Homework Questions

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Homework Check

Properties of NumbersSection 2.1

1. I am able to identify properties of addition and multiplication.

2. I am able to use the properties to add and multiply numerical expressions mentally.

Learning Targets

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Why do we need to know the properties of numbers?

Is this You?

Changing the order of the values you are adding or multiplying does not change the sum or product.

Commutative Property - NP

Adding

Multiplying

Changing the grouping of the values you are adding or multiplying does not change the sum or product.

Associative Property - NP

Adding

Multiplying

The sum of any number and zero is the original number. The product of any number and 1 is the original number.

Identity Property - NP

When you add a number and 0, the sum equals the original number. The additive identity is 0.

When you multiply a number and 1, the product equals the original number. The multiplicative identity is 1.

Identity Property - NP

The product of any number and zero is zero.

Multiplication Property of Zero

17 + x + 3 = 17 + 3 + x

( 36 x 2) 10 = 36 ( 2 x 10)

km = km • 1

Identifying the Properties - NP

Identifying the Properties

5 • 7 = 7 • 5

c • 1 = c

7 + a = a + 7

5 (xy) = (5x) y

Carlos rented a set of golf clubs for $7 and a golf cart for $12. He paid a greens fee of $23. Find his total cost.

How can the properties make this problem work mentally?

How it Works

Real World

Suppose you buy the school supplies shown at the left. Use mental math to find the cost of the supplies.

Suppose you buy school supplies costing $.45, $.65, and $1.55. Use mental math to find the cost of these supplies.

Example – Mental Math - NP

(20 • 13) • 5

Mental Math - NP

Use mental math to simplify (81 + 6) + 9.

Name the property used.

Use mental math to simplify 6 + 7 + 14.

Mental Math

Use mental math to simplify 8 + 0 + 2 + (–7).

Use mental math to simplify 5 + 12 + 18 + 5.

Use mental math to simplify 19 + (–30) + 21.

Practice

You spend $6 for dinner, $8 for a movie, and $4 for popcorn. Find your total cost. Explain which property or properties you used.

Practice – NP Quick Check

Name the property shown: 3 + 6 = 6 + 3.

Name the property shown: 8 = 1 · 8.

Name the property shown: (3z)m = 3(zm).

Quick Check - NP

Use mental math to simplify (4 • 9) • 5

Use mental math to simplify 25 · (3 · 4).

Use mental math to simplify 3 · 1 · (–5) · 8.

More Mental

Use mental math to simplify 2(–8)(–15).

Use mental math to simplify 5 · 9 · 6 · (–2) · (–1).

More Mental

Check 4 Understanding

Check 4 Understanding

Practice 2.1

Homework