1. Chapter 1
Whole Numbers
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2. Copyright © 2010 Pearson Education, Inc. All rights reserved.
1.2 Adding Whole Numbers
Objectives
1. Add two single-digit numbers.
2. Add more than two numbers.
3. Add when regrouping (carrying) is not required.
4. Add with regrouping (carrying).
5. Use addition to solve application problems.
6. Check the answers in addition.
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Parallel
Example 1
Adding Two Single-Digit Numbers
Add, and then change the order of numbers to write another addition problem.
7 + 6 = 13 and = 13
b = 15 and = 15
c = 10 and = 10
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The sum of may be found as follows.
(6 + 7) + 8 = = 21
Another way to add the same numbers is
6 + (7 + 8) = = 21
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Parallel
Example 2
Adding More Than Two Numbers
Add 3, 4, 6, 2, and
3 + 4 = 7
7 + 6 = 13
= 15
= 20 20
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Parallel
Example 3
Adding without Regrouping
Add
Hundreds, tens and ones in a column 5 5 9
Sum of ones
Sum of tens
Sum of hundreds
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Parallel
Example 4
Adding with Regrouping
Add 48 and 1 8 4
8 ones and 6 ones = 14 ones
Regroup 14 ones as 1 ten and 4 ones. Write 4 ones in the ones column and write 1 ten in the tens column.
Add the digits in the tens column, including the regrouped 1.
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Parallel
Example 5
Adding with Regrouping (Carrying)
Add 1 1 2
Sum the ones column (29). Write 9 in the ones column and write 2 in the tens column.
Sum the tens column (19). Write 9 in the tens column and write 1 in the hundreds column.
Sum the hundreds column, including the regrouped 1. 8 9 9
Sum the thousands column, including the regrouped 1.
The sum is 8099.
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Parallel
Example 6
Applying Addition Skills
On this map of the Walt Disney World area in Florida, the distance in miles from one location to another is written alongside of the road. Find the shortest route from Orlando to Belle Isle. Solution
Add the mileage along various routes to determine the distances from Orlando to Belle Isle.
Orlando to Resort 9
Resort to Pine 6
Pine to Belle _3_
18 miles
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11. Applying Addition Skills
Parallel
Example 6
Applying Addition Skills
On this map of the Walt Disney World area in Florida, the distance in miles from one location to another is written alongside of the road. Find the shortest route from Orlando to Belle Isle. Solution
Another possible route:
Orlando to Clear Lake 9
Clear Lake to Shadow 6
Shadow to Conway 3
Conway to Belle _6_
24 miles
The shortest route is from Orlando to Resort Area to Pine Castle to Belle Island, 18 miles
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Parallel
Example 7
Finding a Total Distance
Use the map to find the total distance from Bertha to Clear Lake to Shadow Hills and back to Bertha. Solution
Add the mileage from Bertha to Clear Lake to Shadow Hills to Bertha.
Bertha to Winter Park
Winter Park to Clear Lake
Clear Lake to Shadow Hills 11
Shadow Hills to Bertha _
34 miles
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Parallel
Example 8
Finding a Perimeter
Find the number of feet of fencing needed enclose the farm pasture shown. Solution
1575 ft
Find the perimeter, or total distance around the pasture by adding the lengths of all the sides.
375 ft
375 ft
1575
375
+ 375
1575 ft
3900 miles
The amount of fencing needed is 3900 ft.
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Parallel
Example 9
Checking Addition
Check the following addition
7 6 6
Add down.
7 6 6
To check, add up.
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15. Chapter 1
Whole Numbers
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16. 1.3 Subtracting Whole Numbers
Objectives
1. Change addition problems to subtraction and
subtraction problems to addition.
2. Identify the minuend, subtrahend, and difference.
3. Subtract when no regrouping (borrowing) is needed.
4. Check subtraction answers by adding.
5. Subtract with regrouping (borrowing).
6. Solve application problems with subtraction.
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Parallel
Example 1
Changing Addition Problems to Subtraction
Change the addition problem = 8 to a subtraction problem. Two subtraction problems are possible. 8 – 2 = 6 or 8 – 6 = 2 8 – 2 = 6 8 – 6 = 2
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Parallel
Example 2
Changing Subtraction Problems to Addition
Change each subtraction problem to an addition problem.
9 – 4 = 5
9 = 4 + 5
It is also correct to write 9 =
21 – 8 = 13
21 = or 21 =
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In subtraction, as in addition, the numbers in a problem have names. 12 – 8 = 4 12 is the minuend 8 is the subtrahend 4 is the difference or answer 12 – 8 = 4
Difference
Minuend
Subtrahend
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Parallel
Example 3
Subtracting Two Numbers
Subtract – 2 4 1
Digits are lined up.
