NSCC SUMMER LEARNING SESSIONS
NUMERACY SESSION
Module 4 – Decimals
Acknowledgement
Large portions (pages 9-45) of these modules were created using Level III and Level IV ALP locally
developed math resources. These ALP resources are the intellectual property of the NS
Department of Labour and Advanced Education (LAE). David Pilmer, the author and LAE
Curriculum Consultant, has given permission to NSCC for the use of his materials in the creation of
these learning modules.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 2
Welcome!
The Numeracy session has six modules. This is module number 4 – Decimals.
In this package you will find everything you need to complete this module.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 3
Contents
Acknowledgement ............................................................................................................................................. 2
Welcome! ............................................................................................................................................................ 3
LEARNING OUTCOMES – What will I learn? .............................................................................................. 6
EXTRA RESOURCES ...................................................................................................................................... 7
Dividing Whole Numbers.................................................................................................................................. 9
Questions........................................................................................................................................................ 9
Answers in back ............................................................................................................................................ 9
Answers ........................................................................................................................................................ 11
Decimals ........................................................................................................................................................... 13
Converting Decimals to Fractions................................................................................................................. 16
Practice ......................................................................................................................................................... 17
Answers - Decimals to Fractions .............................................................................................................. 19
Adding and Subtracting Decimals ................................................................................................................ 19
Multiplying Decimals ....................................................................................................................................... 24
Dividing Decimals ............................................................................................................................................ 26
Problem Solving with Decimals..................................................................................................................... 28
Answers ........................................................................................................................................................ 31
