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
- Solve for a reference amount when a part and its percent are known.
- 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
Eighteen students are 30% of a group. How many students are in the whole group?
Why this math matters
Write part = rate × whole to decide which quantity is missing. 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.
Recover a whole from a percentage part
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Eighteen students are 30% of a group. How many students are in the whole group?
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
0.30 × whole = 18
Thirty percent applies to the unknown total.
Connect the parts
whole = 18 ÷ 0.30
Undo multiplication by the decimal percentage.
State and check the result
Whole group = 60 students
Check: 30% of sixty is eighteen.
The result
Whole group = 60 students
Check: 30% of sixty is eighteen.
Common mistakes to catch
- Do not multiply the known part by the percentage again.
- Distinguish finding a part, finding a whole, and finding a rate.
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
Twelve is 25% of what number?
Show a hint
A quarter is one of four equal parts.
Reveal answer and explanation
48
Four copies of twelve make forty-eight.
Practice 2
What percent of 50 is 15?
Show a hint
Divide the part by the whole.
Reveal answer and explanation
30%
15/50 = 0.3 = 30/100.
Take the idea with you
Write part = rate × whole to decide which quantity is missing.
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: Divide by a fractional measure
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.