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 6 chapters and video availability01 · Read and understand
What you will learn
- Interpret and compute the ratio of two fractional quantities.
- Explain your method and check what the result means in the stated situation.
Before you start
Fraction and decimal operations, whole-number factors, measurement units, and reading simple tables.
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
How many 2/3 m lengths fit into 5/6 m, allowing a fractional piece count?
Why this math matters
Distinguish how many portions fit from how much material remains. The worked example shows how to connect the situation, its mathematical representation, and a check on the result.
Set up the model
A useful answer starts with clear assumptions:
- Use the units, grouping rules, and reference whole stated in the question.
- Treat the supplied counts and measurements as exact within the classroom model, unless an estimate or a random outcome is requested.
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.
Divide by a fractional measure
PausedQuestion: Start with the question. Paused.
Question
Start with the question
How many 2/3 m lengths fit into 5/6 m, allowing a fractional piece count?
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 situation
Use sixths: (5/6) ÷ (4/6)
Both lengths can be counted in sixth-metres.
Connect the parts
5 ÷ 4 = 5/4
The common unit cancels in the ratio.
State and check the result
5/6 ÷ 2/3 = 5/4 = 1¼ piece-lengths
One full piece uses four sixths; the remaining sixth is one quarter of a piece.
The result
5/6 ÷ 2/3 = 5/4 = 1¼ piece-lengths
One full piece uses four sixths; the remaining sixth is one quarter of a piece.
Common mistakes to catch
- A fractional piece count differs from leftover length.
- Dividing by a nonzero fraction multiplies by its reciprocal, but the model explains why.
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
Find 3/4 ÷ 1/2.
Show a hint
Rename a half as two fourths.
Reveal answer and explanation
3/2 = 1½
Three fourth-sized units contain one and a half groups of two fourths.
Practice 2
If only complete 2/3 m pieces are allowed in the main problem, how many and what leftover?
Show a hint
Separate the whole quotient from its fraction.
Reveal answer and explanation
1 full piece with 1/6 m left
5/6 − 2/3 = 1/6 m, which is one quarter of the requested piece length.
Take the idea with you
Distinguish how many portions fit from how much material remains.
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: Use negative numbers relative to a reference
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