Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to order negative fractions and decimals.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Equivalent fractions and decimal place value.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Order −0.6, −2/3, and −5/8 from least to greatest without rounding them to one decimal place.
Why this math matters
On the negative side of a number line, the number closer to zero is greater. Use exact fractions or enough decimal places when comparing small differences in measured deviations.
Set up the model
A useful answer starts with clear assumptions:
- The decimal −0.6 is exact.
- Least to greatest means left to right on the number line.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Order negative fractions and decimals
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Order −0.6, −2/3, and −5/8 from least to greatest without rounding them to one decimal place.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
−0.6 = −3/5
Convert the terminating decimal to an exact fraction.
Apply the relationship
−3/5 = −72/120; −2/3 = −80/120; −5/8 = −75/120
A common denominator lets the signed numerators be compared directly.
Check and interpret
−2/3 < −5/8 < −0.6
−80 is less than −75, which is less than −72.
The result
−2/3 < −5/8 < −0.6
−80 is less than −75, which is less than −72.
Common mistakes to catch
- Comparing magnitudes alone reverses the order of negative values.
- Premature rounding can turn distinct numbers into apparent ties.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Which is greater: −7/10 or −3/4?
Show a hint
Compare −0.70 with −0.75.
Reveal answer and explanation
−7/10
−0.70 is closer to zero and lies farther right.
Practice 2
Place a rational number strictly between −1/2 and −1/4.
Show a hint
Find their midpoint or use eighths.
Reveal answer and explanation
For example, −3/8
−1/2 = −4/8 and −1/4 = −2/8, so −3/8 lies strictly between them.
Take the idea with you
Use exact fractions or enough decimal places when comparing small differences in measured deviations.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Distribute a negative factor to every term
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