Testinar Grade 6 math

Comparing and Ordering Rational Numbers

Students will build Grade 6 mastery of comparing and ordering rational numbers using models, equations, and test-style reasoning.

CH02-10 The Number System

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

Which list shows the numbers in order from least to greatest? \(\)-2.5,\ \ \frac{1}{4},\ \ -3,\ \ 1.75\(\)
1. \(-3,\ -2.5,\ \frac{1}{4},\ 1.75\)
2. \(\frac{1}{4},\ 1.75,\ -2.5,\ -3\)
3. \(-2.5,\ -3,\ \frac{1}{4},\ 1.75\)
4. \(1.75,\ \frac{1}{4},\ -2.5,\ -3\)
Compare \(-4\) and \(-1\) using \(<\), \(>\), or \(=\). Which symbol belongs in the box? \(\)-4 \square -1\(\)
1. \(<\)
2. \(>\)
3. \(=\)
4. Cannot be determined
Order these numbers from greatest to least: \(\)0.6,\ -\frac{3}{4},\ 0.1,\ -2\(\)
1. \(-2,\ -\frac{3}{4},\ 0.1,\ 0.6\)
2. \(0.6,\ 0.1,\ -\frac{3}{4},\ -2\)
3. \(0.1,\ 0.6,\ -\frac{3}{4},\ -2\)
4. \(0,\ 0.1,\ 0.6,\ -\frac{3}{4},\ -2\)
Which number is less than \(-5\)?
1. \(-3\)
2. \(2\)
3. \(0\)
4. \(-6\)
What is the relationship between points \(P\) and \(Q\)?
1. \(P > Q\)
2. \(P\) is 3 units greater
3. \(P = Q\)
4. \(P < Q\)
Which comparison is true?
1. \(-2.3 > 0.5\)
2. \(\frac{1}{2} < -\frac{1}{2}\)
3. \(\frac{3}{4} > 2\)
4. \(-0.8 < -0.3\)
A temperature of \(-8° F\) is compared to \(-3° F\). Which statement is correct?
1. \(-8° F\) is warmer
2. \(-3° F\) is colder
3. \(-8° F\) is colder
4. They are the same temperature
Which list is in order from least to greatest?
1. \(0.3,\ 0.8,\ -0.5,\ -0.2\)
2. \(-0.5,\ -0.2,\ 0.3,\ 0.8\)
3. \(-0.2,\ -0.5,\ 0.3,\ 0.8\)
4. \(0.8,\ 0.3,\ -0.2,\ -0.5\)

Teacher and parent reference

Answer key and explanations

A. \(-3,\ -2.5,\ \frac{1}{4},\ 1.75\)
On a number line, more negative numbers are less. \(-3<-2.5<0<\frac{1}{4}<1.75\).
A. \(<\)
\(-4\) is further left on a number line than \(-1\), so \(-4\) is less than \(-1\).
B. \(0.6,\ 0.1,\ -\frac{3}{4},\ -2\)
Positive numbers are greater than negative numbers. Among positives: \(0.6>0.1\). Among negatives: \(-\frac{3}{4}=-0.75>-2\).
D. \(-6\)
\(-6<-5\) because \(-6\) is further left on the number line.
D. \(P < Q\)
\(P\) is at \(-1\) and \(Q\) is at \(2\). Since \(-1 < 2\), point \(P\) is less than point \(Q\).
D. \(-0.8 < -0.3\)
\(-0.8\) is further left on the number line than \(-0.3\), so it is less. All other comparisons are false.
C. \(-8° F\) is colder
\(-8 < -3\), so \(-8° F\) represents a lower (colder) temperature.
B. \(-0.5,\ -0.2,\ 0.3,\ 0.8\)
All negatives come before zero, and all zeros come before positives. Among negatives, \(-0.5<-0.2\). Among positives, \(0.3<0.8\).