Percents ............................................................................................................................................................ 32
Questions: .................................................................................................................................................... 36
FINAL STEPS: Finishing up the module ..................................................................................................... 46
Coming up next… Module 5 – Order of Operations .............................................................................. 46
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 4
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 5
LEARNING OUTCOMES – What will I learn?
In this module you will learn and practice…
•
•
•
•
•
Reading and writing decimal numbers
Expressing decimal numbers in expanded form
Adding, subtracting, multiplying and dividing decimal numbers
Solving problems with decimal numbers
Developing a math study sheet for decimal numbers
This is an important part of working towards the session learning objectives:


Use decimal numbers as a foundation for more advanced math concepts
Complete a math study sheet to summarize the learning about decimals
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 6
EXTRA RESOURCES
In case you’d like to explore more resources, here about some to check out:
www. Kutasoftware.com
Stepping It Up. Foundations for Success in Math. Whole Numbers. Published by Pearson.
First Canadian Author: Michael Delgaty.
http://www.youtube.com/watch?v=x-Dqe5U1TXA (place values in decimal numbers)
http://www.youtube.com/watch?v=nmaUyeKpwSM (adding decimals)
http://www.youtube.com/watch?v=joF4sYmuC88 (subtracting decimals)
http://www.youtube.com/watch?v=3H9DYeR5Wmg (multiplying decimals)
http://www.youtube.com/watch?v=HlEx1TN-dqY (dividing decimals)
http://www.khanacademy.org/ (various topics)
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 7
DECIMALS
Study Sheet
+ Addition +
-Subtraction –
X Multiplication X
Real Life examples
÷ Division ÷
and
Key Words
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 8
Dividing Whole Numbers
Questions
Answers in back
Divide:
(a) 40 ÷ 5 =
(b) 7 ÷ 7 =
(c) 16 ÷ 2 =
(d) 63 ÷ 9 =
(e) 18 ÷ 3 =
(f) 20 ÷1 =
(g) 72 ÷ 8 =
(h) 35 ÷ 7 =
Divide:
(a) 45 ÷ 9 =
(b) 14 ÷ 7 =
(c) 16 ÷ 4 =
(d) 54 ÷ 9 =
(e) 18 ÷ 2 =
(f) 8 ÷ 8 =
(g) 63 ÷ 7 =
(h) 35 ÷ 5 =
Divide:
(a) 40 ÷ 8 =
(b) 9 ÷1 =
(c) 12 ÷ 2 =
(d) 36 ÷ 4 =
(e) 21 ÷ 3 =
(f) 10 ÷10 =
(g) 36 ÷ 6 =
(h) 72 ÷ 9 =
Divide:
(a) 27 ÷ 9 =
(b) 70 ÷ 7 =
(c) 45 ÷ 5 =
(d) 28 ÷ 4 =
(e) 24 ÷ 3 =
(f) 9 ÷1 =
(g) 63 ÷ 9 =
(h) 25 ÷ 5 =
Divide:
(a) 24 ÷ 6 =
(b) 14 ÷ 7 =
(c) 18 ÷ 2 =
(d) 54 ÷ 6 =
(e) 28 ÷ 7 =
(f) 8 ÷ 8 =
(g) 32 ÷ 8 =
(h) 63 ÷ 9 =
Divide:
(a) 20 ÷ 5 =
(b) 28 ÷ 4 =
(c) 27 ÷ 3 =
(d) 45 ÷ 9 =
(e) 21 ÷ 7 =
(f) 20 ÷ 2 =
(g) 63 ÷ 9 =
(h) 15 ÷ 5 =
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 9
Divide:
(a) 16 ÷ 4 =
(b) 9 ÷1 =
(c) 32 ÷ 4 =
(d) 72 ÷ 8 =
(e) 18 ÷ 2 =
(f) 24 ÷ 3 =
(g) 35 ÷ 5 =
(h) 54 ÷ 9 =
Divide:
(a) 48 ÷ 6 =
(b) 28 ÷ 7 =
(c) 8 ÷ 2 =
(d) 36 ÷ 9 =
(e) 12 ÷ 3 =
(f) 24 ÷ 4 =
(g) 27 ÷ 3 =
(h) 20 ÷ 5 =
Divide:
(a) 32 ÷ 4 =
(b) 49 ÷ 7 =
(c) 18 ÷ 2 =
(d) 18 ÷ 6 =
(e) 40 ÷ 8 =
(f) 30 ÷10 =
(g) 42 ÷ 6 =
(h) 81 ÷ 9 =
Divide:
(a) 14 ÷ 2 =
(b) 40 ÷ 5 =
(c) 32 ÷ 8 =
(d) 27 ÷ 9 =
(e) 12 ÷ 6 =
(f) 7 ÷1 =
(g) 72 ÷ 8 =
(h) 30 ÷ 6 =
Divide:
(a) 63 ÷ 7 =
(b) 32 ÷ 8 =
(c) 12 ÷ 2 =
(d) 48 ÷ 8 =
(e) 72 ÷ 9 =
(f) 8 ÷ 8 =
(g) 54 ÷ 6 =
(h) 25 ÷ 5 =
Divide:
(a) 35 ÷ 5 =
(b) 21 ÷ 7 =
(c) 18 ÷ 2 =
(d) 36 ÷ 9 =
(e) 56 ÷ 7 =
(f) 27 ÷ 3 =
