What is a Part-Part-Whole Word Problem?

S1-SA1-0747

Grade Level:

Class 3

Maths, NLP, AI, Logic

Definition

What is it?

A Part-Part-Whole word problem is a type of math problem where you are given two 'parts' and asked to find the 'whole' total, or you are given the 'whole' and one 'part' and asked to find the missing 'part'. It helps us understand how smaller amounts combine to make a larger amount, or how a larger amount can be broken down.

Simple Example

Quick Example

Imagine you have a box of ladoos. If there are 5 motichoor ladoos and 3 boondi ladoos, how many ladoos are there in total? Here, 5 is one part, 3 is another part, and you need to find the 'whole' number of ladoos.

Worked Example

Step-by-Step

PROBLEM: Priya has 12 colourful bangles. 7 of them are red and the rest are green. How many green bangles does Priya have?

Step 1: Understand what is given. We know the 'whole' number of bangles (12) and one 'part' (7 red bangles).
---Step 2: Understand what we need to find. We need to find the other 'part' (number of green bangles).
---Step 3: To find a missing part, we subtract the known part from the whole.
---Step 4: Set up the subtraction: Total Bangles - Red Bangles = Green Bangles.
---Step 5: Calculate: 12 - 7 = 5.
---Answer: Priya has 5 green bangles.

Why It Matters

Understanding Part-Part-Whole problems builds strong logical thinking, which is key in many fields. It's fundamental for careers in data analysis, where you combine different data sets, or even in AI, where algorithms break down complex information into smaller parts. It teaches you to break down big problems into manageable steps.

Common Mistakes

MISTAKE: Always adding the numbers given, even when finding a missing part. | CORRECTION: Read carefully to see if you need to combine parts (add) or find a missing part from a whole (subtract).

MISTAKE: Not identifying the 'whole' or the 'parts' correctly. | CORRECTION: Clearly label the given numbers in your mind or on paper as 'Part 1', 'Part 2', or 'Whole' before solving.

MISTAKE: Getting confused by extra information not needed for the problem. | CORRECTION: Focus only on the numbers and keywords that tell you about the parts and the whole.

Practice Questions

Try It Yourself

QUESTION: On a school trip, there are 15 boys and 10 girls. How many students are there in total? | ANSWER: 25 students

QUESTION: A auto-rickshaw driver earned Rs. 350 in the morning and Rs. 420 in the afternoon. What was his total earning for the day? | ANSWER: Rs. 770

QUESTION: There are 28 books on a shelf. 12 are storybooks, 8 are comic books, and the rest are textbooks. How many textbooks are there? | ANSWER: 8 textbooks

MCQ

Quick Quiz

Which of these is a Part-Part-Whole problem where you need to find the 'whole'?

Rohan had 20 marbles. He lost 5. How many are left?

There are 7 red roses and 9 yellow roses in a garden. How many roses are there in total?

A baker made 30 cookies. He sold 22. How many are unsold?

My friend has 15 stickers. I have 8 fewer. How many do I have?

The Correct Answer Is:

Option B asks to combine two parts (7 red roses and 9 yellow roses) to find the total (the whole). The other options involve finding a missing part after subtraction.

Real World Connection

In the Real World

When you manage your mobile data, you might have a total data pack (the 'whole'), and you use some data for social media (one 'part') and some for streaming videos (another 'part'). Understanding Part-Part-Whole helps you figure out how much data you have left, or how much you used for different activities.

Key Vocabulary

Key Terms

PART: A smaller amount or group that makes up a larger total | WHOLE: The total amount or entire group | ADDITION: Combining two or more numbers to find a total | SUBTRACTION: Taking one number away from another to find the difference | PROBLEM-SOLVING: The process of finding solutions to difficult or complex issues

What's Next

What to Learn Next

Next, you can explore multi-step word problems, which often combine several Part-Part-Whole situations. This will make you even better at solving complex problems in everyday life and in higher-level math!