Problem Based on Multiplications

**Category : **3rd Class

The numbers can be multiplied in either order or on changing the order of the numbers then the resulting product of the numbers does not change. The product of 56 and 67, 67 x 56 = 3752. The product of the numbers 56 and 67 on changing their order = 56 x 67 = 3752 is same as the product in the previous order. Therefore, multiplication is commutative.

**The product of two numbers M and N is same as the product of the numbers A and B. Which one of the following options is correct about the above statement? **

(a) M x N = A x B

(b) M x A = N x B

(c) Both A and B

(d) M x B = N x A

(e) None of these

** **

**Answer (a)**

**Explanation **

Explications Product of M and N is equal to the product of A and B. Hence,

M x M = A x B.

**Associative or Grouping Property of Multiplication**

The product of three numbers remains same even if the group of the numbers is changed. The product of the numbers 21, 4 and 25 when written in the order of (21 x 4) x 25 = 84 x 25 = 2100 and the product of the same numbers 21, 4 and 25 is same when written in the order of 21 x (4 x 25) = 21 x 100 = 2100. If three numbers are denoted by a, b and c then their product (a x b) x c = a x (b x c).

**The product of group of the numbers A and B with a number C is same as the another group of A and C with B. Which one of the following options is correct about the above statement?**

(a)

(b)

(c)

(d) All of these

(e) None of these

**Answers (b) **

**Explanation** According to the associative property of multiplication (A x B) x C = (A x C) x B is a true statement.

**Multiplicative Property of Zero (Or Null property)**

The product of a number and zero is always zero. Therefore, 34 x 0 = 0, 0 x 45 = 0.

For a number N, the product of N by zero is zero or N x 0 = 0, 0 x N = 0.

**What should be multiplied with the number 58765 to get zero?**

(a) 2

(b) 1

(c) 0

(d) All of these

(e) None of these

** **

**Answers (c)**

** ****Explanations: **The given number should be multiplied with zero to get zero as their product.

**Multiplicative Property of 1 or Multiplicative Identity Property**

The product of a number with 1 is the number itself. Therefore, 34 x 1 = 31. For a number N, the product of N and 1 is the number itself or N x l = N, 1 x N = N.

**What should be multiplied with the number 10876 to get the number itself?**

(a) 1

(b) 2

(c) 0

(d) All of these

(e) None of these

** **

**Answers (a)**

** ****Explication **To get the multiplicand itself the multiplicand should be multiplied with 1.

**Multiplicative Series**

When a group of numbers is arranged in such a way that there are some common relation between the numbers are obtained, the numbers in the group are called in series. In the group of numbers: 2, 4, 6, 8, 10, 12, the group of the numbers are starting from 2 and every next number is 2 more than the previous number. Therefore, the next number after 12 is 12 + 2 = 14.

**Find odd one out from the numbers: 16, 48, 8, 26, 64**

(a) 16

(b) 48

(c) 26

(d) 64

(e) None of these

** **** **

**Answer (c)**

** ****Explanation **26 is odd because except 26 all the numbers are the multiples of 8.

**Multiplication of Decimal Numbers**

The following steps are used for the multiplication of the decimal numbers by decimal numbers (345.67 and 234.54):

**Step 1:** Convert the decimal numbers into whole numbers, 5.67 into 567 and 4.54 into 454.

**Step 2:** Multiply the converted numbers by simple multiplication method, 567 x 454 = 257418

**Step 3:** Put the decimal point in the resulting product by counting the number of digits form left which is equal to the sum of number of decimal digits of multiplicand and multiplier = 2 + 2 = 4. Therefore, the decimal point will be placed in the product of the both decimal numbers by counting 4 from ones or right = 25.7418

