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
- State what each side of a ratio compares.
- 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
A tile design has 6 blue and 9 white tiles. Compare blue to white and blue to all tiles.
Why this math matters
Read mixture or survey ratios by first identifying the reference quantity. 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.
Distinguish part-to-part from part-to-whole
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A tile design has 6 blue and 9 white tiles. Compare blue to white and blue to all tiles.
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
Blue:white = 6:9 = 2:3
This ratio compares the two separate color counts.
Connect the parts
All tiles = 6 + 9 = 15
The whole includes both colors.
State and check the result
Blue:all = 6:15 = 2:5
Two thirds describes blue relative to white; two fifths describes blue relative to the whole.
The result
Blue:all = 6:15 = 2:5
Two thirds describes blue relative to white; two fifths describes blue relative to the whole.
Common mistakes to catch
- Name both compared quantities.
- A part-to-part denominator is not the whole.
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
A box has 4 pens and 7 pencils. What is pens:all writing tools?
Show a hint
Add the two categories for the whole.
Reveal answer and explanation
4:11
There are eleven tools, four of them pens.
Practice 2
If red:yellow is 3:2, what fraction of those two colors is red?
Show a hint
The whole has five ratio parts.
Reveal answer and explanation
3/5
Three red parts out of five combined parts gives three fifths.
Take the idea with you
Read mixture or survey ratios by first identifying the reference quantity.
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: Build a table of equivalent ratios
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.