Mathematics is important to all world cultures, including our world of work. The following are just some of the ways in which studying math will help you:

- You will know how much money you are spending at the store.
- You will know if the cashier has given you the right change.
- You will know how to use measurements to build things.
- Your science classes will be easier and more interesting.
- You will understand music on a whole new level.
- You will be empowered to qualify for and land a rewarding job.

Addition and subtraction are important parts of life. Test grades and stock market changes are calculated using them, as well as batting averages and other sports statistics, baker’s ingredients, and chemical formulas. You don’t usually go through a day without needing to add or subtract something. Addition and subtraction are also the building blocks for more advanced math.

Adding One-Digit Numbers

One-digit numbers are all around you. They are the basis of any number system. One-digit numbers include the following whole numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The next whole number, 10, represents a group of ten ones. Once you learn how to add one-digit numbers and how to regroup them, adding larger numbers will be a snap.

Adding One-Digit Numbers without Regrouping

One-digit addition without regrouping will give you a sum that is less than ten. Here are all the one-digit numbers whose sums are less than ten.

The sum of 3 + 4 is the same as the sum of 4 + 3.

3 + 4 = 7 and 4 + 3 = 7

Adding One-Digit Numbers with Regrouping

6 ones + 5 ones = 11 ones

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The sum of 6 + 5 is the same as the sum of 5 + 6. This property of addition, called the commutative property.

Column Addition

Column addition is the addition of three or more numbers. You use column addition when you go shopping, add test grades, or find the number of inches of rainfall for a given month, season, or year.

Column Addition without Regrouping

Suppose you are a meteorologist (weather forecaster) and you have to keep track of the rainfall for one week. It rained 2 inches on Monday, 3 inches on Wednesday, and 4 inches on Saturday. What was the total rainfall for the week?

The order in which these numbers are added will not change the answer, or sum. The numbers to be added are called addends.

Add 2 + 3 + 4

In column addition, arrange the numbers that you are going to add underneath each other, in a column.

Step 1: Add the first two numbers. 2 + 3 = 5

Step 2: Add the answer in step 1 to 5 the third number. 5 + 4 = 9

The total rainfall for the week was 9 inches.

Adding Two-Digit Numbers

Accountants add two-digit numbers every day. They keep accounts for companies, public offices, and private households. An accountant was given the responsibility to add the following two-digit numbers: 56 and 31. Here is how to find the sum for the accountant.

Adding Two-Digit Numbers without Regrouping

When adding two-digit numbers, first add the numbers in the ones column. Then add the numbers in the tens column. Addition is always done from right to left, beginning in the ones column.

Add 56 + 31

Step 1: Add ones. 56 + 31 =?7

Record 7 ones.

Step 2: Add tens. 56 + 31 = 87

Record 8 tens.

The addends are 56 and 31. The sum of 56 and 31 is 87. You did not have to regroup, since the ones column did not add up to more than 9.

Adding Two-Digit Numbers with Regrouping

Add the numbers in the ones column. When there are ten or more ones, use regrouping. Exchange 10 ones for 1 ten and regroup ones.

Add 87 + 49

Step 1: Add the ones. 87 + 49 =?6

(7 + 9 = 16ones).

Record 1 ten 6 ones.

Next add tens and regroup them if necessary. When there are ten or more tens, use regrouping. Exchange 10 tens for 1 hundred.

Step 2: Add tens. 87 + 49 = 136

(1 + 8 + 4 = 13 tens).

Record 1 hundred 3 tens.

Adding Three-Digit Numbers

Adding Three-Digit Numbers without Regrouping

When adding three-digit numbers without regrouping, first add the ones column. Next add the tens column. Finally add the hundreds column. Remember to always add from right to left, recording each column sum until all the addition is complete.

Add 543 + 136

Step 1: Add ones. 543 + 136 =??9

Step 2: Add tens. 543 + 136 =?79

Step 3: Add hundreds. 543 + 136 = 679

Adding Three-Digit Numbers with Regrouping

Remember that regrouping occurs when a column sum is greater than 9. When a column sum is regrouped, that number must be added to the column on its immediate left.

Add 758 + 467

Step 1: Add ones (8 + 7 = 15 ones). 758 + 467 =??5 – Record 1 ten 5 ones.

Step 2: Add tens (1 + 5 + 6 =12 tens). 758 + 467 =?25 – Record 1 hundred 2 tens.

