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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

1. Rational Numbers

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Exercise 48 Page 8

The absolute value of a number is non-negative.

n ≥ 0

Practice makes perfect

We can start by looking at the given equation. n+|- n|=2n We want to check whether n ≥ 0 or n≤ 0 for our equation. We can do so by substituting example positive and negative integers into the equation. We can start by substituting an arbitrary positive integer, 4, for n. Remember that the absolute value of a number is always non-negative.

n+|- n|? =2n

n= 4

4+|- 4|? =2( 4)

|-4|=4

4+4? =2(4)

Multiply

4+4? =8

Add terms

8=8 ✓

Next, we can substitute an arbitrary negative integer, - 4, for n.

n+|- n|? =2n

n= - 4

- 4+|- ( -4)|? =2( - 4)

- (- a)=a

- 4+|4|? =2(- 4)

|4|=4

- 4+4? =2(- 4)

a(- b)=- a * b

- 4+4? =- 2(4)

Multiply

-4+4? =- 8

Add terms

0≠- 8

The results are the same for all integers greater than or less than 0. This means that n≥0 for the given equation.

Extra

Absolute Value

We can recall some facts about the absolute value.

The absolute value of a number is its distance from 0 on the number line.
Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0.
The absolute value of a non-negative number is equal to the number, while the absolute value of a negative number is equal to its opposite.

Let's consider the distances between different numbers and 0 on the number line.

Subchapter links

Try It p.4-5

Self-Assessment for Concept & Skills p.5

Self-Assessment for Problem Solving p.6

Review & Refresh p.7

Concept, Skills, & Problem Solving p.7-8