Testinar Grade 6 math

Opposites and Absolute Value

Students will build Grade 6 mastery of opposites and absolute value using models, equations, and test-style reasoning.

CH02-07 The Number System

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

What is the value of \(|-12|\)?
1. \(12\)
2. \(0\)
3. \(-12\)
4. \(24\)
Which number is the opposite of \(7\)?
1. \(-7\)
2. \(\frac{1}{7}\)
3. \(0\)
4. \(7\)
What is \(|-8|\)?
1. \(-8\)
2. \(8\)
3. \(0\)
4. \(16\)
The opposite of the opposite of \(-5\) is:
1. \(5\)
2. \(10\)
3. \(0\)
4. \(-5\)
Which pair of numbers are opposites?
1. \(3\) and \(\frac{1}{3}\)
2. \(-4\) and \(4\)
3. \(6\) and \(12\)
4. \(-2\) and \(-2\)
What is the opposite of \(-15\)?
1. \(15\)
2. \(-15\)
3. \(0\)
4. \(\frac{1}{15}\)
On a number line, which number is farthest from zero?
1. \(|-3|\)
2. \(|5|\)
3. \(|-2|\)
4. \(|1|\)
Which expression with a negative number equals \(10\)?
1. \(|-10|\)
2. The opposite of \(10\)
3. \(|10|\)
4. \(-10\)

Teacher and parent reference

Answer key and explanations

A. \(12\)
The absolute value of a number is its distance from zero on a number line, always non-negative. \(|-12|=12\).
A. \(-7\)
The opposite of a positive number is its negative. The opposite of \(7\) is \(-7\), equidistant from zero on the other side.
B. \(8\)
Absolute value measures distance from zero. Distance is always positive or zero, so \(|-8|=8\).
D. \(-5\)
The opposite of \(-5\) is \(5\). The opposite of \(5\) is \(-5\). So the opposite of the opposite returns to the original number.
B. \(-4\) and \(4\)
Opposites are numbers equidistant from zero on opposite sides of the number line. \(-4\) and \(4\) are opposites.
A. \(15\)
The opposite of a negative number is its positive version. The opposite of \(-15\) is \(15\).
B. \(|5|\)
We compare absolute values: \(|-3|=3\), \(|5|=5\), \(|-2|=2\), \(|1|=1\). The largest is \(5\).
A. \(|-10|\)
\(|-10|=10\) because absolute value is distance from zero.