**What is the product of the decimal numbers 638.23 and 0.76?**

(a) 485.0548

(b) 485.4805

(c) 4.8548

(d) All of these

(e) None of these

** **

**Answer (a)**

**8 calendars were distributed in 10 factories. How many calendars were distributed?**

(a) 80

(b) 81

(c) 82

(d) 83

(e) None of these

** **

**Answer (a)**

**Explanation** The total number of distributed calendars to 10 factory = 10 x 8 = 80.

**A bucket contains 5 litres of water. How much water do 1324 such buckets can contain?**

(a) 5545 litres

(b) 6620 litres

(c) 6045 litres

(d) All of these

(e) None of these

** **

**Answer (b)**

**Explanation** Quantity of water in 1324 such buckets = 1324 x 5 = 6620 litres of water.

**In a function, there are 30 chairs in each row. If the number of rows is 40 then how many number of chairs are there in all?**

(a) 1250

(b) 1300

(c) 1200

(d) 1400

(e) None of these

** **

**Answer (c)**

**Explanations **Total number of chairs = Number of rows x Number chairs in one row = 40 x 30 = 1200.

**A bike travels a distance of 65 km in 1 hour. How many kilometers will it cover in 10 days if bike runs 4 hours a day?**

(a) 2600km

(b) 2649km

(c) 2660km

(d) All of these

(e) None of these

** **

**Answer (a)**

**Explanation** The distance travelled by the bike in a day = 65 x 4 = 260 km.

Hence, distance travelled by bike in 10 days = 260 x 10 = 2600 km.

**The speed of an aeroplane is 249 km in 1 hour. If the aeroplane takes 3.00 hours to cover the distance between two towns then the distance between the towns is:**

(a) 815km

(b) 747km

(c) 810km

(d) 801km

(e) None of these

** **

**Answer (b)**

**Explanation** Distance covered by aeroplane in 3 hours = 249 x 3 = 747 km

**There are 87 books each with 220 pages and 50 other books each with 350 pages. What is the total number of pages?**

(a) 36640

(b) 36635

(c) 36639

(d) 36630

(e) None of these

** **

**Answer (a)**

**Explanation** Total number of pages = (220 x 87) + (350 x 50) = 19140 + 17500 = 36640. Therefore, option (a) is correct and rest of the options is incorrect.

**There are 987 students in Junior sections in a school and 453 students are in senior sections. Each student contributes Rs 2 for the Teacher's day. What is the total collection?**

(a) Rs 2890

(b) Rs 2880

(c) Rs 2810

(d) Rs 2800

(e) None of these

** **

**Answer (b)**

**Explication **Total number of students = 987 + 453 = 1440. Total collection = Rs 2 x 1440 = Rs 2880.

**What is the total salary of 10 workers, if each gets Rs 2756.50 excluding the amount of Rs 34.75 for ESI?**

(a) Rs 28902.50

(b) Rs 28803.50

(c) Rs 27912.50

(d) Rs 28003.50

(e) None of these

** **

**Answer (c)**

**Explanation: **Salary of each worker = 2756.50 + 34.75 = Rs 2791.25.

Therefore, total salary of 10 workers = 2791.25x10 = Rs 27912.50.

- Multiplication means repeated addition.
- The product of the numbers does not change on reversing their order.
- If a number is multiplied by 0 then the result is zero.
- In a multiplication the number which is multiplied is known as multiplicand.
- The number by which it is multiplied is known as multiplier and the answer or the result of multiplication is known as product.
- In a series of numbers, one number is related to another
- The product of two decimal numbers is the product of their whole and decimal parts.
- The product of a group of numbers does not change on changing the order of the numbers.
- The product of a whole number by 10, 100 and 1000 is obtained by placing the same number of zero after the number.
- The product of a number by 1 is the number itself.

- Multiplication sign is also denoted by simply a dot between two numbers.
- On the key board of computers symbol for multiplication is denoted by
- The word product comes from the Latin word produce.
- Babylonians method for multiplication was very similar to the method that is used today.
- The modern method of multiplications is based on Hindu Arabic numerals which was first discovered by Indian mathematicians.

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