(g) 24 ÷ 4 =
(h) 64 ÷ 8 =
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 10
Answers – Dividing Whole Numbers
Divide:
(a) 40 ÷ 5 = 8
(b) 7 ÷ 7 = 1
(c) 16 ÷ 2 = 8
(d) 63 ÷ 9 =7
(e) 18 ÷ 3 = 6
(f) 20 ÷1 = 20
(g) 72 ÷ 8 =9
(h) 35 ÷ 7 = 5
Divide:
(a) 45 ÷ 9 = 5
(b) 14 ÷ 7 = 2
(c) 16 ÷ 4 = 4
(d) 54 ÷ 9 = 6
(e) 18 ÷ 2 = 9
(f) 8 ÷ 8 = 1
(g) 63 ÷ 7 = 9
(h) 35 ÷ 5 = 7
Divide:
(a) 40 ÷ 8 = 5
(b) 9 ÷1 = 9
(c) 12 ÷ 2 = 6
(d) 36 ÷ 4 = 9
(e) 21 ÷ 3 = 7
(f) 10 ÷10 = 1
(g) 36 ÷ 6 = 6
(h) 72 ÷ 9 = 8
Divide:
(a) 27 ÷ 9 = 3
(b) 70 ÷ 7 = 10
(c) 45 ÷ 5 = 9
(d) 28 ÷ 4 = 7
(e) 24 ÷ 3 = 8
(f) 9 ÷1 = 9
(g) 63 ÷ 9 = 7
(h) 25 ÷ 5 = 5
Divide:
(a) 24 ÷ 6 = 4
(b) 14 ÷ 7 = 2
(c) 18 ÷ 2 = 9
(d) 54 ÷ 6 = 9
(e) 28 ÷ 7 = 4
(f) 8 ÷ 8 = 1
(g) 32 ÷ 8 = 4
(h) 63 ÷ 9 = 7
Divide:
(a) 20 ÷ 5 = 4
(b) 28 ÷ 4 = 7
(c) 27 ÷ 3 = 9
(d) 45 ÷ 9 = 5
(e) 21 ÷ 7 = 3
(f) 20 ÷ 2 = 10
(g) 63 ÷ 9 = 7
(h) 15 ÷ 5 = 3
Divide:
(a) 16 ÷ 4 = 4
(b) 9 ÷1 = 9
(c) 32 ÷ 4 = 8
(d) 72 ÷ 8 = 9
(e) 18 ÷ 2 = 9
(f) 24 ÷ 3 = 8
(g) 35 ÷ 5 = 7
(h) 54 ÷ 9 = 6
Divide:
(a) 48 ÷ 6 = 8
(b) 28 ÷ 7 = 4
(c) 8 ÷ 2 = 4
(d) 36 ÷ 9 = 4
(e) 12 ÷ 3 = 4
(f) 24 ÷ 4 = 6
(g) 27 ÷ 3 = 9
(h) 20 ÷ 5 = 4
Divide:
(a) 32 ÷ 4 = 8
(b) 49 ÷ 7 = 7
(c) 18 ÷ 2 = 9
(d) 18 ÷ 6 = 3
(e) 40 ÷ 8 = 5
(f) 30 ÷10 = 3
(g) 42 ÷ 6 = 7
(h) 81 ÷ 9 = 9
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 11
Divide:
(a) 14 ÷ 2 = 7
(b) 40 ÷ 5 = 8
(c) 32 ÷ 8 = 4
(d) 27 ÷ 9 = 3
(e) 12 ÷ 6 = 2
(f) 7 ÷1 = 7
(g) 72 ÷ 8 = 9
(h) 30 ÷ 6 = 5
Divide:
(a) 63 ÷ 7 = 9
(b) 32 ÷ 8 = 4
(c) 12 ÷ 2 = 6
(d) 48 ÷ 8 = 6
(e) 72 ÷ 9 = 9
(f) 8 ÷ 8 = 1
(g) 54 ÷ 6 = 9
(h) 25 ÷ 5 = 5
Divide:
(a) 35 ÷ 5 = 7
(b) 21 ÷ 7 = 3
(c) 18 ÷ 2 = 9
(d) 36 ÷ 9 = 4
(e) 56 ÷ 7 = 8
(f) 27 ÷ 3 = 9
(g) 24 ÷ 4 = 6
(h) 64 ÷ 8 = 8
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 12
Decimals
Like fractions, decimals are used to represent part of a whole.
Area Model
Fraction
Decimal
3
4
0.75
When a number is written as a decimal,
it is comprised of three parts:
1) whole number part
2) decimal point
3) decimal part
Whole
Numbe
r Part
Decimal
Part
571.806
Decimal
Point
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 13
Place names and place values for the whole number and decimal parts of fractions are shown in the
chart below.
1000
100
1
and
Ten
Thousandths
Hundredths
Tenths
.
10
Thousandths
Decimal Part
Units
Tens
Hundreds
Thousands
Whole Number Part
1
1
1
1
10
100
1000
10000
Example 1:
Express the following numbers in expanded form.
(a) 165.32
(b) 67.891
Answers:
3
2
+
10 100
8
9
1
(b) 67.891 = 60 + 7 + +
+
10 100 1000
(a) 165.32 = 100 + 60 + 5 +
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 14
Example 2:
Write each number in words.
(a) 35.6
(b) 165.32
(c) 67.871
(d) 307.05
(e) 2019.083
Answers:
(a) 35.6 is “thirty-five and six tenths.”
(b) 165.32 is “one hundred sixty-five and thirty-two hundredths.”
(c) 67.871 is “sixty-seven and eight hundred seventy-one thousandths.”
(d) 307.05 is “three hundred seven and five hundredths.”
(e) 2019.083 is “two thousand nineteen and eighty-three thousandths.”
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 15
Converting Decimals to Fractions
Examples:
8
3.8 = three and eight tenths = 3 10
1.56 = one and fifty six hundredths = 1
56
100
587
40.587 = forty and five hundred eighty seven thousandths = 40 1000
2
169.2 = one hundred sixty nine and two tenths = 169 10
8
56.08 = fifty six and eight hundredths = 56 100
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 16
Decimals to Fractions
Practice
Express each decimal as a
fraction.
