# Ways to Multiply and Divide

## Overview

This chapter introduces students to various multiplication and division strategies using real-life scenarios. It emphasizes breaking numbers into simpler parts (expanded form), solving word problems, understanding area, and interpreting division as sharing and grouping.

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## Key Topics Covered

### 1. Multiplication Strategies

- **Breaking Numbers (Expanded Form)**:
Example:
\( 65 \times 31 = (65 \times 1) + (65 \times 30) \)
\( = 65 + 1950 = 2015 \)

- **Bela’s Method (Column-wise Multiplication)**:
Multiply units and tens separately and then add the results.
Practice examples:
- \( 32 \times 46 \)
- \( 67 \times 18 \)

- **Using Place Value**:
Multiply each digit with respect to its place value.
e.g., \( 60 \times 30 = 1800 \), \( 5 \times 30 = 150 \)

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### 2. Word Problems in Daily Life

- **Monthly Salary Calculation**:
Calculate monthly or yearly wages by multiplying daily wage with number of days.

- **Examples**:
- Cook’s salary for 31 days = \( 65 \times 31 \)
- Shantaram’s salary for 28 days = \( 165 \times 28 \)
- Minister's yearly salary = \( 195 \times 365 \)

- **Water Consumption and Heartbeats**:
- 8 glasses/day → monthly/yearly water intake
- 72 heartbeats/minute → hourly, daily, yearly beats

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### 3. Area and Cost of Land

- **Area = Length × Breadth**
- Field A: \( 28 \times 27 \)
- Field B: \( 36 \times 12 \)
- Field C: \( 27 \times 19 \)

- **Cost Calculation**:
- Multiply area by rate per square metre to get total cost.

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### 4. Wages and Labour Laws

- **Daily Wage Comparison**:
Different states have different minimum wages.

- **Inequality in Wages**:
Thulasi is paid less than her husband for the same work.
Practice:
- Thulasi’s earning = \( 55 \times 49 \)
- Husband’s earning = \( 58 \times 42 \)

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### 5. Real-life Case Studies

- **Kamla Bai and the Cow**:
- Cow cost shared between Kamla and Govt.
- Monthly expense: \( 85 \times 30 \)
- Milk production: \( 8 \times 30 \)
- Income: milk sold at ₹9 per litre

- **Satish’s Earnings**:
- Looks after 17 goats, ₹1 per goat per day
- Monthly earnings = \( 17 \times 30 \)
- Compare with family loan repayment ₹5000/month

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### 6. Division Strategies

- **Equal Distribution**:
Loan amount divided into 6 equal parts
→ \( 9588 ÷ 6 \)

- **Step-wise Long Division**:
Understand partial subtraction and remainders.

- **Common Division Problems**:
- 976 children into 25 per bus
- 969 pencils divided among children with 4 pencils each

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### 7. Practice Word Problems

- Solve using multiplication or division:
- Milk sale: \( 210 \times 11 \)
- Water sale: \( 240 \times 12 \)
- Books, wages, packed items

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### 8. Fun with Patterns and Tricks

- **Number Patterns**:
- e.g., \( (12345 \times 9) + 6 = 111111 \)
- **Multiplication Puzzles**:
- Use letters to represent digits and solve


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## New Terms and Their Simple Meanings

| Term | Meaning in Simple Words |
|---------------------|---------------------------------------------------------|
| Multiply (गुणा करना) | To find total by repeating a number a certain number of times |
| Divide (भाग करना) | To split something equally into parts |
| Salary (वेतन) | Money given for doing a job |
| Area (क्षेत्रफल) | Space inside a shape, like a field |
| Cost (कीमत) | How much money is needed to buy something |
| Remainder (शेष) | What is left over after division |
| Pattern (पैटर्न) | A repeated arrangement of numbers or shapes |
| Rate (दर) | Price for one item or one unit |
| Minimum wage (न्यूनतम वेतन) | Least amount of money allowed for a day’s work |
| Expense (खर्च) | The money that you spend |

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## Practice Sums

### Easy (सरल)

1. **Multiply: 23 × 5**
**Solution**:
\( 23 \times 5 = 115 \)
(23 five times is 115)

2. **Divide: 56 ÷ 7**
**Solution**:
\( 56 ÷ 7 = 8 \)
(7 times 8 is 56)

3. **A milkman sells 12 litres of milk daily. How much does he sell in 10 days?**
**Solution**:
\( 12 \times 10 = 120 \) litres

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### Medium (मध्यम)

4. **A worker earns ₹98 per day. How much does he earn in 15 days?**
**Solution**:
\( 98 \times 15 = 1470 \)

5. **A total of 576 books are to be packed in boxes of 24 books each. How many boxes are needed?**
**Solution**:
\( 576 ÷ 24 = 24 \) boxes

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### Difficult (कठिन)

6. **A farmer has to pay ₹2,750 every month for 2 years. How much will he pay in total?**
**Solution**:
\( 2750 \times 24 = ₹66,000 \)

7. **A field is 27 m × 19 m. What is the area and total cost if cost is ₹120 per m²?**
**Solution**:
Area = \( 27 \times 19 = 513 \) m²
Cost = \( 513 \times 120 = ₹61,560 \)

8. **Kamla Bai sells 8 litres of milk daily at ₹9/litre. What is her monthly income (30 days)?**
**Solution**:
\( 8 \times 9 = ₹72 \)/day
\( 72 \times 30 = ₹2160 \)/month

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### Very Difficult (बहुत कठिन)

9. **Divide ₹9588 equally into 6 parts. How much is each part?**
**Solution**:
\( 9588 ÷ 6 = ₹1598 \)

10. **Satish takes care of 17 goats and earns ₹1/day/goat. Does he earn enough to help pay a loan of ₹5000/month?**
**Solution**:
\( 17 \times 30 = ₹510 \)
No, ₹510 is not enough to pay ₹5000.

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