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
- Find target divided by original as a scale multiplier.
- Multiply and simplify fractions.
- Check the result using a per-serving amount.
Before you start
Multiply fractions, simplify common factors, and interpret equal sharing.
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 recipe uses 3/4 cup of rice for 6 equal servings. How much rice does the same model require for 10 servings?
Why this math matters
Scaling preserves a recipe's relationships while changing its size. A multiplier can be larger than one, smaller than one, or fractional. Finding that multiplier first is more dependable than adding an arbitrary amount to each ingredient.
Set up the model
A useful answer starts with clear assumptions:
- Each serving is the same size and ingredients scale directly with the serving count.
- This is a proportional arithmetic model; cooking time is not assumed to scale the same way.
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.
Scale a recipe to a different number of servings
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional recipe uses 3/4 cup of rice for 6 equal servings. How much rice does the same model require for 10 servings?
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.
Find the multiplier
10 servings / 6 servings = 5/3
The serving units cancel. Since the target is larger, the multiplier must exceed one.
Scale the ingredient
(3/4 cup)(5/3) = 15/12 cup = 5/4 cup
Multiply numerators and denominators, or cancel the factor of three before multiplying. The remaining quantity is still measured in cups.
Check one serving
(3/4)/6 = 1/8 cup; 10(1/8) = 1 1/4 cups
Dividing by six gives the rice assigned to one serving in this model. Multiplying that unit amount by ten confirms the scaled total.
The result
The proportional model calls for 1 1/4 cups of rice.
Multiplication does not always make a number larger. Scaling this recipe to three servings would use a multiplier of 1/2 and halve the rice amount.
Common mistakes to catch
- Using original divided by target reverses the multiplier.
- Adding four servings does not mean adding four cups to every ingredient.
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 mixture uses 2/3 cup for 4 servings. How much is needed for 6 servings?
Show a hint
Multiply by 6/4.
Reveal answer and explanation
1 cup
(2/3)(6/4) = 12/12 = 1 cup. The serving count and ingredient amount both increase by a factor of 1.5.
Practice 2
How many portions of 3/8 litre fit into 1 1/2 litres?
Show a hint
Divide the total amount by one portion; multiply by the divisor's reciprocal.
Reveal answer and explanation
4 portions
(3/2)/(3/8) = (3/2)(8/3) = 4. Four portions use exactly 12/8 litres.
Take the idea with you
Choose one multiplier and apply it to two ingredients. Check that their original ratio is preserved.
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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