(a)
2.4 =
Express each decimal as a
fraction.
(a) 23.7 =
Express each decimal as a
fraction.
(a) 9.4 =
(b)
3.81 =
(b) 3.67 =
(b) 13.52 =
(c)
0.5 =
(c) 0.04 =
(c) 0.06 =
(d)
0.07 =
(d) 0.7 =
(d) 0.9 =
Express each decimal as a
fraction.
(a)
107.8 =
Express each decimal as a
fraction.
(a) 73.19 =
Express each decimal as a
fraction.
(a) 212.4 =
(b)
34.93 =
(b) 40.8 =
(b) 342.46 =
(c)
0.2 =
(c) 0.6 =
(c) 6.05 =
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 17
(d)
0.06 =
(d) 1.04 =
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 18
(d) 0.1 =
Answers - Decimals to Fractions
Express each decimal as a
fraction.
4
(a) 2.4 = 2 10
(b) 3.81 = 3
5
(c) 0.5 =10
81
100
7
(d) 0.07 =10
Express each decimal as a
fraction.
8
(a)
107.8 =107 10
93
(b) 34.93 =34 100
2
(c) 0.2 =10
6
(e) 0.06 =100
Express each decimal as a
fraction.
7
(a) 23.7 =2310
67
(b) 3.67 =3100
4
(c) 0.04 =100
(d) 0.7 =10
Express each decimal as a
fraction.
19
(a) 73.19 =73 100
6
(c) 0.6 =10
(b) 13.52 = 13
6
(c) 0.06 =100
52
100
9
(d) 0.9 =10
7
(b) 40.8 = 40
Express each decimal as a
fraction.
4
(a) 9.4 = 9 10
8
10
4
(d) 1.04 =1 100
Express each decimal as a
fraction.
4
(a) 212.4 = 212 10
(b) 342.46 =342
5
(c) 6.05 =6 100
1
(d) 0.1 =10
Adding and Subtracting Decimals
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 19
46
100
Adding decimals is similar to adding whole numbers. We line up the decimal points so that we
can add corresponding place value digits (e.g. tenths with tenths, hundredths with hundredths, and
so on). As with whole numbers, we start from the right and carry when it is necessary.
Example 3:
Add: 42.08 + 208.95.
Answer:
1
Example 4:
Add: 36.07 + 9.065.
Answer:
1
4 2
+ 2 0 8
.
.
1
1
0 8
9 5
3 6
.
0 7
9
.
0 6 5
2 5 1 . 0 3
+
1
4 5 . 1 3 5
Subtracting decimals is similar to subtracting whole numbers. We line up the decimal points so
that we can subtract corresponding place value digits (e.g. tenths from tenths, hundredths from
hundredths, and so on). As with whole numbers, we start from the right and borrow when it is
necessary.
Example 5:
Subtract: 57.62 - 6.18
Answer:
Answer:
12
7
6 2
1 8
9 8
− 3 2
5
5 7
6
−
Example 6:
Subtract: 98.04 - 32.801
.
.
5 1 . 4 4
10
.
.
3
10
0 4 0
8 0 1
6 5 . 2 3 9
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 20
1. Adding .
(a) 42.13 + 30.65
(b) 107.63 + 41.029
(c) 6.93 + 34.68
(d) 78.073 +105.96
(e) 9.8562 + 6.2153
(f) 0.793 + 8.6254
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 21
(g) 32.06 + 7.42 + 11.23
2. Subtracting.
(a) 46.37 - 14.12
(c) 328.46 - 41.28
(h) 0.645 + 1.39 + 2.0431
(b) 27.891 - 4.24
(d) 489.231 - 25.65
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 22
(e) 3.2935 - 0.326
(g) 15.064 - 9.38
(f) 8.03 - 5.56
(h) 2.050 - 0.462
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 23
Multiplying Decimals
Step 1:
Initially ignore the decimal points and multiply as if both of the factors are whole
numbers.
Step 2:
Now the decimal point must be positioned in the product. The number of decimal
places in the product is the sum of the number of places in the factors (count places from the
right).
