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What is a Multiplicative Comparison Word Problem?
Grade Level:
Class 4
Maths, NLP, AI, Logic
Definition
What is it?
A multiplicative comparison word problem is a math problem where you compare two quantities by saying one is 'how many times' bigger or smaller than the other. It uses multiplication or division to find the relationship between the two numbers.
Simple Example
Quick Example
Imagine your cricket team scored 150 runs. The opposing team scored 50 runs. To compare, you might say your team scored '3 times' more runs than the other team. This '3 times' is a multiplicative comparison.
Worked Example
Step-by-Step
QUESTION: My mom bought a new mobile phone for ₹18,000. My dad's old phone cost ₹6,000. How many times more expensive is my mom's new phone than my dad's old phone?
---1. Identify the two quantities: Mom's phone cost = ₹18,000, Dad's phone cost = ₹6,000.
---2. Understand the question: We need to find 'how many times more expensive'. This means we should divide the larger amount by the smaller amount.
---3. Set up the division: 18,000 ÷ 6,000.
---4. Perform the division: 18,000 / 6,000 = 3.
---5. State the answer clearly: My mom's new phone is 3 times more expensive than my dad's old phone.
Why It Matters
Understanding multiplicative comparisons is crucial for problem-solving in math and science. In fields like AI, it helps in comparing data patterns, and in logic, it builds foundational reasoning skills. This skill is vital for careers in data analysis, engineering, and even business management.
Common Mistakes
MISTAKE: Adding or subtracting the numbers instead of multiplying or dividing. | CORRECTION: Look for keywords like 'times as many', 'times more', 'times less' which signal multiplication or division.
MISTAKE: Dividing the smaller number by the larger number. | CORRECTION: Always divide the larger quantity by the smaller quantity to find 'how many times' one is bigger than the other.
MISTAKE: Not understanding what 'times' means in the context of the problem. | CORRECTION: Remember 'times' means multiplication, or if you're finding the comparison, it means division.
Practice Questions
Try It Yourself
QUESTION: A small packet of biscuits costs ₹10. A family pack costs ₹50. How many times more expensive is the family pack than the small packet? | ANSWER: 5 times
QUESTION: My friend's house is 24 km from school. My house is 8 km from school. How many times closer is my house to school than my friend's house? | ANSWER: 3 times
QUESTION: During a sale, a t-shirt costs ₹300. Its original price was ₹900. By what factor was the original price more than the sale price? | ANSWER: 3 times
MCQ
Quick Quiz
Which of these is a multiplicative comparison word problem?
Rohan has 5 mangoes, and Priya has 3 mangoes. How many mangoes do they have together?
A bus travels 60 km in 1 hour. How far does it travel in 3 hours?
There are 10 red balloons and 2 blue balloons. How many more red balloons are there?
A recipe needs 2 cups of flour. If you want to make 4 times the recipe, how much flour do you need?
The Correct Answer Is:
D
Option D uses '4 times the recipe', which is a direct multiplicative comparison. The other options involve addition, simple multiplication (without comparison), or subtraction.
Real World Connection
In the Real World
When you compare mobile data plans, like a 2 GB plan versus an 8 GB plan, you're using multiplicative comparison to see that one offers '4 times' more data. This is also used by e-commerce companies like Flipkart to show how much more storage a premium laptop has compared to a basic one.
Key Vocabulary
Key Terms
QUANTITY: An amount or number of something | COMPARE: To look at two or more things to see how they are similar or different | MULTIPLICATION: The process of combining numbers to find their product | DIVISION: The process of splitting a number into equal parts | FACTOR: A number that divides another number exactly
What's Next
What to Learn Next
Next, you can explore 'Additive Comparison Word Problems' to understand how they differ from multiplicative ones. This will help you choose the right operation for any comparison problem you encounter.