Step 3: Add hundreds (1 + 7 + 4 = 12 hundreds). 758 + 467 = 1225

Adding Greater Numbers

We can add greater numbers using place value and partial sums. Greater numbers consist of whole numbers that have four or more digits, such as 1,542; 59,871; and 990,245. You can add two four-digit numbers using place value.

Adding Greater Numbers Using Place Value

Basic Fact: 4 + 1 = 5

By putting a zero to the right of each number, you now have:

40 + 10 = 50, or 4 tens + 1 ten = 5 tens

Five tens is the same as fifty.

Basic Fact: 1 + 6 = 7

By attaching three zeros to the right of each number, you now have: 1,000 + 6,000 = 7,000, or

1 thousand + 6 thousands = 7 thousands

Add 1,542 + 6,315 using place value

Step 1: Write the value. 1,542 + 6,315 = (1 + 6 thousands),(5 + 3 hundreds)(4 + 1 tens)(2 + 5 ones)

Step 2: Write the sum. 7,857

Adding Greater Numbers Using Partial Sums

Partial sums is another method used when adding greater numbers. Partial sums uses place value to find the sum of two or more numbers.

To add 28,634 and 57,918 by partial sums, first list the place value of each digit.

Add 28,634 + 57,918

Step 1: Add ones. 4 + 8 = 12

Step 2: Add the partial sum 12 to the sum of tens. 12 + 30 + 10 = 52

Step 3: Add the partial sum 52 to the sum of hundreds. 52 + 600 + 900 = 1,552

Step 4: Add the partial sum 1,552 to the sum of thousands. 1,552 + 8,000 + 7,000 = 16,552

Step 5: Add 16,552 to the sum of ten thousands. 16,552 + 20,000 + 50,000 = 86,552

Addition Properties

You can use the basic addition properties to solve problems.

There are three basic addition properties:

1. Commutative Property

2. Associative Property

3. Zero Property

Commutative Property

The commutative property of addition means that, when adding any two numbers, the order in which you add them does not change the sum. You can remember the name by thinking about

people who commute to work. When they commute, they change places.

Is the sum of 10 + 30 the same as the sum of 30 + 10?

Add: 10 + 30 = 40

Add: 30 + 10 = 40

The sums are the same. So, order is not important when adding two numbers.

Associative Property

The associative property of addition means that when adding three or more numbers, the way in which the numbers are grouped, or associated, does not affect the sum. You can try this with the problem on the following page.

Your best friend loves to eat fruit. In one week he ate 5 pears, 6 peaches, and 4 apples. How many pieces of fruit did your best friend eat that week?

Add: 5 + 6 + 4

You can group these numbers in two different ways. You can place parentheses around the first two numbers:

(5 +6) +4 or you can place the parentheses around the second two numbers:

5 + (6 + 4)

Always do the work in the parentheses first.

Is the sum of (5 + 6) + 4 the same as the sum of 5 + (6 + 4)?

(5 + 6)+ 4 = 11 + 4 = 15

5 + (6 + 4) = 5 + 10 = 15

The sums are the same. The way in which you group three or more numbers does not affect the sum.

The Zero Property

The zero property of addition means that the sum of any number and zero is always that number.

Add: 3+ 0 = 3

Add: 57+ 0 = 57

When you add any number and zero, the sum will always be the number.

Adding Time Values

Units of Time

1 minute = 60 seconds

1 hour = 60 minutes

1 day = 24 hours

1 week = 7 days

1 year = 52 weeks

1 year = 12 months

1 year = 365 days

1 decade = 10 years

1 century = 100 years

Adding Time Values without Regrouping

To add measurements of time, add measurements with the same units.

Add 4 hours 40 minutes + 3hours 10 minutes

Step 1: Add minutes. 4 hours 40 minutes + 3 hours 10 minutes =? hours 50 minutes

Step 2: Add hours. 4 hours 40 minutes + 3 hours 10 minutes = 7 hours 50 minutes

Adding Time Values with Regrouping

To add time with regrouping, add measurements of the same units. If the sum of the minutes is sixty or greater, change minutes to hours.

