What is Dividing in a Given Ratio?

S1-SA2-0313

Grade Level:

Class 5

Maths, Finance, Chemistry, Computing, AI

Definition

What is it?

Dividing in a given ratio means sharing a total quantity into parts according to a specific proportion. Instead of splitting equally, some parts get more or less based on the numbers in the ratio. It's like sharing a pizza where some friends get bigger slices than others.

Simple Example

Quick Example

Imagine you have 10 laddoos and want to share them between your two younger siblings, Rahul and Priya, in the ratio 2:3. This means for every 2 laddoos Rahul gets, Priya gets 3. So, Rahul would get 4 laddoos and Priya would get 6 laddoos.

Worked Example

Step-by-Step

Let's say a prize money of Rs. 1500 needs to be divided between two friends, Ajay and Bala, in the ratio 2:3.

Step 1: Add the parts of the ratio. 2 + 3 = 5 total parts.
---Step 2: Find the value of one ratio part. Divide the total amount by the total number of parts. Rs. 1500 / 5 = Rs. 300 per part.
---Step 3: Calculate Ajay's share. Ajay's ratio is 2, so multiply 2 by the value of one part. 2 x Rs. 300 = Rs. 600.
---Step 4: Calculate Bala's share. Bala's ratio is 3, so multiply 3 by the value of one part. 3 x Rs. 300 = Rs. 900.
---Step 5: Check your answer. Add Ajay's and Bala's shares to see if it equals the total amount. Rs. 600 + Rs. 900 = Rs. 1500.

Answer: Ajay gets Rs. 600 and Bala gets Rs. 900.

Why It Matters

This concept is super useful in many fields! Businesses use it to share profits, chemists use it to mix ingredients in correct proportions, and even computer programmers use it to allocate resources. Understanding ratios can help you manage money, understand recipes, and even design things correctly.

Common Mistakes

MISTAKE: Dividing the total amount by just one number in the ratio (e.g., 1500/2) | CORRECTION: Always add all the parts of the ratio first to find the total number of 'shares' before dividing the total amount.

MISTAKE: Forgetting to multiply each part of the ratio by the 'value of one part' | CORRECTION: After finding the value of one part, remember to multiply it by EACH number in the original ratio to get the individual shares.

MISTAKE: Getting the order of the ratio wrong (e.g., giving the first person the second ratio number) | CORRECTION: Pay close attention to which person or item corresponds to which number in the given ratio. The order matters!

Practice Questions

Try It Yourself

QUESTION: Share 25 chocolates between Rohan and Seema in the ratio 3:2. How many chocolates does Seema get? | ANSWER: Seema gets 10 chocolates.

QUESTION: A sum of Rs. 2400 is to be divided among three friends, Ali, Ben, and Chetan, in the ratio 1:2:3. How much money does Ben receive? | ANSWER: Ben receives Rs. 800.

QUESTION: Two teams, Team A and Team B, played a cricket match. The total runs scored by both teams combined was 320. If the runs scored by Team A and Team B were in the ratio 5:3, how many more runs did Team A score than Team B? | ANSWER: Team A scored 80 more runs than Team B.

MCQ

Quick Quiz

A packet of 45 biscuits is shared between two friends, Kavya and Diya, in the ratio 4:5. How many biscuits does Diya get?

20 biscuits

25 biscuits

30 biscuits

9 biscuits

The Correct Answer Is:

The total ratio parts are 4+5=9. Each part is 45/9=5 biscuits. Diya gets 5 parts, so 5x5=25 biscuits. Kavya gets 4 parts, so 4x5=20 biscuits.

Real World Connection

In the Real World

Imagine you and your friends start a small business selling handmade crafts. If you invest money in a ratio of 2:3:5, you would divide the profits in the same ratio. This ensures everyone gets a fair share based on their contribution, just like how companies like Paytm or Flipkart distribute shares to investors.

Key Vocabulary

Key Terms

RATIO: A comparison of two or more numbers showing their relative sizes | PROPORTION: A part, share, or number considered in comparative relation to a whole | TOTAL QUANTITY: The entire amount of something that needs to be divided | SHARE: The portion of something that a person or group receives

What's Next

What to Learn Next

Great job learning about dividing in a given ratio! Next, you can explore 'Proportions and Direct/Inverse Variation'. This will help you understand how changes in one quantity affect another, building on your ratio knowledge.