to compare measurements in the same units. You can compare in millimeters or centimeters.

To compare the crabs in millimeters, you have to convert the measurement of Layla’s crab into millimeters. To convert from centimeters to millimeters, use multiplication because centimeters to millimeters, use multiplication because centimeters are the larger measurement unit.

1 cm = 10 mm

2.8 cm × 10 = 28 mm

Layla’s crab is 28 mm long.

34 mm > 28 mm

Ryan has the longer crab.

Problem 8 :

Which is the smaller unit of measurement, centimeter or millimeter ?

Solution :

The smaller unit of measurement is millimeter.

Problem 9 :

In the example problem, multiplication was used to convert centimeters to millimeters. What operation would you use to convert millimeters to centimeters ?

Solution :

Division was used to convert centimeters to milmeters.

Problem 10 :

Look at the example problem. Ryan and Layla’s friend Jan also has a hermit crab, Jan measures her hermit crab to be 3.3 cm long.

a. Who has the longer crab, Jan or Layla ?

b. Who has the longer crab, Jan or Ryan ?

Solution :

a.  Layla’s crab is 28 mm long.

b. Ryan has the longer crab.

Problem 11 :

Geno has two hamsters, Zippy and Popcorn. Zippy is 94 millimeters long, and Popcorn is 8.7 centimeters long. How much longer is Zippy in millimeters ? Explain.

Solution :

Length of the Zippy = 94 millimeters

Length of the Popcorn = 8.7 centimeters

1 centimeters = 10 millimeters

= 10 × 8.7

= 87 millimeters

Length of the Zippy = 94 – 87

= 7 millimeters

Problem 12 :

Carissa’s gerbil has a tail that is the same length as its body length. Its tail is 102 millimeters. How long is her gerbil in centimeters ?

Solution :

Length of the tail = 102 millimeters

1 millimeters = 0.1 centimeters

102 millimeters = 102 × 0.1

= 10.2 centimeters

Length of the gerbil is 10.2 centimeters.

Problem 13 :

Diego’s parakeet is 13 centimeters, 4 millimeters tall. How tall is his parakeet in millimeters ?

Solution :

Diego’s parakeet = 13 centimeters

Tall = 4 millimeters

1 centimeters = 10 millimeters

13 centimeters = 13 × 10 millimeters

= 130 millimeters

Total = 130 + 4

= 134

So, 134 tall is his parakeet in millimeters.

Problem 14 :

Amelia takes her two cats, Sparkle and Twinkle, to the vet. The vet says that Sparkle is 464 mm long and Twinkle is 46 cm long. Which of Amelia’s cats is longer ? Explain.

Solution :

Number of cats = 2

Length of sparkle = 464 mm

Length of the twinkle = 46 cm

1 centimeters = 10 millimeters

46 centimeters = 46 × 10 millimeters

= 460

Total length = 464 + 460

= 924

So, length of Amelia cats is 924.

Problem 15 :

Audrey’s dog is 40 inches tall. How tall is her dog in feet and inches ?

Solution :

1 feet = 12 inches 

40 inches = 40/12

= 3 with remainder of 4

That means that 40 inches , when converted to feet and inches.

Her dog is 3 feet and 4 inches.

Problem 16 :

Denver is called the “Mile High City” because the city’s official elevation is 1 mile, or 5,280 feet, above sea level. What is Denver’s elevation in yards ? Circle the letter of the correct answer.

A) 15,840 yards  B) 5,277 yards

C) 1760 yards D) 440 yards

Katherine choose A as the correct answer. How did she get that answer ?

Solution :

1 yard = 3 feet 

5280 feet = 5280/3

= 1760 yards

So, correct option is C.

Problem 17 :

Jake and Nice both measured their thumbs. Jake’s thumb is 55 millimeters long. Nico’s thumb is 5.7 centimeters long. Who has the longer thumb ? Explain how you know.

Solution :

Length of the Jake's thumb = 55 millimeter

Length of the Nico's thumb = 5.7 centimeters

1 millimeters = 0.1 centimeters

55 millimeters = 55 ×  0.1

= 5.5 centimeters

Length of the Jake's thumb = 5.5 centimeters

Length of the Nico's thumb = 5.7 centimeters

So, Length of the Nico's thumb is 5.7 centimeters.

Problem 18 :

Toby’s house is 25 feet high. How high is Toby’s house in yards and feet ?

Solution :

Height of the Toby's house = 25 feet

1 yard = 3 feet

25 feet = 25/3

= 8.3

= 8 yards

So, Toby’s house in 8 yards and 3 feet.

Problem 19 :

Mica is making a paste mixture for an art project. He mixes 8 cubs of water with glue. If he wants to make a double batch, how many quarts of water does he need ? How much water is that in gallons ?

Solution :

Cubs of water = 8

Number of batches = 2

1 quart = 4 cups

8 cups = 8/4

8 cups = 2 quarts

4 quarts in 1 gallon.

2 quarts =  2/4

2 quarts = 1/2 gallon

He needs one more quart.

That is half of a gallon.