Add 8 hours 35 minutes + 9 hours 50 minutes

Step 1: Add minutes. 7 hours 35 minutes + 8 hours 50 minutes =? hours 85 minutes

Step 2: Regroup minutes for hours. 85 minutes = 1 hour and25 minutes

Step 3: Add hours. 1 hour (regrouped) + 6 hours + 9 hours + 25 minutes = 16 hours 25 minutes

Adding Decimals

People have been studying the decimal system for over 2,500 years. Before the decimal system was created, shopkeepers used wooden or metal counters. The decimal system made it easy to do arithmetic with only paper and pencil.

Look at the following number: 13.25 (1 tens + 3 ones + 2 tenths + 5 hundredths).

Values to the left of the decimal point represent whole numbers, and values to the right of the decimal point represent fractions. The place to the immediate right of a decimal point has the fractional value of tenths, and the place to the right of that has a fractional value of hundredths.

Adding Decimals with the Same Number of Decimal Places

Add 3.9 + 1.7

Step 1: Line up the decimals. 3.9 + 1.7

Step 2: Add tenths. 3.9 + 1.7 =?.6

Regroup if necessary (16 tenths = 1 one 6 tenths).Place the decimal point in the sum.

Step 3: Add ones. 1 + 3.9 + 1.7 = 5.7

Adding Decimals with Different Numbers of Decimal Places

When adding decimals with different numbers of decimal places, you can add zeros to the right of the last digit. The zeros are called placeholders. Then each number will have the same number of digits.

Add 5.6 + 3.59

Step 1: Line up the decimals. 5.6 + 3.59

Step 2: Insert a zero as a placeholder. 5.60 + 3.59

Step 3: Add hundredths. 5.60 + 3.59 =?.?9

Step 4: Add tenths. 5.60 + 3.59 =?.19

Regroup (6 + 5 = 11 tenths = 1 one 1 tenth).

Place the decimal point in the sum.

Step 5: Add ones. 1.19 + 5.00 + 3.00 = 9.19

Make a list of household objects that include measurements with decimals. Remember to check the kitchen cabinets and freezer.

Adding Monetary Values

Currency or money, represents monetary value. The ability to add and subtract monetary value is a skill used in many daily situations. You often use coins and paper currency to purchase items you need.

Coins Value in cents Value in dollars

1 penny = $0.01

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

1 half-dollar = $0.50

A teacher bought a book and gave the cashier 3 halfdollars, 4 quarters, 5 dimes, and 1 nickel. The cashier asked the teacher for three pennies. How much did the book cost?

Solution: Using addition, figure out the total value for each type of coin.

2* $0.5 = $0.5 + $0.5 = $1

3* $0.25 = $0.25 + $0.25 + $0.25 = $0.75

4* $0.1 = $0.1 + $0.1 + $0.1 + $0.1 = $0.4

1* $0.$05 = $0.05

3* $0.$01 = $0.$03

1 + $0.75 + $0.4 + $0.$05 + $0.03 = $1 + $0.7$0 + $0.40 + $0.13 = $1 + $1.1 + $0.13 = 2.23

Adding Integers

When you first learned to count, you used the set of counting numbers: 1, 2, 3, 4,…

If you include a zero in this set, you have the set of whole numbers: 0, 1, 2, 3, 4,…

You can expand this set by adding negative numbers to the left of zero on the number line. These are the set of integers.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Integers to the right of zero are called positive numbers. Integers to the left of zero are called negative numbers.

Adding Fractions

Fractions are used by carpenters to measure the materials for woodworking projects, by dressmakers to determine the amount of material needed to make a garment, and by cooks to follow recipes. Fractions show the relationship between a part and the whole item. The numerator is the number at the top of the fraction. It tells you how many parts are being considered. The denominator is the number on the bottom of the fraction. It tells you the total number of parts there are.

Adding Like Fractions

Like fractions are fractions with the same, or common, denominator.

For example, 1/4and are like fractions because they have a common denominator of 4.

Step 1: Add the numerators and place them over the common denominator. (1+3)/4

(1+3) are numerators and 4 is denominator.

Step 2: Find the sum. (1+3)/4 = 4/4

Step 3: Reduce to lowest terms. 4/4 = 1

4/4 is the same as one whole.

Adding Unlike Fractions

Add 1/3 + 1/6

Step 1: Find a common denominator. 1/3 is the same as 2/6.

Step 2: Add the numerators and place them over the denominator. 2/6 + 1/6 = (2+1)/6 = 3/6

Step 3: Reduce to lowest terms. 3/6 = (3:3)/(6:3) = 1/2