Introduction to Fractions

Subtraction of Fractions

When subtracting mixed numbers, you may need to “borrow” a whole number to
subtract the fractions.

Example:

5 1/5 - 2 3 /10 = _______________

Step 1: Convert the fractions with unlike denominators (bottom numbers) to
fractions with the same denominator.

5 1/5 - 2 3/10 =
5 2/10 - 2 3/10 =

Step 2: Before we can subtract the fractions, we must borrow 1 (10/10) from the 5.

5 2/10 - 2 3/10 =
4 12/10 - 2 3/10 =

Step 3: Separate the whole numbers and fractions.

4 12/10 - 2 3/10 =

Step 4: Subtract the whole numbers.

4 - 2 = 2

Step 5: Subtract the fractions.
12/10 - 3/10 = 9/10

Step 6: Combine the results.

Therefore: 5 1/5 - 2 3/10 = 2 9/10

Skill Check

21. 2 2/3 - 1 ¾ = _______________

22. 8 7/20 - 2 ¾ = _______________

23. 9 1/6 - 3 8/9 = _______________

24. 4 ½ - 2 5/16 = _______________

25. 16 ¼ - 7 5/8 = _______________

Multiplication of Fractions

To multiply with mixed numbers, first you must change the mixed numbers into
improper fractions.

Steps for changing mixed numbers to improper fractions:

Step 1: Find the product of the denominator of the fraction and the whole number.
Put the product over the denominator.

Step 2: Add the two fractions.

Example: Change 3 2/3 into an improper fraction.

Step 1: Multiply the denominator (3) by the whole number (3). Put the product (9)
over the denominator (3).

Step 2: Add the two fractions.

3 2/3 = 9/3 + 2/3 = 11/3

To multiply one or more mixed numbers, the first step is to change all to improper
fractions.

Steps for multiplying mixed numbers:

Step 1: Change every mixed number into an improper fraction.

Step 2: Add the fractions.

Example: Multiply 2¾ × 1/3

Step 1: Change 2 to an improper fraction. 2 = 8/4

Step 2: Add 8/4 and ¾ = 11/4
(2¾ = 2 + ¾ = 8/4 + ¾ = 11/4)

Step 3: Multiply the improper fraction from Step 2 (11/4) by the other fraction
(1/3).

11/4 × 1/3 = 11/12

Note: Multiply the whole number by the denominator and add the numerator .
 
 

denominator	whole number		numerator
		denominator remains the same (4)

Skill Check

Multiply the following mixed numbers:

26. ¾ × 1¼ = _______________

27. 3 × 4½ = _______________

28. 2¾ × 3 4/5 = ______________
_
29. 4 1/3 × 3 4/5 = _______________

30. 6 1/3 × 4 = _______________

Division of Fractions

Dividing fractions is simply finding out how many times one number will go into another
number. Dividing fractions take it one step further than multiplying fractions.

Steps for dividing fractions:

Step 1: To divide by a fraction, multiply by its reciprocal (invert the divisor the
number you’re dividing by). Turn the fraction upside down. Before you can
divide, you must find the reciprocal . Before you can change to its reciprocal,
invert the divisor. You must first change it to a fraction if it’s not one already.

Step 2: Change the division sign to multiplication.

Step 3: Multiply to get the answer.

Steps for dividing fractions by fractions:

Step 1: To divide by a fraction, multiply by its reciprocal. Find the reciprocal of the
fraction you are dividing by (the divisor) and multiply.

Step 2: Invert the fraction (divisor)

Step 3: Change the division sign to multiplication.

Step 4: Multiply

Example: Divide 7/8 by 2/3
 

Invert fraction	Change sign
Answer:	21/16 = 1 5/16

Skill Check

31. 3/6 ÷ 1/3 = _______________

32. 7/8 ÷ ½ = _______________

33. 1/3 ÷ 3/8 = _______________

34. 2/3 ÷ 2/3 = _______________

35. 2/3 ÷ 1/2 = _______________

Now select your area of work and then turn to the appropriate page for “Let’s Apply to
Your Workplace” questions:
Nursing Assistant ---------------------- Page 137 - 138
Dietary Services ----------------------- Page 139 - 140
Environmental Services --------------- Page 141 - 142

Let’s Apply to Nurse Assistant
Mathematics – Lesson 6 of 7

Nursing assistants use fractions in many different places . An example would be
calculating the amount of a meal a resident has consumed. Nursing assistants must
determine the fractional portion consumed and then record the amount on the
resident’s chart.

Example

Ellie May is one of the residents that you are responsible for. You are to chart the
amount of solid food that Ellie May consumes. For the noon meal today she ate 1/2 of
a 3-ounce serving of meat loaf and 3/4 of her 3-ounce serving of mashed potatoes and
1-ounce serving of gravy. She also ate 1/3 of a 2-ounce serving of green beans and
one slice (1 ounce) of bread. How many ounces of solid food did Ellie May consume?

