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 5 chapters and video availability01 · Read and understand
What you will learn
- Interpret fraction multiplication as selecting part of a part.
- Explain your method and check what the result means in the stated situation.
Before you start
Multi-digit operations, equivalent fractions, decimal place value, and rectangular area.
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 gardener uses 3/4 of a plot, and 2/3 of that used part grows beans. What fraction of the whole grows beans?
Why this math matters
Track nested shares by stating what whole each fraction refers to. 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.
Take a fraction of a fraction
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A gardener uses 3/4 of a plot, and 2/3 of that used part grows beans. What fraction of the whole grows beans?
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
First share: 3/4
The garden's whole plot remains the reference unit.
Connect the parts
2/3 × 3/4 = 6/12
Split each fourth into thirds and select two thirds of the three chosen fourths.
State and check the result
6/12 = 1/2 of the whole plot
The bean region is smaller than the used three-fourths region.
The result
6/12 = 1/2 of the whole plot
The bean region is smaller than the used three-fourths region.
Common mistakes to catch
- The second fraction's base is the selected part, not automatically the original whole.
- Multiplication by a positive fraction below one makes a positive amount smaller.
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
What is 3/5 of 1/2?
Show a hint
Multiply selected counts and partition counts.
Reveal answer and explanation
3/10
Three fifths of a half covers three of ten equal whole-plot pieces.
Practice 2
Why is multiplying by 2/3 a decrease for a positive amount?
Show a hint
Two thirds is less than one whole copy.
Reveal answer and explanation
It takes only part of that amount
Selecting two of three equal shares removes one third of the starting amount.
Take the idea with you
Track nested shares by stating what whole each fraction refers to.
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: Multiply a mixed amount
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