Subtract from right to left. 6 3 3
7 tens – 4 tens
4 ones – 1 one
8 hundreds – 2 hundreds
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Parallel
Example 4
Checking Subtraction by Using Addition
Use addition to check the answer. If the answer is incorrect find the correct answer – 1 2 3 2 3 3
Match
Rewrite as an addition problem.
233
+ 123
356
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Parallel
Example 5
Subtracting with Regrouping
Subtract 28 from – 2 8 6 12
2 is less than 8, so we must regroup 1 ten as 10 ones.
7 tens – 1 ten = 6 tens 4 4
Now subtract 8 ones from 12 ones in the ones column. Then subtract 2 tens from 6 tens in the tens column.
You can check by adding 44 and 28; you should get 72.
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Parallel
Example 6
Subtracting with Regrouping
Subtract by regrouping when necessary. a – 2 4 5 4 13 6 7 8
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Parallel
Example 6
Subtracting with Regrouping
Subtract by regrouping when necessary. b – 4 5 3 12 6 2 12 2 7 9
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Parallel
Example 7
Regrouping with Zeros
Subtract – 9 6 10 18 3 5 2 9
There are no tens that can be regrouped into ones. So you must first regroup 1 hundred as 10 tens.
Now we may regroup from the tens position.
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Parallel
Example 8
Regrouping with Zeros
Subtract – 9 9 7 10 10 10 5 1
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Parallel
Example 10
Applying Subtraction Skills
Use the table to find how much more, on average, a person with a Professional degree earns each year than a person with a Bachelor’s degree. Solution
Find the average earnings of each type of degree and subtract.
Professional $118,785
Bachelor’s $ 56,655
$62,130 more earnings
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28. Chapter 1
Whole Numbers
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29. 1.7 Rounding Whole Numbers
Objectives
1. Locate the place to which a number is to be rounded.
2. Round numbers.
3. Round numbers to estimate an answer.
4. Use front end rounding to estimate an answer.
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Parallel
Example 2
Using Rounding Rules for 4 or Less
Round 643 to the nearest hundred. Step 1 Step 2 Step 3
Locate the place to which the number is being rounded. Draw a line under that place.
643
Because the next digit to the right of the underlined place is 4, which is 4 or less, do not change the digit in the underlined place.
Next digit is 4 or less.
643
6 remains 6.
Change all digits to the right of the underlined place to zeros.
643 rounded to the nearest hundred is 600.
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Parallel
Example 3
Using Rounding Rules for 5 or More
Round 27,621 to the nearest thousand. Step 1 Step 2 Step 3
Locate the place to which the number is being rounded. Draw a line under that place.
27,621
Because the next digit to the right of the underlined place is 6, which is 5 or more, add 1 to the underlined place.
Next digit is 5 or more.
27,621
Change 7 to 8.
Change all digits to the right of the underlined place to zeros.
27,621 rounded to the nearest thousand is 28,000.
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Parallel
Example 4
Using Rounding Rules
a. Round 2271 to the nearest ten. Step 1 Step 2 Step 3
2271
The next digit to the right is 1, which is 4 or less.
Next digit is 4 or less.
2271
Leave 7 as 7.
Change to 0.
2270
2271 is closer to 2270 than to 2280.
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Parallel
Example 4
Using Rounding Rules
b. Round 14,972 to the nearest hundred. Step 1 Step 2 Step 3
14,972
The next digit to the right is 7.
Next digit is 5 or more.
14,972
Change 9 to 10; write 0 and regroup 1 into thousands place.
Change to 0.
15,072
14,972 is closer to 15,000 than to 14,000.
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35. Rounding Large Numbers
Parallel
Example 5
Rounding Large Numbers
Round 48,751 to the nearest ten-thousand. Step 1 Step 2 Step 3
48,751
The next digit to the right is 8.
Next digit is 5 or more.
48,751
Change 4 to 5.
58,751
Change to 0.
48,751 rounded to the nearest ten-thousand is 50,000.
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Parallel
Example 6
Rounding to Different Places
Round 736 to the (a) nearest ten and (b) the nearest hundred.
nearest ten
b. nearest hundred
Next digit is 5 or more.
736
Tens place (3 + 1 = 4)
736 rounded to the nearest ten is 740.
Next digit is 4 or less.
736
Hundreds place stays the same.
736 rounded to the nearest hundred is 700.
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Parallel
Example 8
Using Rounding to Estimate an Answer
Estimate each answer by rounding to the nearest ten. a. 28 30 41 40
Rounded to the
nearest ten 91 90 + 46 + 50
210
Estimated answer
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Parallel
Example 8
Using Rounding to Estimate an Answer
Estimate each answer by rounding to the nearest ten. b. 65 70
Rounded to the
nearest ten 38 – 40 – 30
Estimated answer
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Parallel
Example 8
Using Rounding to Estimate an Answer
Estimate each answer by rounding to the nearest ten. c. 72 70
Rounded to the
nearest ten 46 x 50 x
3500
Estimated answer
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Parallel
Example 9
Using Rounding to Estimate an Answer
Estimate each answer by rounding to the nearest hundred. a.