1 1/2 + 2 1/4 + 3/4 + 1 1/2 + 1 =

3/2 + 9/4 + 3/4 + 3/2 + 1 =

6/4 + 9/4 + 3/4 + 6/4 + 4/4 = 28/4 = 7 ounces of solid food consumed

Exercise

1. You are assisting the in-charge nurse preparing medications that will be
administered to the residents this evening. If she has a supply of 17 1/2 ounces
of a particular medication, and each resident’s dose is 1 1/4 ounces, how many
residents will the in-charge nurse be able to administer a proper dose to?

Answer: ___________________________

2. You are a medication aid and are required to administer 26 doses of a medication
of which you need 1 1/3 ounces per dose. If you only have one 32-ounce bottle of
the medication on hand, how many doses will you be able to administer?

Answer: ___________________________

Is there enough medication on hand to administer a dose to each of the 26
residents?

Answer: ___________________________

3. You are responsible for charting the liquid intake of one of the residents on your
floor. During your shift the resident had a 6-ounce glass of juice, but only drank
2/3 of it. In addition, he drank 3/4 of an 8-ounce cup of coffee. He also had 12
1/2 ounces of water. How many ounces of liquid did he consume during your
shift?

Answer: ___________________________

Let’s Apply to Dietary Services
Mathematics – Lesson 6 of 7

Dietary Services workers use fractions in many different places. An example would be
calculating the amount of an ingredient required when a recipe is being doubled or
tripled. Dietary Services workers must determine the correct fractional amounts
required so that each batch will turn out properly.

Example

Your supervisor has instructed for you to make 15 apple pies for tomorrow’s deserts.
You review the recipe and see that each pie requires 1 1/4 teaspoons of cinnamon.
When you check the supplies, you discover that the cinnamon container is almost empty
and find out that more cinnamon is on order , but will not be delivered until tomorrow.

You measure the cinnamon that you have on hand and determine that there is 12 1/2
teaspoons full. How many apple pies will you be able to make?

12 1/2 ÷ 1 1/4 =

25/2 ÷ 5/4 =

25/2 × 4/5 = 100/10 = 10There is enough cinnamon on hand
to make up 10 apple pies.

Exercise

1. You are preparing a drink mix for the evening meal. The instructions say to use
3/4 cup of sugar for each gallon of drink you are mixing and your instructions say
to make up 4 1/2 gallons of drink. How much sugar will you need?

Answer: ___________________________

2. You are making the deserts for the evening meal. You are to make up three sheet
cakes and a double batch of cookies. How much cooking oil will you need if each
cake requires 2 1/4 cups and each batch of cookies requires 1 1/3 cups of oil?

Answer: ___________________________

3. You are to make up a large batch of vegetable soup for tomorrow’s lunch. The
recipe says to add 2 1/2 cups of beef stock for each 1/2 gallon of soup. How
much beef stock will you need if you are making 5 gallons of vegetable soup?

Answer: ___________________________

Let’s Apply to Environmental Services
Mathematics – Lesson 6 of 7

Environmental Services workers occasionally use fractions in their workplace. An
example would be calculating the correct amount of disinfecting concentrate to be
added to water to make up a cleaning solution.

Example

You are to mix up a bucket of disinfecting solution and wash down the walls and floors
of the showers in both the men and women’s bathrooms. The directions on the
container of disinfecting concentrate say to add 1/3 cup of concentrate to each quart of
water. How much concentrate will you need to add to 5 1/4 quarts of water to obtain
the proper mixture?

1/3 × 5 1/4 =
1/3 × 21/4 = 21/12 = 1 9/12 = 1 3/4 cups of concentrate

Exercise

1. You are preparing to strip and re-wax the main hall floor. The directions on the
stripper concentrate say to mix 1 1/2 cups of the concentrate with each gallon of
warm water. If you have 5 gallons of water, how many cups of stripper
concentrate will you need to add to have the proper stripping solution?

Answer: ___________________________

2. You are assigned to work in the laundry area today to fill in for an employee who
is off sick. The automatic soap dispenser on the washing machine is not working
and you are told to measure and add 2/3 cup of soap powder to each load that
you run. How many cups of soap powder will you need to wash 9 loads of bed
linens ?

Answer: ___________________________

3. You have the assignment of mixing up a disinfecting solution and then washing
down the walls, furniture and floors in one of the rooms. The directions for
mixing the solution say to add 1/4 cup of bleach to each 1 1/2 quarts of water. If
you have 4 1/2 quarts of water in a bucket, how many cups of bleach should you
add to have the proper mixture?

Answer: ___________________________