Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Estimating with Whole Numbers
In mathematics, you can find an estimate when an exact answer is
not needed. An estimate is close to the exact answer.
You can use rounding to estimate sums and differences.
A. Estimate the sum by rounding to
the hundreds.
23,848
→
24,000
+ 7,136 → + 7,100
− 16,132
→
− 16,000
___________________________
___________________________
3,478
→
B. Estimate the difference by rounding
to the thousands.
3,500
10,600
8,000
Estimate each sum or difference by rounding to the place value
indicated.
1. hundreds
2. thousands
789
→
+ 453
→
+
4,987
→
− 2,348
→
−
___________________________
___________________________
_______________________________________
________________________________________
3. tens
4. tens
456
→
+ 875
→
+
876
→
− 432
→
−
___________________________
___________________________
_______________________________________
________________________________________
5. hundreds
6,898
6. thousands
→
+ 2,671 →
+
1,857
→
+ 3,598
→
+
___________________________
___________________________
_______________________________________
________________________________________
7. hundreds
8,813
8. thousands
→
− 2,384 →
−
9,128
→
− 4,716
→
−
___________________________
___________________________
_______________________________________
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Estimating with Whole Numbers (continued)
You can use rounding and basic facts to estimate products. Count
the number of zeros in your rounded numbers. They will appear to
the right of the basic fact in your estimate.
Estimate 8 × 532.
8 × 532
↓ ↓
8 × 500 Round each factor.
↓ ↓
4,000
two zeros
Use rounding to estimate each product.
9. 28 × 5
↓ ↓
_______________
10. 78 × 11
↓
↓
_______________
11. 67 × 19
↓
↓
_______________
12. 93 × 7
↓ ↓
________________
Compatible numbers are numbers that are easy to compute
mentally. One compatible number divides evenly into the other.
Estimate the quotient of 553 ÷ 8.
Step 1: What are the multiples of 8?
8 16 24 32 40 48 56 64
Which multiple is closest to 55?
56 is close to 55.
8 and 560 are compatible numbers.
Step 2: Divide. 560 ÷ 8 = 70
Use compatible numbers to estimate each quotient.
13. 748 ÷ 25
_______________
14. 557 ÷ 8
_______________
15. 417 ÷ 7
_______________
16. 241 ÷ 3
________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Divide Multi-Digit Whole Numbers
Division is used to separate a quantity into a given number of equal parts.
It is also used to separate a quantity into parts of a specific size.
A division algorithm breaks division with greater numbers into a series of lesser
divisions. Follow the steps for each lesser division:
Step 1: Divide and write the number in the first correct place the quotient.
Step 2: Multiply the divisor by the number in the quotient.
Step 3: Subtract.
Step 4: Bring down the next digit in the dividend.
Repeat these steps until there are no digits from the dividend left to bring down.
÷
×
−
↓
repeat
Jon bought a package of 792 labels. There are 24 sheets of labels in the package.
How many labels are on each sheet?
24 792
÷
×
−
↓
33
Problem 1
24 792
− 72
_____
Problem 2
repeat
Divide to find the number of labels per sheet.
792 labels ÷ 24 sheets
Divide. 79 ÷ 24 = 3. Place 3 in the tens place.
Multiply. 24 × 3 = 72
Subtract. 79 − 72 = 7
Bring down the next digit in the dividend: 2.
72
− 72
Repeat the process.
Divide.72 ÷ 24 = 3. Place 3 in the hundreds place.
____
Multiply. 24 × 3 = 72
0
Subtract. 72 − 72 = 0
792 ÷ 24 = 33. There are 33 labels on each sheet.
Use the 4-step process to answer the division.
The art teacher has a box of 473 markers. She wants to distribute them evenly among
11 tables. How many markers will she put on each table?
Divide: 47 ÷________ = ________
÷
×
−
↓
repeat
Multiply: 11 × ________ = ________
11 473
Subtract: 47 − ________ = ________
Bring down the ________.
Repeat the steps.
Divide: ________ ÷ ________ = ________
Multiply: ________ × ________ = ________
Subtract: ________ − ________ = ________
Answer: ________ markers
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Exponents
You can write a number in exponential form to show repeated
multiplication. A number written in exponential form has a base
and an exponent. An exponent tells you how many times a number,
called the base, is used as a factor.
8 ← exponent
↑
base
4
Write the expression in exponential form.
6×6×6
6 is used as a factor 3 times.
3
6×6×6=6
Write each expression in exponential form.
1. 8 × 8 × 8 × 8 × 8
_______________
2. 3 × 3
_______________
3. 5 × 5 × 5 × 5
_______________
4. 7 × 7 × 7
________________
You can find the value of expressions in exponential form.
