3
2
1
Guided Practice

An inequality statement compares two quantities that are not equal. The symbols > and < are used to make inequality statements.

1/8<2/3 ← 1 eighth is less than 2 thirds.
3/4>2/3 ← 3 fourths is greater than 2 thirds.

Given the comparisons above, you can order the rational numbers:

1/8 < 2/3 < 3/4

The absolute value of a number is the distance of the number from 0 on a number line.

For example, –3 is 3 units from 0 on the number line. So, the absolute value of –3 is 3. We write the absolute value of –3 like this:

|–3| = 3

The absolute value of +3 is also 3, since +3 is also 3 units from 0 on a number line:

|–3| = |3| = 3

Compare the rational numbers in each pair. Write is less than, is equal to, or is greater than.

1/2 2/3

3/4 1/3

2/4 1/2

Enter >, <, or = to correctly compare the rational numbers.

2/9 3/9

3/9 1/3

1/9 1/3

Enter >, <, or = to correctly compare the rational numbers.

4/8 3/8

1/2 4/8

1/4 2/8

Enter >, <, or = to correctly compare the rational numbers.

2/5 3/5

3/5 3/6

3/5 1/2

Estimate the location of 29 different rational numbers on the number line shown. Press the checkmark when you're done.

Your PAE average is 0, for 0 trial(s).

Determine the absolute value of each number.

|–1/4| =

|2| =      

|0| =      

Determine the absolute value of each number.

|–5/6| =  

|–8/3| =  

|–10/10| =

You can order fractions, decimals, and numbers with absolute values from least to greatest or greatest to least. For example, given this list of values:

1/3, |–0.5|, 1/4

You can determine that |–0.5| is the same as 1/2, so the correct order of the values from least to greatest is 1/4, 1/3, |–0.5|.

To order the values at the right, drag the red circle to the least number or greatest number, then place the circles in the order they are connected on top of the remaining values to order them from least to greatest or greatest to least.

Double click on a circle to unstick it. (Or just drag to a new location.)
To convert a decimal to a fraction, write the number as a numerator over 10 or 100 (or 1000, etc.). Then, write an equivalent fraction.

0.35 = 35/100 = 7/20

To convert a fraction to a decimal, write an equivalent fraction with a denominator of 10 or 100 (or 1000, etc.). Then, write the number as a decimal.

5/8 = 625/1000 = 0.625

A negative number is a number that is less than 0. All negative numbers are usually to the left of 0 on the number line.

Counting to the left on the number line, you get 0, –1, –2, –3, –4, and so on. The absolute value of –1, or |–1| is equal to 1. The absolute value of
–3, or |–3| is equal to 3. The absolute value of 0, or |0|, is equal to 0.

You can see that –2 < –1. And –3 > –4.
But –3 < |–4|.

Name the point located at each number on the number line.

|–|2:   

|–3|:   

||–3:   

–4.5:

Write the number of each point's location on the number line. Use decimals and whole numbers.

B:

C:

A:

D:

Write the number of each point's location on the number line. Use decimals and whole numbers. Point E is located halfway between two tick marks.

A:

C:

E:

Write the number of each point's location on the number line. Write each as an absolute value expression using the vertical bar key (|).

A:

B:

D:

Write the number of each point's location on the number line. Write each as an absolute value expression using the vertical bar key (|). Use decimals and whole numbers.

A:

B:

C:

D:

Let's practice comparing and ordering rational numbers. Enter four different rational numbers on the left that are greater than 0 and less than 1.

Press the checkmark when you have entered all four rational numbers.

Complete the sentences with the terms "less than", "greater than", and "equal to".

A rational number greater than 0 and less than 1 has a numerator the denominator.

A rational number equal to 1 has a numerator the denominator.

On the left, when you make a rational number greater than 1, its bar turns black. Enter four different rational numbers that are greater than 1.

Press the checkmark when you have entered all four rational numbers.

Press the button to set the rational numbers on the left.

Order the rational numbers from least to greatest. Write each of the rational numbers with a slash (/).

< < <

Press the button to set the rational numbers on the left.

Order the rational numbers from least to greatest. Write each of the rational numbers with a slash (/).

< < <

Press the button to set the rational numbers on the left.

Order the rational numbers from least to greatest. Write each of the rational numbers with a slash (/).

< < <

Complete the sentence with the term "less than", "greater than", or "equal to".

When two rational numbers have the same numerators, the number with the smaller denominator is the other number.

Write an example of this by writing an inequality statement.

<

Press the button to set the rational numbers on the left.

Order the rational numbers from greatest to least. Write each of the rational numbers with a slash (/).

> > >

Press the button to set the rational numbers on the left.

Order the rational numbers from greatest to least. Write each of the rational numbers with a slash (/).

> > >

Press the button to set the rational numbers on the left.

Order the rational numbers from greatest to least. Write each of the rational numbers with a slash (/).

> > >

Complete the sentence with the term "less than", "greater than", or "equal to".

When two rational numbers have the same denominators, the number with the smaller numerator is the other number.

Write an example of this by writing an inequality statement.

<

Enter 3/8 on the left. Then, enter three other rational numbers that are equivalent to 3/8.

Enter 5/6 on the left. Then, enter three other rational numbers that are equivalent to 5/6.

Enter 24/30 on the left. Then, enter three other rational numbers that are equivalent to 24/30.

Order the rational numbers 0.4, 3/5, 0.1, and 1/1.5 from greatest to least.

> > >

Write 1/1.5 as a ratio of two integers:

Order the rational numbers 0.35, 3/6, 0.8, and 0.3/2.1 from greatest to least.

> > >

Write 0.3/2.1 as a ratio of two integers:

Order the rational numbers 0.9, 9/12, 0.72, and 1.6/2 from greatest to least.

> > >

Write 1.6/2 as a ratio of two integers:

To compare two rational numbers written as fractions, look at the denominators. If they are the same, compare the numerators. The number with the smaller numerator is the smaller number.

1/3 < 2/3

If the denominators are different but the numerators are the same, compare the denominators. The number with the larger denominator is the smaller number.

2/5 < 2/4

To compare two rational numbers that have different numerators and denominators, first multiply or divide the numerator and denominator of one or both numbers by the same number to get equivalent numbers. Then compare.

So, 3/5 > 2/9.

The symbol > means "is greater than." The symbol < means "is less than."

Write >, <, or = to compare the rational numbers in each pair.

5/8 7/8

2/5 2/9

Write >, <, or = to compare the rational numbers in each pair.

2/3 3/8

3/4 7/10