Lesson 2 Addition & Subtraction

VUB Math Foundations Lesson2:AdditionandSubtractionof WholeNumbers
7
LESSON 2 – ADDITION AND SUBTRACTION OF WHOLE
NUMBERS
We will continue our study of mathematics by learning about adding and subtract i ng
whole numbers. Addition and subtraction are the basis of all mathematics. Addition is the basic
operation of increasing while subtraction is the operation of decreasing. We will begin working
with these operations first using only whole numbers and move on to more complex addition
and subtraction concepts in later chapters.
The table below shows the specific whole-number related objectives that are the achievement
goal for this lesson. Read through them carefully now to gain initial exposure to the terms and
concept names for the lesson. Refer back to the list at the end of the lesson to see if you can
perform each objective.
LessonObjectives
Find the sum of a given set of numbers.
Find the difference between a given set of numbers.
Applications with whole numbers
The key terms listed below will help you keep track of important mathematical words and
phrases that are part of this lesson. Look for these words and circle or highlight them along
with their definition or explanation as you work through the MiniLessons.
 Sum
 Carrying
 Addition Property of 0
 Commutative Property of Addition
 Associative Property of Addition
 Difference
 Borrowing
 Subtraction Properties of 0
KEY TERMS
INTRODUCTION

8
The answer to an addition problem is called the sum or total. If you have $5 and someone gives
you $3 more, you now have increased your total amount of money to $8.
Example 1: Find the sum of 42 + 37
Step 1 Line up the digits with ones under ones, 42
tens under tens, and so on. + 37
79
Step 2 Add each column.
Example 2: Find the sum of 2,973 + 651 + 48
1
Step 1 Line up the digits so the place values 2,973
correspond, then add the place values. 651
+ 48
Step 2 Carrying – when the sum of digits in 2
corresponding place values is 3+1+8=12 ones or 1 ten + 2 ones
more than 9, carrying is necessary.
11
Step 3 Continue adding the place values 2,973
carrying as necessary and adding in 651
the carried numbers. + 48
72
1+7+5+4=17 tens or 1 hundred + 7 tens
111
672
1+9+6=16 hundreds or 1 thousand + 6 hundreds
111
3,672
1+2=3 thousands
ADDITION OF MULTI-DIGIT WHOLE NUMBERS

9
There are a few properties of addition that you may have already known. The first property we
will review is the addition property of zero. This property reminds us that the sum of 0 and any
number is that same number.
The second property we will review is the commutative property of addition. This property
reminds us that changing the order of two numbers does not change the total when we add those
two numbers together.
The third property we will review is the associative property of addition. This property reminds
us that when adding numbers, the grouping of the numbers can be changed without changing
the sum. This can be a very helpful property when adding large groups of numbers together.
In our example we use parentheses to group numbers. They indicate which numbers to add
first.
The commutative and associative properties tell us that we can add whole numbers using any
order and grouping that we want.
When adding several numbers, it is often helpful to look for two or three numbers whose sum
is 10, 20 and so on. Why? Adding multiples of 10 such as 10 and 20 is easier.
AdditionProperty of 0
The sum of 0 and any number is that number. For example,
5 + 0 = 5
0 + 5 = 5
CommutativeProperty of Addition
Changing the order of two numbers does not change their sums. For example,
1 + 2 = 3
2 + 1 = 3
AssociativeProperty of Addition
Changing the grouping of numbers does not change their sums. For example,
1 + (2 + 3) = 1 + 5 = 6 and (1 + 2) + 3 = 3 + 3 = 6

