7th Grade Math

Lesson 1D Expressions 39

Real-World Link

American Lance

Armstrong won the

Tour de France seven

times in a row from

1999 through 2005.

R

A

TOUR DE FRANCE The Tour de France is a cycling race through

France that lasts 22 days. If a cyclist averages 90 miles per day,

about how far does he travel?

Use the Distributive Property to multiply 90 × 22 mentally.

90 (22) = 90 (20 + 2) Rewrite 22 as 20 + 2.

= 90 (20) + 90 (2) Distributive Property

= 1,800 + 180 Multiply.

= 1,980 Add.

The cyclist travels about 1,980 miles.

c. MONEY Jennifer saved $120 each month for five months. How

much did she save in all? Explain your reasoning.

Properties are statements that are true for all numbers.

Real Number Properties

Commutative

Properties

The order in which two numbers are added or

multiplied does not change their sum or product.

a + b = b + a a · b = b · a

Associative

Properties

The way in which three numbers are grouped when

they are added or multiplied does not change their

sum or product.

a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c

Identity

Properties

The sum of an addend and 0 is the addend. The

product of a factor and 1 is the factor.

a + 0 = a a · 1 = a

Use Properties to Evaluate Expressions

Evaluate 4 · 12 · 25 mentally. Justify each step.

4 · 12 · 25 = 4 · 25 · 12 Commutative Property of Multiplication

= (4 · 25) · 12 Associative Property of Multiplication

= 100 · 12 or 1,200 Multiply 100 and 12 mentally.

Evaluate each expression. Justify each step.

d. 40 · (7 · 5) e. (89 + 15) + 1

Mental Math Mental Math Look for

sums or products that end

in zero. They are easy to

compute mentally.

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