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.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Distinguish part-to-part and part-to-whole ratios.
- Find the amount represented by one ratio part.
- Check the total and the preserved ratio.
Before you start
Multiply and divide positive whole numbers; interpret simple fractions.
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 fictional craft mixture uses 2 equal measures of blue paint for every 3 of white. How much of each colour makes 15 measures altogether?
Why this math matters
A ratio describes a relationship, not a fixed batch size. Counting all the parts lets you scale a mixture while keeping its proportions. The same reasoning works for sets of coloured beads and other countable collections.
Set up the model
A useful answer starts with clear assumptions:
- Every measure has the same capacity.
- The target refers to the sum of the measured inputs; the exercise does not model physical volume changes.
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.
Mix a colour using parts, not guesses
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional craft mixture uses 2 equal measures of blue paint for every 3 of white. How much of each colour makes 15 measures altogether?
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.
Count the ratio parts
2 blue parts + 3 white parts = 5 total parts
Blue is two of the five total parts. The ratio 2:3 compares blue with white, not blue with the whole mixture.
Assign a size to one part
15 measures / 5 parts = 3 measures per part
The batch is three times the basic two-plus-three recipe. Both colours need that same multiplier.
Scale and check
blue = 2 × 3 = 6; white = 3 × 3 = 9
Six plus nine equals fifteen. Dividing both quantities by three returns the original ratio 2:3, so both checks succeed.
The result
Use 6 measures of blue and 9 measures of white in the classroom model.
Blue forms 2/5 of the total, or 40%. It is also 2/3 of the amount of white. Both fractions are valid because they answer different comparison questions.
Common mistakes to catch
- Taking 2/3 of the total confuses the whole with the white component.
- Adding the same amount to both colours usually changes their ratio.
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 red-to-white ratio is 3:2. Split a total of 20 measures.
Show a hint
There are five ratio parts in the total.
Reveal answer and explanation
12 red and 8 white
One part is 20/5 = 4 measures. Red uses 3(4) = 12 and white uses 2(4) = 8.
Practice 2
A blue-to-white ratio is 2:5. If blue uses 10 measures, how much white is needed?
Show a hint
The two blue parts represent ten measures.
Reveal answer and explanation
25 measures of white
Each part is 10/2 = 5 measures. Five white parts require 25, making 35 measures altogether.
Take the idea with you
Before using any ratio, label both quantities and say whether the second number describes another part or the whole.
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.
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