10
Example 3: Add 13 + 2 + 7 + 8 + 9
Step 1 Find numbers whose sums are easier to add together
13 + 2 + 7 + 8 + 9
20 + 10 + 9
30
The answer to a subtraction problem is called the difference. Similar to our example for
addition, if you have $8 and you purchase a soda-pop for $2, you have $6 left. Subtraction is
finding the difference between numbers.
Notice that addition and subtraction are very closely related. In fact, subtraction is defined in
terms of addition.
8 – 2 = 6 because 6 + 2 = 8
This means that subtraction can be checked by addition, and we say that addition and subtraction
are reverse operations.
Example 4: Find the difference between 18 and 7.
Step 1 Put the larger number, 18, on top. 18
Line the digits up with units under units, - 7
Tens under tens, and so on. Start 1
Subtracting with the units. 8 – 7 = 1
Step 2 Continue subtracting with the units. 18
1 – 0 = 1 - 07
There is an imaginary 0 in the tens place 11
for single digit numbers.
SUBTRACTION OF MULTI-DIGIT WHOLE NUMBERS

11
Example 5: Find the difference between 145 and 739.
Step 1 Put the larger number, 739, on top. 739
Line the digits up with units under units, - 145
Tens under tens, and so on. Start 4
Subtracting with the ones. 9 – 5 = 4
Step 2 Borrowing - when the second number is 739
Larger than the first number, then - 145
borrowing is necessary. 4
In this situation, the 4 is larger than the 3 in
our tens column so we need to borrow from
the hundreds column.
7 – 1 = 6 6 13
hundreds hundred hundreds 7 3 9 1 + 3 = 13
- 1 4 5 hundred tens tens
4
Step 3 Regroup and subtract from the tens 6 13
column. 7 3 9
- 1 4 5
13 – 4 = 9 9 4
Step 4 Subtract from the hundreds column. 6 13
7 3 9
- 1 4 5
6 – 1 = 5 5 9 4
Subtraction Properties of 0
The difference of any number and that same number is 0. For example,
45 – 45 = 0
The difference of any number and 0 is that same number. For example,
45 – 0 = 45

12
YOU TRY
1. Find the sum of the following problems.
5 + 48 = 7,548
+ 2,361
329 + 157 = 2,137
824
+ 8,672
2. Solve each problem.
62 – 39 = 36,225 – 9,949 =
4,005 – 689 = 487 – 412 =

13
“Applications” ask you to use math to solve real-world problems. To solve these problems
effectively, begin by identifying the information provided in the problem (GIVEN) and
determine what end result you are looking for (GOAL). The GIVEN should help you
write mathematics that will lead you to your GOAL. Once you have a result, CHECK that
result for accuracy then present your final answer in a COMPLETE SENTENCE
Even if the math seems easy to you in this application, practice writing all the steps, as the
process will help you with more difficult problems.
Example 6: Xzavier solved 23 homework problems on Monday, 14 on Tuesday, 40 on
Wednesday, 7 on Thursday, and took a test with 115 problems on Friday. How many
problems did he solve this week?
GIVEN: [Write down the information that is provided in the problem. Diagrams can be
helpful as well.]
GOAL: [Write down what it is you are asked to find. This helps focus your efforts.]
MATH WORK: [Show your math work to set up and solve the problem.]
CHECK: [Is your answer reasonable? Does it seem to fit the problem? A check may not
always be appropriate mathematically but you should always look to see if your result
makes sense in terms of the goal.]
FINAL RESULT AS A COMPLETE SENTENCE: [Address the GOAL using a
complete sentence.]
APPLICATIONS WITH WHOLE NUMBERS

14
YOU TRY
3. In 2015, 135 students attended the Veterans Upward Bound refresher courses on
Tuesdays and Thursdays. 26 students attended either the Saturday or Evening classes
that were offered and 11 students completed Individual Study Programs. How many
total students went through the VUB program in 2015?
GIVEN:
GOAL:
MATH WORK:
CHECK:
FINAL RESULT AS A COMPLETE SENTENCE:

15
Example 7: Bryan has completed 2,756 hours of coursework towards his degree. He must
complete a total of 3,200 hours in order to graduate. How many hours does he still need to
complete?
GIVEN: [Write down the information that is provided in the problem. Diagrams can be
helpful as well.]
GOAL: [Write down what it is you are asked to find. This helps focus your efforts.]
MATH WORK: [Show your math work to set up and solve the problem.]
CHECK: [Is your answer reasonable? Does it seem to fit the problem? A check may not
always be appropriate mathematically but you should always look to see if your result
makes sense in terms of the goal.]
FINAL RESULT AS A COMPLETE SENTENCE: [Address the GOAL using a
complete sentence.]

