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### Properties of Numbers

• To commute means “to change places”; this helps to explain the commutative properties of addition and multiplication: a + b = b + a and a • b = b • a.
• To associate means “to gather in groups”; this helps to explain the associative properties of addition and multiplication: (a + b) + c = a + (b + c) and (a • b) • c = a • (b • c).
• The properties of addition and multiplication often let you do mental computations more easily.
• The Commutative Property, the Associative Property, and the Identity Property apply to both addition and multiplication of rational numbers.

### Properties of Numbers

7.4 + 10 + 3.6 =
• 7.4 + 3.6 + 10
• 11 + 10 =
21
21 + 5 + 39 + 5 =
• (21 + 39) + (5 + 5) =
• 60 + 10 =
70
3 + 16 + 87 + 14 =
• (3 + 87) + (16 + 14) =
• 90 + 30 =
120
25 × 17 × 30 =
• 25 ×30 ×17 =
• 750 ×17 =
12,750
2 × 180 × 5 =
• 2 ×5 ×180 =
• 10 ×180 =
1,800
5 × 11 × 5 =
• 25 ×11 =
275
Brendon bought a scarf for \$ 3.65, a donut for \$ 2.50, and a briefcase for \$ 26.35. How much did Brendon spend total?
• \$ 3.65 + \$ 2.50 + \$ 26.35 =
• \$ 3.65 + \$ 26.35 + \$ 2.50 =
• \$ 30.00 + \$ 2.50 =
\$ 32.50
Larissa bought 17 bananas, 34 strawberries, 6 apples, and 53 cherries. How many fruits did she buy total?
• 17 + 34 + 6 + 53 =
• (17 + 53) + (34 + 6) =
• 70 + 40 =
110 fruits
Gregory ran 4 miles on Monday, 7 miles on Tuesday, 6 miles on Wednesday, 9 miles on Thursday, 1 mile on Friday, 1 mile on Saturday, and 2 miles on Sunday. How many miles did he run this week?
• 4 + 7 + 6 + 9 + 1 + 1 + 2 =
• (4 + 6) + (7 + 1 + 2) + (9 + 1) =
• 10 + 10 + 10 =
30 miles
There is a pie - eating contest. Jessica ate 9 pies, Trevor ate 15 pies, George at 11 pies, Natalie ate 5 pies, and Luke ate 10 pies. How many pies were eaten total?
• 9 + 15 + 11 + 5 + 10 =
• (9 + 11) + (15 + 5) + 10 =
• 20 + 20 + 10
50 pies

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Properties of Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:16
• Commutative Properties: Addition and Multiplication
• Associative Properties: Addition and Multiplication
• Vocabulary Cont. 3:08
• Identity Properties: Addition and Multiplication
• Recognizing Properties 3:55
• Examples: Which Property is Illustrated?
• Using Properties of Numbers 5:07
• Using Mental Math to Find the Total Cost
• Using Properties of Numbers 6:29
• Using Mental Math to Simplify
• Extra Example 1: Using Properties of Numbers 8:29
• Extra Example 2: Using Properties of Numbers 9:06
• Extra Example 3: Using Properties of Numbers 10:02
• Extra Example 4: Using Properties of Numbers 10:32