723
700
285
300
Rounded to the
nearest hundred
197
200 +
644 +
600
1800
Estimated answer
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Parallel
Example 9
Using Rounding to Estimate an Answer
Estimate each answer by rounding to the nearest hundred. b.
832
800
Rounded to the
nearest hundred –
274 –
300
500
Estimated answer
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A convenient way to estimate an answer is to use front end
rounding. With front end rounding, we round to the highest
possible place so that all digits become 0 except for the first
one.
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43. Copyright © 2010 Pearson Education, Inc. All rights reserved.
Parallel
Example 10
Using Front End Rounding to Estimate an Answer
Estimate each answer using front end rounding. a. 38 40
All digits changed to
0 except first digit,
which is rounded
1624
2000
4178
4000 +
339 +
300
6340
Estimated answer
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Parallel
Example 10
Using Front End Rounding to Estimate an Answer
Estimate each answer using front end rounding. b.
5162
5000
First digit rounded and
all others changed to 0. –
875 –
900
4100
Estimated answer
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Parallel
Example 10
Using Front End Rounding to Estimate an Answer
Estimate each answer using front end rounding. c.
8250
8000
First digit rounded and
all others changed to 0. x 36 x 40
320,000
Estimated answer
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46. Chapter 1
Whole Numbers
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47. 1.4 Multiplying Whole Numbers
Objectives
1. Identify the parts of a multiplication problem.
2. Do chain multiplication.
3. Multiply by single-digit numbers.
4. Use multiplication shortcuts for numbers ending in zero.
5. Multiply by numbers having more than one digit.
6. Solve application problems with multiplication.
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Parallel
Example 1
Multiplying Two Numbers
Multiply.
a. 4 × 7 =
b. 8 ∙ 0 =
c. 7(6) = 28 42
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51. Multiplying Three Numbers
Parallel
Example 2
Multiplying Three Numbers
Multiply 5 × 4 × 3.
(5 × 4) × 3 20
× 3
= 60
Also,
5 × (4 × 3)
5 × 12
= 60
Either grouping results in the same product.
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Parallel
Example 3
Multiplying with Regrouping
Multiply × 4 1 2
2 5 8
4 × 7 = 28 ones, write 8 ones; write 2 tens in the tens column.
4 × 2 = 8 tens, add the 2 regrouped tens to get 10 tens. Write 0 tens and 1 hundred in the hundreds column.
4 × 6 hundreds = 24 hundreds; add the1 regrouped hundred to get 25 hundreds.
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Parallel
Example 4
Using Multiples of 10 to Multiply
Multiply.
a. 29 × 10 =
b. 53 × 100 =
c × 1000 =
290
Attach 0.
5300
Attach 00.
409,000
Attach 000.
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Parallel
Example 5
Using Multiples of 10 to Multiply
Multiply. 25 × 5000
Multiply 25 by 5, then attach the three zeros. 25
× 5
125
25 × 5000 = 125,000
Attach 000.
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Parallel
Example 6
Multiplying with More Than One Digit
Multiply 58 and 24. First multiply 58 by 4. 3
Regrouping is needed here. 58
× 4
232
Now multiply 58 by 20. 58
× 20
1160
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56. Multiplying with More Than One Digit
Parallel
Example 6
continued
Multiplying with More Than One Digit
Multiply 58 and 24.
Add the results. 58
× 24
232
+ 1160
58 × 4
58 × 20
1392
Add.
Both 232 and 1160 are called partial products. To save time, the 0 in the 1160 is usually not written.
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Parallel
Example 7
Using Partial Products
Multiply.
3 4 4 ×
6 8 8
Tens lined up.
Hundreds lined up.
4 1, 6 2 4
Product
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Parallel
Example 8
Multiplying with Zeros
Multiply.
5 2 9 ×
0 0 0
Tens lined up.
Hundreds lined up.
2 1 2, 6 5 8
Product
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Parallel
Example 9
Applying Multiplication Skills
Find the cost of 27 lamps priced at $92 each.
Approach
Multiply the number of lamps (27) by the cost of one lamp ($92).
Solution
2 7
× 9 2
5 4
2 4 3
The total cost of the lamps is $2484.
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60. Chapter 1
Whole Numbers
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61. 1.8 Exponents, Roots, and Order of Operations
Objectives
1. Identify an exponent and a base.
2. Find the square root of a number.
3. Use the order of operations.
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Parallel
Example 1
Simplifying Expressions
Identify the exponent and the base and then simplify each expression.
a. 35
Exponent
Base 35
35 = 3 × 3 × 3 × 3 × 3
= 243
b. 73
73 = 7 × 7 × 7
= 343
The base is 7 and the exponent is 3.
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Parallel
Example 2
Using Perfect Squares
Find each square root. a. b. c.
= 8
= 11
= 14
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