16
YOU TRY
4. Tarquin’s gross pay for two weeks is $1,356. If her deductions are $238, what is her
net pay?
GIVEN:
GOAL:
MATH WORK:
CHECK:
FINAL RESULT AS A COMPLETE SENTENCE:

17
LESSON 2 – PRACTICEPROBLEMS
1. Solve each problem
a. 62 + 39
b. 158 + 237
c. 3,009 + 5,478
d. 461,345 + 28 + 495
e. 6,540 + 32 + 812 + 8 + 18
2. Find the difference.
a. 62 - 39
b. 765 - 496
c. 5,002 – 3,874
3. Solve each of the following applications showing as much work as
possible. Use the problem-solving process described in the lesson to write
your solution.
a. Mark deposited $450, $312, $125, and $432 in his bank account this
month. He also made deductions of $205 and $123. If his balance at the
beginning of the month was $1233, what was his balance at the end of the
month?
b. Jenelle financed a 2012 Chevy Camaro on 60-month terms for $673 per
month. If the MSRP on the car was $35,000 and she put no money down,
how much over the MSRP did she end up paying?
c. In the winter, the farmer’s market sees an average of 1516 visitors each
Sunday. In the summer, they see an average of 4278 visitors each Sunday.
How many more visits are there in the summer than in the winter (on
average)?
3. Solve each of the following applications showing as much work as possible. Use the problem-
solving process described in the lesson to write your solution.
a. Mark deposited $450, $312, $125, and $432 in his bank account this month. He
also made deductions of $205 and $123. If his balance at the beginning of the
month was $1233, what was his balance at the end of the month?
b. Jenelle financed a 2012 Chevy Camaro on 60-month terms for $673 per month.
If the MSRP on the car was $35,000 and she put no money down, how much
over the MSRP did she end up paying?
c. In the winter, the farmer’s market sees an average of 1516 visitors each Sunday.
In the summer, they see an average of 4278 visitors each Sunday. How many
more visits are there in the summer than in the winter (on average)?

18
LESSON 2 – ASSESS YOUR LEARNING
Solve each of the following applications showing as much work as possible. Use the problem-
solving process described in the lesson to write your solution.
1. The Cleveland Indians won 81 games in 2015. They won 85 in 2014, 92 in 2013, 68 in 2012,
80 in 2011 and 69 in 2010. How many total games have they won in that time span?
2. As a franchise, the Cleveland Indians have a record of 8037 wins and 7738 losses from 1915-
2015. How many more wins than losses do they have?
How many wins did they have between 1915 and 2010? (refer to question 5)
3. According to baseball-reference.com, Cleveland has had a professional baseball team since
1901. That year, the Cleveland Blues had a record of 54 wins and 82 losses. In 1902, the team
was called the Cleveland Bronchos and went 69-67. The team changed their name to the
Cleveland Naps (after Napoleon Lajoie) in 1903 and went on to have a successful run from
1903-1914 with a record of 937-883. They have been known as the Cleveland Indians since
1915 (8037-7738 as Indians). What are the total wins and losses for the Cleveland professional
baseball teams since 1901?
4. Amy deposited $325, $473, $224 and $653 into her checking account one month. She paid
bills in the amounts of $54, $127, $96 and $685. How much money does she have left over
after paying her bills?

Lesson 2 Addition & Subtraction

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

Similar to Lesson 2 Addition & Subtraction

Similar to Lesson 2 Addition & Subtraction (20)

Recently uploaded

Recently uploaded (20)

Lesson 2 Addition & Subtraction