Lesson 7.2Opposites of Rational Numbers
Start hereWords, worked example, and sentence starters
Learning target I can place rational numbers, including fractions and decimals, on a number line.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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, −2.85 |
| FractionSpanish: Fracción | A number that shows part of a whole, like 3/4. | 3/4 means 3 out of 4 equal parts — like 3 slices of a pizza cut into 4 |
| DecimalSpanish: Decimal | A number with a dot, like 0.5, that shows a part less than one. | 0.5 is half of one |
| Number lineSpanish: Recta numérica | A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right. | left is less, right is more |
| EquivalentSpanish: Equivalente | Having the same value, just written a different way. | 1/2 = 0.5 = 2/4 — all name the same point on the number line |
| IntegerSpanish: Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. | ..., -3, -2, -1, 0, 1, 2, 3, ... |
How it worksWorked exampletaking the opposite twice
These numbers are not on your problems. The steps are. Follow them with your own numbers.
What number is the opposite of the opposite of −6.35? Use a number line to show your reasoning.
- Locate the starting number. −6.35 sits 6.35 units to the left of 0.
- First opposite: same distance, other side of 0. 6.35
- Second opposite: flip back across 0. −6.35
- The two flips undo each other, so you land on the number you started with.
Answer: The opposite of the opposite of −6.35 is −6.35.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
What number is the opposite of the opposite of 5.72? Use a number line to show your reasoning.
- Locate the starting number. 5.72 sits units to the of 0.
- First opposite: same distance, other side of 0.
- Second opposite: flip back across 0.
- Two flips undo each other, so the result is .
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The opposite of is because .
- After one flip I land on ; after two flips I land on .
- Both numbers sit units from zero, but on sides.
- is a rational number because it can be written as .
Word bank oppositefliprational numberdecimalfractionnumber linedistancezeronegativepositivesideequal parts
Watch outA common mistake
A common mistake in Rational Numbers on the Number Line is treating the numerator and denominator of a negative fraction as two separate integers instead of one value between two integers — for example, plotting -3/4 by going to -3 and then counting 4 more units to the left, landing (incorrectly) at -7, instead of recognizing that -3/4 = -0.75, which sits between 0 and -1. Before you submit an answer, find the two integers your value falls between, then split that space into equal parts.
Lesson 7.2Opposites of Rational Numbers
Apply Day · Version ASupported practice
Learning target I can place rational numbers, including fractions and decimals, on a number line.
-
1Complete each step, then write the final answer.
A point is halfway between −9 and −8. What number is it?
Show your workHint Halfway between 8 and 9 is 8.5. This point is left of 0.
Final answer: -
2Complete each step, then write the final answer.
The space from 0 to −1 has 4 equal parts. What number is 1 part to the left of 0?
Show your workHint Each part is 1/4. Left of 0 is negative.
Final answer: -
3Complete each step, then write the final answer.
Which integer is just to the left of −0.5 on a number line?
Show your workHint −0.5 is between two integers. Pick the one farther from 0.
Final answer:
Lesson 7.2Opposites of Rational Numbers
Apply Day · Version BCore practice
Learning target I can place rational numbers, including fractions and decimals, on a number line.
-
1Circle the letter of the best answer. Show how you know.
Ray says −4.5 goes halfway between −4 and −3. Is he right? Where does −4.5 go?
- AHalfway between −5 and −4
- BHalfway between −4 and −3
- CHalfway between 4 and 5
- DAt −45
Show your work -
2Complete each step, then write the final answer.
What number is 3 of 10 equal parts from 0 toward −1? Write a decimal.
Show your workFinal answer: -
3Complete each step, then write the final answer.
A point is halfway between −6 and −5. What number is it?
Show your workFinal answer:
Lesson 7.2Opposites of Rational Numbers
Apply Day · ChallengeExtension
Learning target I can place rational numbers, including fractions and decimals, on a number line.
-
1Circle the letter of the best answer. Show how you know.
Between which two consecutive integers does −3.5 fall on a number line?
- A−3 and −2
- B3 and 4
- C−4 and −3
- D−5 and −4
Show your work -
2Complete each step, then write the final answer.
Lia plots −1 1/3. She splits −1 to −2 into 3 parts. Then she counts 1 part to the right of −1. What number did she really plot?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Point R is between −6 and −5. It is 0.3 units from −5. What number is R?
Show your workFinal answer: