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
- Choose a common denominator.
- Add equivalent fractions.
- Interpret an improper fraction as a mixed number.
Before you start
Identify numerator and denominator; multiply small whole numbers and recognize equivalent 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
One bowl contains 3/4 cup of dry oats and another contains 2/3 cup. What total measured amount of oats do the two bowls represent?
Why this math matters
Fractions count parts of a specified whole. Adding thirds to fourths directly is like adding different measuring units without converting. Equivalent fractions let us describe both amounts with one shared part size.
Set up the model
A useful answer starts with clear assumptions:
- Both measurements use the same cup unit.
- The task adds the stated measured quantities; packing or compression changes are outside the model.
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.
Combine recipe amounts with unlike fractions
PausedQuestion: Start with the question. Paused.
Question
Start with the question
One bowl contains 3/4 cup of dry oats and another contains 2/3 cup. What total measured amount of oats do the two bowls represent?
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.
Choose equal-sized parts
A common denominator for 4 and 3 is 12.
Twelfths work because a fourth contains three twelfths and a third contains four twelfths. Each original amount keeps its value.
Rename and add
3/4 + 2/3 = 9/12 + 8/12 = 17/12 cup
Now the numerator counts seventeen equal twelfth-cup parts. The denominator remains twelve because the part size has not changed.
Separate the whole cup
17/12 = 12/12 + 5/12 = 1 5/12
Twelve twelfths make one whole cup, leaving five twelfths. Both fraction forms express exactly the same total.
The result
The measured amounts total 1 5/12 cups.
Both original amounts exceed half a cup, so the result should exceed one cup. Neither reaches a full cup, so the result must remain below two. These bounds support the answer.
Common mistakes to catch
- Adding denominators would change the part size and give an incorrect result.
- A common denominator need not be the smallest, but a smaller valid one simplifies the arithmetic.
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
Add 5/6 cup and 1/4 cup.
Show a hint
Rewrite both in twelfths.
Reveal answer and explanation
1 1/12 cups
5/6 = 10/12 and 1/4 = 3/12. Their sum is 13/12, or 1 1/12.
Practice 2
A container starts with 2 cups. After removing 3/8 cup, how much remains?
Show a hint
Express two whole cups as eighths.
Reveal answer and explanation
1 5/8 cups
2 = 16/8, so 16/8 − 3/8 = 13/8 = 1 5/8 cups.
Take the idea with you
Sketch a one-cup strip divided into twelfths. Use the same strip length to show each addend and the total.
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: Scale a recipe to a different number of servings
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.