6th Grade Ordering Rational Numbers and Absolute Value Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Ordering Rational Numbers and Absolute Value – Maths PDF

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This compare absolute value answers for 6th Grade covers ordering rational numbers and absolute value (Common Core 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7c, 6.NS.C.7d), with a free PDF to print.

Check your comparisons here. Each solution places the numbers on a number line, names which is farther right or left, and states the inequality or absolute value in bold. Contexts are explained in words.

Grade 6 · Common Core State Standards: 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7c, 6.NS.C.7d

Compare absolute value answers: exercises 1 to 10

Exercise 1 – Compare an integer pair

On a number line, the number farther to the right is greater.

\(-3\) is to the left of \(2\).

\(-3 < 2\)

Exercise 2 – Compare two negatives

On a number line, the number farther to the right is greater.

\(-7\) is to the left of \(-4\).

\(-7 < -4\)

Exercise 3 – Compare decimals

\(-0.5\) is \(-0.50\), which is farther left than \(-0.25\).

\(-0.5 < -0.25\)

Exercise 4 – Compare fractions

Write \(-\frac{1}{2} = -\frac{2}{4}\).

\(-\frac{3}{4}\) is 3 fourths left of 0 and \(-\frac{2}{4}\) is 2 fourths left, so \(-\frac{3}{4}\) is farther left.

\(-\frac{3}{4} < -\frac{1}{2}\)

Exercise 5 – Order integers

Least is farthest left.

\(-5, -1, 0, 2, 3\)

From left to right: least to greatest.

Exercise 6 – Order rational numbers

Negative numbers: \(-3.1 < -2.5 < -2\), then the positive number \(1.5\).

\(-3.1, -2.5, -2, 1.5\)

Exercise 7 – Write an inequality

A is \(-4\) and B is \(1\). A is to the left of B.

\(-4 < 1\) (or \(1 > -4\))

Exercise 8 – Absolute value of a negative

Absolute value is the distance from 0 on a number line. \(-8\) is 8 units from 0.

\(|-8| = 8\)

Exercise 9 – Absolute value practice

(a) 5 is 5 units from 0. (b) 0 is 0 units from 0. (c) \(-3.5\) is 3.5 units from 0.

5; 0; 3.5

Exercise 10 – Distance from zero

\(|-6| = 6\) and \(|6| = 6\).

Both are 6 units from 0. Opposites have the same absolute value.

Exercises 11 and up

Exercise 11 – Ocean depths

\(-80\) is to the right of \(-120\), so \(-80 > -120\).

\(-80 > -120\); Diver A is higher.

Exercise 12 – Colder temperature

\(-12\) is farther left, so \(-12 < -5\).

\(-12 < -5\); Tuesday was colder.

Exercise 13 – Debt and magnitude

Liam: \(-50\). Maya: \(-30\).

\(-50 < -30\), but \(|-50| = 50 > 30 = |-30|\).

Liam owes more money. Greater debt means a smaller (more negative) number.

Exercise 14 – Distance below the surface

\(|-35| = 35\).

The submarine is 35 feet below the surface (35 units from 0).

Exercise 15 – Compare absolute values

\(|-9| = 9\) and \(|6| = 6\).

\(|-9| > |6|\)

Exercise 16 – True or false?

\(-2\) is 2 units left of 0 and \(-5\) is 5 units left of 0. \(-2\) is farther right.

True.

Negative 2 is to the right of negative 5.

Exercise 17 – Order with absolute value

\(|-4| = 4\), \(|2| = 2\), \(-|5| = -5\).

The values are 4, \(-3\), 2, \(-5\).

\(-|5|, -3, |2|, |-4|\) (that is, \(-5, -3, 2, 4\))

Exercise 18 – Golf scores

\(-5 < -3 < 0 < 2\).

Priya (-5), Dylan (-3), Jamal (0), Maya (+2). Priya has the best score.

Exercise 19 – Same absolute value

The numbers 7 units from 0 are 7 and \(-7\).

\(7\) and \(-7\)

Both are 7 units from 0.

Exercise 20 – City temperatures

Order from least to greatest: \(-15, -11, -8, -2\).

Cities: Duluth, Buffalo, Fairbanks, Denver.

\(|-15| = 15\) is the greatest absolute value.

Duluth, Buffalo, Fairbanks, Denver; Duluth has the greatest absolute value

Key facts behind this compare absolute value answers

Key facts

Numbers increase from left to right on a number line.
Every positive number is greater than every negative number.
Among negatives, the one closer to 0 is greater.
Absolute value is the distance from 0, so it is never negative.
A number can be less than another and still have the greater absolute value.

How to use this compare absolute value answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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