Lesson 7.3Understand Absolute Value of Rational Numbers
Start hereWords, worked example, and sentence starters
Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| IntegerSpanish: Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. | ... -3, -2, -1, 0, 1, 2, 3 ... shown on a number line with 0 in the center |
| PositiveSpanish: Positivo | A number bigger than zero, to the right of zero on a number line. | +5 means 5 above zero, like 5 floors above ground level |
| NegativeSpanish: Negativo | A number smaller than zero, to the left of zero on a number line. | -3 means 3 below zero, like 3 floors underground |
| Absolute valueSpanish: Valor absoluto | How far a number is from zero. It is never negative. | |−3| = 3 and |3| = 3 |
| OppositeSpanish: Opuesto | Two numbers the same distance from zero, on opposite sides, like 3 and -3. | −3 and 3 are opposites |
| Rational numberSpanish: Número racional | A number that can be written as a fraction of two integers, with a bottom number that is not zero. | −3/4, 0.5, 7, −50 |
How it worksWorked exampleusing absolute value to see which number is closer to 0
These numbers are not on your problems. The steps are. Follow them with your own numbers.
One freezer logged −23 degrees and another logged 17 degrees. Which reading sits closer to 0?
- Absolute value measures distance from 0, so the sign does not matter here.
- Distance from 0 for the first reading: −23 = 23
- Distance from 0 for the second reading: 17 = 17
- Compare the two distances; the shorter distance sits closer to 0.
Answer: |−23
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A fish swims at −31 meters and a gull flies at 28 meters. Which one is closer to the water surface at 0?
- Absolute value measures from 0, so the sign does not matter.
- Distance from 0 for the fish: −31 =
- Distance from 0 for the gull: 28 =
- Compare the distances; the distance is closer, so the is closer.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The absolute value of is because it sits units from zero.
- and share the same absolute value because .
- An absolute value is never negative because .
- The number closer to zero is because its distance is .
Word bank absolute valuedistancemagnitudezeronumber lineoppositeunitscloserfarthernegativepositivesign
Watch outA common mistake
A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer. Absolute value measures distance from zero and is always positive or zero, but that distance does not decide which integer is greater — only left-to-right order on the number line does. Before you submit, ask: am I comparing distance from zero (absolute value) or position on the number line (greater/less than)?
Lesson 7.3Understand Absolute Value of Rational Numbers
Version ASupported practice
Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
-
1Write the letter of the matching item on each line.
Match each integer to its absolute value.
- -5
- 3
- -8
- 0
- -1
- 7
- A5
- B3
- C8
- D0
- E1
- F7
Hint Each integer matches its distance from zero. Negative signs disappear; positives stay the same.
-
2Mark and label each value on the number line.
Plot these integers on the number line: -6, -2, 0, 4, 7
Hint Negatives go LEFT of 0 and positives go RIGHT. Zero sits in the middle.
Show your thinking
-
3Circle the letter of the best answer. Show how you know.
What is the absolute value of -9?
- A-9
- B0
- C1
- D9
Hint Absolute value asks: how FAR is -9 from zero? It's about distance, not direction.
Show your work -
4Circle the letter of the best answer. Show how you know.
Which integer has the GREATEST absolute value: -3, 7, -5, 2?
- A-5
- B-3
- C2
- D7
Hint 'Greatest absolute value' means farthest from zero — the sign doesn't matter.
Show your work -
5Circle the letter of the best answer. Show how you know.
What is |0|?
- A1
- B-1
- C0
- DThere is no answer
Hint Absolute value = distance from zero. Here the number inside the bars IS zero.
Show your work -
6Circle the letter of the best answer. Show how you know.
What is |−2.5|?
- A0
- B2.5
- C−2.5
- D25
Hint Where does −2.5 sit on the number line?
Show your work
Explain your thinkingHow does the number line help you see the difference between an integer and its absolute value?
Sentence starter The integer ___ is located ___ units from zero, so its absolute value is ___. Even though ___ is negative, its distance from zero is still ___.
Lesson 7.3Understand Absolute Value of Rational Numbers
Version BCore practice
Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
-
1Mark and label each value on the number line.
Plot these integers and circle pairs that have the same absolute value: -6, 6, -2, 2, -4, 4
Show your thinking -
2Complete the table. Show how you found each value.
Complete the table with each integer's absolute value and its opposite.
Integer Absolute Value Opposite -7 4 -12 0 9 Show your work -
3Write the name of the correct group on each line.
Sort these integers from the GREATEST absolute value to the LEAST absolute value.
- -2
- 8
- -5
- 1
- -10
- 3
-
4Circle the letter of the best answer. Show how you know.
Which statement about absolute value is TRUE?
- A|-4| = |4| because both are 4 units from zero
- B|-4| = -4 because the number is negative
- C|-4| = 0 because negatives cancel out
- D|4| > |-4| because positive is always bigger
Show your work
-
5Circle the letter of the best answer. Show how you know.
Which number has the LEAST absolute value: −1.5, 0.75, −1/4, or 2?
- A0.75
- B−1/4
- C−1.5
- D2
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Confusing Opposite with Absolute Value
- 1ProblemComplete the table for the integer 9: find its absolute value and its opposite.
- 2Student's thinkingAbsolute value and opposite both just make a number positive, so they should give the same answer as each other.
- 3Student's answerAbsolute value of 9 = 9, and opposite of 9 = 9.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingHow does the number line help you see the difference between an integer and its absolute value?
Lesson 7.3Understand Absolute Value of Rational Numbers
ChallengeExtension
Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
-
1Decide whether each pair balances. Check Yes or No, then explain.
Use absolute value to decide which side is greater, or if they are equal.
Left side Right side Balanced? Explain your choice
-
2Find the mistake. Explain it, then show the correct work.
Find the Absolute Value Error
- 1ProblemFind |-6|
- 2Student thinkingThe number is -6, and absolute value makes it the opposite
- 3Student answer|-6| = 6, and since we take the opposite, the answer is -6
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
A submarine is at -150 meters and a bird is flying at +150 meters. A student says the submarine is closer to sea level because -150 is less than 150. Is the student correct? Explain using absolute value.
Write your answer