Example 7:
Multiply: 6.32 × 2.4
Answer:
6. 3
×
2
2. 4
Example 8:
Multiply: 0.832 × 9.31
(2 decimal places)
(1 decimal place)
Answer:
0. 8 3 2
×
9. 3 1
(3 decimal places)
8 3 2
2 4 9 6 0
4 8 8 0 0
2 5 2 8
1 2 6 4 0
1 5. 1 6 8
7
7. 7 4 5 9 2
1. Multiplying.
(a) 6.4 × 2.8
(b) 3.52 × 4.6
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 24
(3 decimal places)
( 2 decimal places)
(5 decimal places)
(c) 40.5 × 5.23
(d) 0.453 × 6.21
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 25
Dividing Decimals
Step 1:
Move the decimal point to the right in the divisor until the devisor
is a whole number.
Step 2:
Move the decimal point to the right in the dividend the same
number of places as was done in Step 1.
Step 3:
Divide through as if you were dividing with whole numbers. Place the decimal point in
the quotient directly above the new decimal point in the dividend.
Example 9:
Divide: 1.792 ÷ 0.32
Answer:
1.792 ÷ 0.32 becomes 179.2 ÷ 32
because we moved the decimal point in
both the dividend and divisor two
places to the right.
5.6
32 179.2
160
192
192
0
Example 10:
Divide: 3.612 ÷ 4.3
Answer:
3.612 ÷ 4.3 becomes 36.12 ÷ 43 because
we moved the decimal point in both the
dividend and divisor one place to the
right.
0.84
43 36.12
344
172
172
0
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 26
1. Dividing
(a) 8.84 ÷ 2.6
(c) 0.279 ÷ 0.45
(b) 1.674 ÷ 0.31
(d) 10.793 ÷ 4.3
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 27
Problem Solving with Decimals
Example 1:
A patient was given injections of 3.2 ml,
2.15 ml, and 1.9 ml of a particular
medication. How much medication did the
patient receive in total of that particular
medication?
Answer:
Add the three numbers.
Example 2:
A school bus driver making $12.50 per
hour was given a raise to $14.05 per hour.
How much is the raise?
Answer:
Subtract the two numbers.
3
1 4
− 1 2
1
3 . 2
2 . 1 5
10
.
.
0 5
5 0
1 . 5 5
+ 1 . 9
The driver received a $1.55 raise.
7 . 2 5
The patient received 7.25 ml of
medication.
Example 3:
Determine the area
of this rectangle.
5.1 m
2.7
m
Answer:
The area of a rectangle is found by
multiplying the length by the width.
Example 4:
A phone company is charging $0.06 per
minute for long distance calls within
Canada. If your bill for a long distance call
within Canada was $4.32, how many
minutes was the call?
Answer:
Divide 4.32 by 0.06.
Change 4.32 ÷ 0.06 to 432 ÷ 6 by
moving the decimal point two places to
the right on both the dividend and the
divisor.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 28
1
5. 1
(1 decimal place)
× 2. 7
(1 decimal place)
72
6 432
42
3 5 7
0 2 0
1 3. 7 7
12
12
(2 decimal places)
0
2
The area of the rectangle is 13.77 m .
The call lasted 72 minutes.
Let’s try a few word problems
1)Find the total cost of these groceries: a 2 kg Steak costing $3.89 per kg, 2 dozen eggs at $2.75
per dozen, 3 loaves of bread at $3.19 per loaf.
2) If you filled your car up with gas and you paid $1.30 per liter. How many liters did you buy if you
paid $78.00 to fill your tank?
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 29
3)If you pay $640.00 per month for rent, how much rent do you pay for one year?
4)At the track and field event Sala finished the dash in 38.9 seconds and Jenn finished the dash in
40.3 seconds. How much longer did it take Jenn to finish?
5) If you had a $50 bill in your pocket and you bought a gift costing $21.87, then you stopped for
lunch and spent $14.75, how much change would you have left?