Find the value.
5
2
Step 1: Write the expression as repeated multiplication.
5
2 =2×2×2×2×2
Step 2: Multiply.
2 × 2 × 2 × 2 × 2 = 32
2 = 32
5
Find each value.
5. 12
3
_______________
6. 6
5
_______________
7. 10
4
_______________
8. 4
6
________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Order of Operations
A mathematical phrase that includes only numbers and operations
is called a numerical expression.
9 + 8 × 3 ÷ 6 is a numerical expression.
When you evaluate a numerical expression, you find its value.
You can use the order of operations to evaluate a numerical expression.
Order of Operations
1. Do all operations within parentheses.
2. Find the values of numbers with exponents.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Evaluate the expression.
2
60 ÷ (7 + 3) + 3
2
60 ÷ 10 + 3
Do all operations within parentheses.
60 ÷ 10 + 9
Find the values of numbers with exponents.
6+9
Multiply and divide in order from left to right.
15
Add and subtract in order from left to right.
Evaluate each expression.
1. 7 × (12 + 8) − 6
7 × _______ − 6
_______
−6
_______________________
4. 2 + (10 − 4)
3
_______________________
7. 5 − (2 × 8) + 9
2
_______________________
2. 10 × (12 + 34) + 3
10 × _______ + 3
_______
+3
10 + _______ − 7
_______
________________________
5. 7 + 3 × (8 + 5)
−7
________________________
6. 36 ÷ 4 + 11 × 8
________________________
8. 3 × (12 ÷ 4) − 2
3. 10 + (6 × 5) − 7
2
________________________
________________________
9. (3 + 10) − 2
3
________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Properties and Mental Math
Commutative Property
Changing the order of addends does not change the sum.
21 + 13 = 13 + 21
Changing the order of factors does not change the product.
5×7=7×5
Associative Property
Changing the grouping of addends does not change the sum.
(3 + 8) + 4 = 3 + (8 + 4)
Changing the grouping of factors does not change the product.
2 × (7 × 4) = (2 × 7) × 4
Distributive Property
When you multiply a number by a sum, you can
• Find the sum and then multiply.
3 × (8 + 4) = 3 × 12 = 36
or
• Multiply the number by each addend and then find the sum.
3 × (8 + 4) = (3 × 8) + (3 × 4) = 24 + 12 = 36
Identify the property shown.
1. 3 × (2 × 6) = (3 × 2) × 6
_______________________________________
3. 4 × (8 + 5) = (4 × 8) + (4 × 5)
_______________________________________
5. 3 × (8 + 4) = (3 × 8) + (3 × 4)
_______________________________________
2. 7 + 18 = 18 + 7
________________________________________
4. 11 × 8 = 8 × 11
________________________________________
6. (3 + 8) + 4 = 3 + (8 + 4)
________________________________________
Identify the property shown and the missing number in each
equation.
7. 9 + 16 = y + 9
_______________________________________
9. 3 × (11 + 4) = (3 × a) + (3 × 4)
_______________________________________
8. 4 × (3 × 2) = (4 × n) × 2
________________________________________
10. 6 × (9 + 14) = (b × 9) + (b × 14)
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Operations and Properties
Review for Mastery: Properties and Mental Math, continued
Find each sum or product.
A. 8 + 9 + 22 + 31
8 + 22 + 9 + 31
Use the Commutative Property.
(8 + 22) + (9 + 31)
Use the Associative Property.
30 + 40
Use mental math to add.
70
B. 5 × 7 × 4
7×5×4
Use the Commutative Property.
7 × (5 × 4) Use the Associative Property.
7 × 20
Use mental math to multiply.
140
Find each sum or product.
11. 3 + 58 + 27 + 22
12. 8 × 3 × 5
_______________________
14. 54 + 32 + 78 + 106
13. 5 × 3 × 4
________________________
15. 84 + 11 + 26 + 39
_______________________
________________________
16. 10 × 3 × 7
________________________
________________________
Find the product.
6 × 34
Step 1: Write one factor as a sum of two numbers.
6 × 34 = 6 × (30 + 4)
Step 2: Use the Distributive Property.
6 × (30 + 4) = (6 × 30) + (6 × 4)
Step 3: Use mental math to multiply and add.
(6 × 30) + (6 × 4) = 180 + 24 = 204
Use the Distributive Property to find each product.
17. 6 × 43
_______________
18. 12 × 34
_______________
19. 53 × 4
_______________
20. 74 × 8
________________
Holt McDougal Mathematics