Properties of Real Numbers

The properties of real numbers. In MathBound, the free Algebra I adventure game, Shell-Game Shelly asks these problems, and the only way past is to solve them.

Part of Expressions and Real Numbers: chapter 1 of the standard course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Commutative and Associative Properties. Identify the commutative or associative property.
Distributive Property. Distribute a positive constant to a binomial.
Identity and Inverse Properties. Identify the additive or multiplicative inverse.
Properties of Zero. Evaluate multiplication involving zero.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Commutative and Associative Properties

Which

statement

is

false?

$3 \cdot 8 = 8 \cdot 3$
$\frac{24}{8} = \frac{8}{24}$
$3 + 8 = 8 + 3$
$(3 + 8) + 4 = 3 + (8 + 4)$

Show the worked steps

$Subtraction$ $and$ $division$ $are$ $neither$ $commutative$ $nor$ $associative.$
$In$ $\frac{24}{8} = \frac{8}{24},$ $the$ $left$ $side$ $is$ $3$ $but$ $the$ $right$ $side$ $is$ $\frac{1}{3} .$

Answer: $\frac{24}{8} = \frac{8}{24}$

Example 2 · Distributive Property

Simplify:

4 (n - 12)

$4 n - 12$
$4 n + 48$
$4 n - 48$
$n - 48$

Show the worked steps

$Multiply$ $4$ $by$ $each$ $term$ $inside,$ $keeping$ $the$ $minus.$
$4 \cdot n = 4 n, 4 \cdot 12 = 48$
$That$ $gives$ $4 n - 48 .$

Answer: $4 n - 48$

Example 3 · Identity and Inverse Properties

Which

pair

of

numbers

are

multiplicative

inverses?

$\frac{- 3}{8}$ $and$ $\frac{3}{8}$
$\frac{- 3}{8}$ $and$ $\frac{8}{3}$
$\frac{- 3}{8}$ $and$ $\frac{- 8}{3}$
$\frac{- 3}{8}$ $and$ $\frac{- 3}{8}$

Show the worked steps

$Multiplicative$ $inverses$ $multiply$ $to$ $1.$
$\frac{- 3}{8} \cdot \frac{- 8}{3} = 1.$

Answer: $\frac{- 3}{8}$ $and$ $\frac{- 8}{3}$

Where it is in your textbook

Textbook	Lessons
Standard course	1.4
CPM Core Connections Algebra	3.2.3
CPS Skyline Algebra	1.1, 4.1
Eureka Math Algebra I (EngageNY)	1.6-1.7
Glencoe Algebra 1	1-3, 1-4
HMH Into Algebra 1	2.1
Math Nation Algebra 1 (Florida B.E.S.T.)	2.6, 2.8
MVP Mathematics I (Integrated Math 1)	1.1
Open Up NC Math 1 (MVP)	1.1
OpenStax Elementary Algebra 2e	1.9
Pearson Algebra 1 Common Core	1-4, 1-7
Reveal Algebra 1	1-3, 1-4

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