Maharashtra Board Class 5 Maths Part One Chapter 4 Multiplication and Division PDF Download

Multiplication And Division

Multiplication

Multiplying A Given Number By A Three-Digit Number

Example (1) There are 754 students in a school. If one child's uniform costs 368 rupees, what will be the cost of the uniforms for all the children in the school?

The total cost of the uniforms is ₹ 2,77,472.

Here, 754 is the multiplicand, 368 is the multiplier and 2,77,472 is the product.

Note: We could have also found out the total cost of the uniforms by taking 368 754 times and adding it up. However, it takes less time and effort to find the answer by multiplication.

Teacher's Note

Multiplication helps us find total cost quickly. For example, if one notebook costs 25 rupees and you buy 40 notebooks, multiply 25 × 40 to get 1000 rupees instead of adding 25 forty times.

Exam Trick

Remember the three steps: multiply by units, multiply by tens, multiply by hundreds. Write each answer one place to the right. Then add all answers.

Points To Remember

Multiplicand is the first number we multiply.
Multiplier is the second number we multiply.
Product is the answer we get.
We multiply by ones, then tens, then hundreds one by one.
We add all the small answers to get the final answer.

Example (2) 3429 × 507 = How many?

Teacher's Note

When the multiplier has a zero in it, that row will be all zeros. For example, 3429 × 0 = 0000. This is normal and correct.

Exam Trick

If multiplier has a zero (like 507), the middle row will have all zeros. Do not skip this row. Write it down and add it.

Points To Remember

When a digit is zero, multiply the number by zero and write zeros.
Each row of answer moves one place to the right.
We add all rows together at the end.
Check by multiplying in different order if time allows.
Write numbers neatly in columns to avoid mistakes.

Example (3) Write a multiplication word problem using the two numbers 25,634 and 78. Solve the problem.

A shopkeeper bought 78 TV sets for ₹ 25,634 each. What is their total cost?

The total cost is ₹ 19,99,452.

Make a habit of holding the carried over numbers in your mind.

Teacher's Note

When shopping in a store, the shopkeeper calculates total cost by multiplying price per item by number of items. This is multiplication in real life.

Exam Trick

Always write what each number means. For example, write "cost of one TV" and "number of TV sets." This helps you avoid mistakes and shows your thinking clearly.

Points To Remember

Read the word problem carefully two times.
Identify which number is what (price, quantity, etc.).
Write the multiplication sentence clearly.
Multiply step by step and add the rows.
Write your final answer with the correct unit (rupees, kilos, etc.).

Problem Set 14

1. Multiply.

(1) 327 × 92
(2) 807 × 126
(3) 567 × 890
(4) 4317 × 824
(5) 6092 × 203
(6) 1177 × 99
(7) 456 × 187
(8) 6543 × 79
(9) 2306 × 832
(10) 6429 × 509
(11) 4,321 × 678
(12) 20,304 × 87

2. As part of the 'Avoid Plastic' campaign, each of 745 students made 25 paper bags. What was the total number of paper bags made?

3. In a plantation, saplings of 215 medicinal trees have been planted in each of the 132 rows of trees. How many saplings are there in the plantation altogether?

4. One computer costs 27,540 rupees. How much will 18 such computers cost?

5. Under the 'Inspire Awards' scheme, 5000 rupees per student were granted for the purchase of science project materials. If 154 students in a certain taluka were covered under the scheme, find the total amount granted to that taluka.

6. If a certain two-wheeler costs 53,670 rupees, how much will 35 such two-wheelers cost?

7. One hour has 3,600 seconds. How many seconds do 365 hours have?

8. Frame a multiplication word problem with the numbers 5473 and 627 and solve it.

9. Find the product of the biggest three-digit number and the biggest four-digit number.

10. One traveller incurs a cost of 7,650 rupees for a certain journey. What will be the cost for 26 such travellers?

Pairing Off Objects From Two Groups In Different Ways

(1) Ajay wants to travel light. So he took with him three shirts – one red, one green and one blue and two pairs of trousers – one white and one black. How many different ways does he have of pairing off a shirt with trousers?

Writing 'S' for shirt and 'T' for trousers, the possible different pairs are:

(Red S, Black T), (Green S, Black T), (Blue S, Black T)
(Red S, White T), (Green S, White T), (Blue S, White T)

Altogether 6 different pairs.

Teacher's Note

This is how we count all possibilities. If Ajay has 3 shirts and 2 pants, he makes 3 × 2 = 6 different outfits. This happens in real life when we get dressed.

Exam Trick

Remember: items in first group × items in second group = total pairs. In this example, 3 shirts × 2 trousers = 6 pairs. This is multiplication in disguise!

Points To Remember

Count items in the first group carefully.
Count items in the second group carefully.
Multiply the two numbers to get total pairs.
Each item from group one pairs with each item from group two.
All pairs are different combinations.

(2) Suresh has three balls of different colours marked A, B and C and three bats marked P, Q and R. He wishes to take only one bat and one ball to the playground. In how many ways can he pair off a ball and a bat to take with him?

How many different pairs have been shown here?

(3) The three friends, Sanju, John and Ali went to the fair. A shop there, had five different types of hats. Each of the boys had photos taken of himself, wearing every type of hat, in turn. Find how many photographs were taken in all.

Sanju – Sanju – Sanju – Sanju – Sanju –
John – John – John – John – John –
Ali – Ali – Ali – Ali – Ali –

How many different pairs were formed? That is, how many photos were taken?

Teacher's Note

At a photo studio, each person wears each type of hat once. With 3 people and 5 hats, they take 3 × 5 = 15 photos. This is pairing in photography.

Exam Trick

Always multiply: number of people × number of hats = total photos. Here it is 3 × 5 = 15 photos. Write this clearly in your answer.

Points To Remember

First count how many people there are.
Then count how many hat types there are.
Multiply these two numbers to get total photos.
Each person wears each hat exactly once.
Do not count same pair twice.

Take two collections, each containing the given number of objects. Make as many different pairs as possible, taking one object from each collection every time. Thus, complete the table below.

What does this table tell us?

The number of different pairs formed by pairing off objects from two groups is equal to the product of the number of objects in the two groups.

Teacher's Note

This rule works always. If group one has 3 items and group two has 4 items, you always get 3 × 4 = 12 pairs. It is like a multiplication table in real life.

Exam Trick

Whenever you see "pairs" or "combinations" in a question, multiply the two numbers. This is the golden rule for pairing questions.

Points To Remember

Pairing means taking one item from group one and one from group two.
The answer is always the product of the two groups.
Order does not matter - pairing works the same way.
Write the multiplication equation clearly.
Check your answer by counting some pairs yourself.

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