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 30
Answers
Adding and Subtracting Decimals
1. (a) 72.78
(e) 16.0715
(b) 148.659
(f) 9.4184
(c) 41.61
(g) 50.71
(d) 184.033
(h) 4.0781
2. (a) 32.25
(e) 2.9675
(b) 23.651
(f) 2.47
(c) 287.18
(g) 5.684
(d) 463.581
(h) 1.588
Multiplying
1. (a) 17.92
(b) 16.192
(c) 211.815
(d) 2.81313
1. (a) 3.4
(b) 5.4
(c) 0.62
(d) 2.51
Word Problems
1) $22.85
2) 60 L 3) $7680.00
Dividing
4) 1.4 seconds
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 31
5) $13.38
Percents
Percent means per one hundred. The % sign is used to show the number of parts out of one
hundred parts. For example, 37% means 37 parts out of 100 parts. This particular percent can also
37
and the decimal 0.37.
be expressed as the fraction
100
Area Model
Fraction
Decimal
Percent
37
100
0.37
37%
Changing Percents to Decimals
• Drop the % symbol and divide by 100 (i.e. move the decimal point two places to the left).
• Examples: 45% = 0.45
87% = 0.87
16% = 0.16
9% = 0.09
2% = 0.02
1.4% = 0.014
0.5% = 0.005
120% = 1.20
113% = 1.13
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 32
Changing Percents to Fractions
• Drop the % sign from the percent, place the number over 100, and simplify the fraction if
possible.
55
60
36
• Examples:
55% =
60% =
36% =
100
100
100
60 ÷ 20
55 ÷ 5
36 ÷ 4
=
=
=
100 ÷ 5
100 ÷ 4
100 ÷ 20
3
11
9
=
=
=
20
5
25
Changing Decimals to Percents
• Multiply by 100 (i.e. move the decimal point two places to the right) and add the % sign.
• Examples: 0.65 = 65%
0.19 = 19%
0.82 = 82%
0.04 = 4%
0.07 = 7%
0.029 = 2.9%
0.009=0.9%
1.06 = 106%
1.13 = 113%
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 33
Changing Fractions to Percents
• Convert the fraction to a decimal using division (by hand or with a calculator), and then
convert the decimal to a percent (i.e. move the decimal point two places to the right and add
the % symbol).
13
7
to a percent.
Convert
to a percent.
• Examples: Convert
25
20
0.52
0.35
25 13.00
20 7.00
125
60
50
100
50
100
0
0
7
13
= 0.35 = 35%
= 0.52 = 52%
20
25
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 34
Taking the Percentage of a Number
•
If you need to find a specific percentage of a number, convert the percentage to a decimal
and multiply that decimal by the number (by hand or with a calculator).
Examples: Find 65% of 180.
0.65 × 180 = 117
Find 7% of 342.
0.07 × 342 = 23.94
•
Find 32% 0f 2100.
0.32 × 2100 = 672
Find 113% of 46.
1.13 × 46 = 51.98
Some of these questions can be done quickly and without a calculator if you are dealing with
"friendly" percentages (e.g. 10%, 20%, 30%,…).
Examples: Find 30% of 150
We know that 10% of 150 is 15, therefore 30% of 150 must be 45 (3 × 15).
Find 20% of 320
We know that 10% of 320 is 32, therefore 20% of 320 must be 64 (2 × 32).
Find 70% of 90
We know that 10% of 90 is 9, therefore 70% of 90 must be 63 (7 × 9).
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 35
Questions:
1. Convert the following percentages to decimals.
(a) 38% =
(b) 21% =
(c) 37% =
(d) 4% =
(e) 6% =
(f) 24.5% =
(g) 3.4% =
(h) 0.8% =
(i) 105% =
(j) 14.2% =
(k) 210% =
(l) 3.6% =
2. Convert the following percentages to fractions.
(a) 45%
(b) 70%
(c) 28%
(d) 80%
(e) 6%
(f) 42%
(g) 72%
(h) 120%
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 36
3. Convert the following decimals to percentages.
(a) 0.92 =
(b) 0.47 =
(c) 0.32 =
(d) 0.07 =
(e) 0.7 =
(f) 0.007 =
(g) 0.042 =
(h) 0.206 =
(i) 1.51 =
(j) 1.8 =
(k) 1.06 =
(l) 1.034 =
4. Convert the following fractions to percentages. You may use a calculator to complete this
question. ()
(a)
2
5
(b)
14
25
(c)
17
20
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 37
(d)
5
8
(e)
3
(f)
8
15
(g)
16
26
(h)
25
9
8
5. Complete each of the following. You may use a calculator to complete this question. ()
(a) Take 35% of 6280.
(b) Take 65% of 580.
(c) Take 9% of 1600.
(d) Take 15% of 74.
(e) Take 3.5% of 56.
(f) Take 113% of 57.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 38
6. Complete each of the following. You may use a calculator ϑ
(a) Take 10% of 430.
