Learning Objectives
- Understand the meaning of the unitary method.
- Learn to find the cost of 1 item when the cost of many items is given.
- Use the value of 1 unit to find the value of any number of units.
- Solve word problems using the two-step unitary method.
Let Us Begin!
Kavita goes to a stationery shop near her school in Jaipur. She sees a sign: "5 pencils for Rs 30." She wants to buy 8 pencils. How much will she pay?
To solve this, we first find the cost of 1 pencil, and then multiply to find the cost of 8 pencils. This clever method is called the Unitary Method because we always find the value of one unit first.
[Image: A step-by-step example: "If 5 pencils cost ₹30, what do 8 pencils cost?" Step 1: Find cost of 1 pencil = ₹30 ÷ 5 = ₹6. Step 2: Cost of 8 pencils = ₹6 × 8 = ₹48. Visual showing the steps with arrows. Title: "Unitary Method — Step by Step".]
Step-by-Step Explanation
What is the Unitary Method?
The unitary method is a way of solving problems where we first find the value of 1 unit (one item), and then use it to find the value of the number of units we need.
Step 1: Find the Value of 1 Unit
If we know the cost of several items, we divide to find the cost of 1 item.
Example: 5 pencils cost Rs 30. Cost of 1 pencil = Rs 30 / 5 = Rs 6.
Think: Why do we divide? Because we are splitting the total cost equally among all the items.
Step 2: Find the Value of the Required Number of Units
Once we know the cost of 1 item, we multiply to find the cost of as many items as we need.
Cost of 8 pencils = Rs 6 x 8 = Rs 48.
Think: Why do we multiply? Because if 1 item costs Rs 6, then 8 items will cost 8 times as much.
The Two Steps -- Always Remember
| Step | What We Do | Operation |
|---|
| Step 1 | Find the value of 1 unit | Divide |
| Step 2 | Find the value of the required units | Multiply |
Writing the Solution Neatly
Always write your solution in this format:
Cost of 5 pencils = Rs 30
Cost of 1 pencil = Rs 30 / 5 = Rs 6
Cost of 8 pencils = Rs 6 x 8 = Rs 48
Think: Rohan buys 4 notebooks for Rs 120. His sister wants 7 notebooks. Can you find the cost? What will you do first?
Examples
Example 1: Cost of Mangoes
6 mangoes cost Rs 90. Find the cost of 10 mangoes.
Cost of 1 mango = Rs 90 / 6 = Rs 15
Cost of 10 mangoes = Rs 15 x 10 = Rs 150
Example 2: Cost of Notebooks
3 notebooks cost Rs 45. Find the cost of 9 notebooks.
Cost of 1 notebook = Rs 45 / 3 = Rs 15
Cost of 9 notebooks = Rs 15 x 9 = Rs 135
Example 3: Cost of Bangles
A shopkeeper in Hyderabad sells 4 bangles for Rs 60. Sita wants to buy 7 bangles. How much will she pay?
Cost of 1 bangle = Rs 60 / 4 = Rs 15
Cost of 7 bangles = Rs 15 x 7 = Rs 105
Key Words
| Word | Meaning |
|---|
| Unitary method | A method where we first find the value of 1 unit, then find the value of many |
| Unit | One single item or thing |
| Cost price | The amount of money needed to buy something |
| Divide | To split equally into parts |
| Multiply | To add a number to itself a certain number of times |
⭐ Key Points to Remember
- The unitary method has two steps: first divide, then multiply.
- Always find the value of 1 unit first.
- Write your solution step by step -- do not skip steps.
- Check: the cost of more items should be greater than the cost of fewer items.
- Use this method for cost, weight, distance, or any quantity.
Practice Questions
A. Fill in the Blanks
1. In the unitary method, we first find the value of unit.
2. To find the cost of 1 item, we the total cost by the number of items.
3. To find the cost of many items, we the cost of 1 item by the number needed.
4. If 4 erasers cost Rs 20, the cost of 1 eraser is Rs .
5. If 1 pen costs Rs 12, then 6 pens cost Rs .
B. Multiple Choice Questions
1. 8 bananas cost Rs 40. What is the cost of 1 banana?
(a) Rs 4(b) Rs 5(c) Rs 8(d) Rs 10
2. If 1 samosa costs Rs 8, what is the cost of 5 samosas?
(a) Rs 13(b) Rs 30(c) Rs 40(d) Rs 45
3. Which step comes first in the unitary method?
(a) Multiply(b) Add(c) Divide(d) Subtract
C. Solve These Word Problems (Show All Steps)
1. 7 colour pencils cost Rs 63. Find the cost of 12 colour pencils.
2. A fruit seller in Chennai sells 5 guavas for Rs 35. Anand wants to buy 9 guavas. How much will he pay?
3. Geeta buys 3 metres of ribbon for Rs 27. How much will 8 metres of ribbon cost?
4. A baker in Lucknow sells 6 biscuit packets for Rs 90. What is the cost of 10 packets?
🎨 Think and Do -- Fun Activity
Market Visit: Ask a family member the price of any 3 items from a nearby shop. Write the details below and use the unitary method to find the cost of a different quantity.
| Item | Quantity Given | Total Cost (Rs) | Cost of 1 Item (Rs) | New Quantity | New Total Cost (Rs) |
|---|
| | | | | |
| | | | | |
| | | | | |