(b) Take 10% of 5800.
(c) Take 20% of 60.
(d) Take 20% of 140.
(e) Take 30% of 70.
(f) Take 40% of 110.
(g) Take 70% of 2000.
(h) Take 60% of 400.
(i) Take 20% of 2500.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 39
(j) Take 40% of 300.
(k) Take 60% of 7000.
(l) Take 30% of 1200.
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 40
A few word problems for percentages
Example 1
I buy a book for $19.95 plus there is 15% tax. What is the total?
•
Remember 15% as a decimal is 0.15 so we multiply 19.95 by 0.15
19.95
X0.15
2.9925 we round that to the nearest cent so we pay 2.99 in tax
To get the total we add the book price to the tax
19.95 + 2.99 = $22.94
Example 2
I wrote a test with 34 questions, each worth 1 point. I got 29 correct. What was my mark as a
percentage on the test?
•
•
•
•
•
Amount correct is 29 out of 34 so we write 29/34.
To convert to a percentage divide top by bottom or divide amount correct by total amount.
29÷34 = 0.8529411
Now we need to change this decimal number to a percentage by multiplying by 100
0.8529411 X 100= 85.29411
To get a final answer we take the nearest whole number, so my mark is 85%
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 41
Some for you to try….
1) Nya’s new speakers cost $154.99 plus 6% tax. What did she pay in total?
2) Jackson’s dinner bill was $29.00 but he left a tip of 25%. What did he pay in total?
3) The TV was $645 but had a discount of 30%. After the discount 14% tax was added on. What
was the total cost of the TV? (2 steps)
4) Kala’s cell phone bill is $28.75 per month plus she pays 1% 911 fee. What is her total bill?
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 42
5) The Shirt Maker Store said they would offer a discount of 2/5 off all regular items. What is the
discount as a percentage? With that sale what would you pat for a new shirt with a tag price of
$39.99?
6) Alejandra got a mark of 37/45 on a math test. Her friend Pablo got a mark of 67/80 on a test.
Who had the highest percentage score? (hint convert each to percent and compare)
7) The purse I want costs $47 plus 15% tax. I had a $20 gift card and will pay for the rest on my
debit card. How much will I need to pay by debit?
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 43
Answers
Percentages
1. (a) 0.38
(e) 0.06
(i) 1.05
9
20
3
(e)
50
(b) 0.21
(f) 0.245
(j) 0.142
(c) 0.37
(g) 0.034
(k) 2.1
(d) 0.04
(h) 0.008
(l) 0.036
2. (a)
(b)
7
10
21
(f)
50
(c)
7
25
18
(g)
25
(d)
3. (a) 92%
(e) 70%
(i) 151%
(b) 47%
(f) 0.7%
(j) 180%
(c) 32%
(g) 4.2%
(k) 106%
(d) 7%
(h) 20.6%
(l) 103.4%
4. (a) 40%
(e) 37.5%
(b) 56%
(f) 93.75%
(c) 85%
(g) 104%
(d) 62.5%
(h) 112.5%
5. (a) 2198
(d) 11.1
(b) 377
(e) 1.96
(c) 144
(f) 64.41
6. (a) 43
(d) 28
(g) 1400
(j) 120
(b) 580
(e) 21
(h) 240
(k) 4200
(c)
(f)
(i)
(l)
12
44
500
360
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 44
4
5
6
(h)
5
Percentage Word Problems
1) $164.29
2) $36.25
3) $514.71
4) 29.04
5) 40% off, will pay $23.99
6) Alejandra 82.2% Pablo 83.75 % so Pablo has the better mark
7) Total bill is $54.05 subtract the gift card, so total paid by debit is $34.05
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 45
FINAL STEPS: Finishing up the module
Well done! You’ve made it to the end of this module. In this module you’ve:
• Read and wrote decimal numbers
• Expressed decimal numbers in expanded form
• Added, subtracted, multiplied and divided decimal numbers
• Solved problems with decimal numbers
• Developed a math study sheet for decimal numbers
This is an important part of your work towards these session learning objectives:
 Use decimal numbers as a foundation for more advanced math concepts
 Complete a math study sheet to summarize the learning about decimals
Coming up next… Module 5 – Order of Operations
SUMMER LEARNING SESSIONS | NUMERACY – Module 4 – Decimals | Page 46