# 3rd Class Mathematics Division Problem Based on Multiplication and Division

Problem Based on Multiplication and Division

Category : 3rd Class

### Division by Forming Groups

There are 24 scissors given below. 24 scissors are arranged in such a way that each group contains 8 scissors. Therefore, 3 groups of scissors containing 8 scissors each will form as shown below. Hence, is defined as if 24 scissors are arranged in 3 groups then each one group will contain 8 scissors. Arrange the following pencils in groups in such a way that each group can contain 5 pencils. How many groups will form? (a) 4

(b) 5

(c) 7

(d) 3

(e) None of these

Explanation

20 - 5 = 4. Hence, 4 groups of 5 pencils in each group will form. Division on Number Line

Division of 24 by 8 on number line is performed by the following steps:

Step 1:    Draw a line and divide it into 24 equal parts. Step 2:   Write numbers on each division.

Step 3:   Start counting for each 8 from right and count how many 8 are there on the number line. Step 3: Therefore 3 is the division of 24 by 8. Which one of the following options is correct for the division of 6 by 2 on number line?

(a) (b) (c) Explanation

In the option (b) a number is divided into 6 equal parts and there are 3 groups of division are there on the number line and each group contains 2 division. Division by Long Division Method

The following steps are used for the division of 4563 by 7:

Step 1: Arrange the numbers as: Step 2: Consider the minimum dividend from 4563 as 45 because 4 is smaller than divisor 7.

Step 3:   Recite the table of 7 till equal to 45 or nearest to 45 and write required number of times of 6 as quotient and their product 42 below 45 and subtract them as shown below.

Step 4: Write the next number from dividend after the remainder.

Recite the table of 7 till equal to 36 or nearest to 36 and write required number of times of 5 as quotient and their product 35 below 36 and subtract them shown below. Step 5: Write the next number from dividend after the remainder. Recite the table of 7 till equal to 17 or nearest to 17 and write required number of times of 2 as quotient and their product 14 below 17 and subtract them shown below. Step 6: Now the remainder is less than the divisor therefore, it cannot be divided further.

According to the division algorithm. Divisor x Quotient + Remainder = Dividend.

Therefore, in the above division 652 is quotient, 3 is remainder and 7 is divisor on putting the values of divisor, quotient and remainder in division algorithm = 7 x 652 + 3 = 4567 is same as the dividend. There are 859 boys in a school. How many groups will form if there are 7 boys in each group?

(a) 123 groups and 6 boys

(b) 124 groups and 5 boys

(c) 122 groups and 5 boys

(d) 121 groups and 5 boys

(e) None of these

Explanation Quotient = 122 Remainder = 5

Hence, 122 groups will form if every group has 7 boys.

Remaining 5 boys will not form the group. Relation between Multiplication and Division

A box contains 12 mangoes therefore, 5 such boxes will contain 12 x 5 = 60 mangoes.

The required number of boxes for 60 mangoes if each contains 12 mangoes will be . Therefore, division is inverse process of multiplication. Division of Decimal Numbers

The following steps are used for the division of a decimal number 34.56 by 4:

Step 1:  Arrange the numbers as shown below.

Step 2: Divide 34.56 by 4 by long division method.  How many zeroes can be put into divisor in the division: ?

(a) 1

(b) 2

(c) 3

(d) All of these

(e) None of these

Expirations Number of zeroes is equal to the number of decimal digits of dividend.  Peter walks 6 km in the morning and 4 km in the evening. If his friend walks half of distance than Peter, then find the distance walked by his friend?

(a) 6km

(b) 5km

(c) 7km

(d) 8km

(e) None of these

Explanation

Distance walked by his friend . How many groups will form if 800 people are divided equally into 8 groups?

(a) 109

(b) 130

(c) 100

(d) 140

(e) None of these

Explanation . Maximum 4 students can sit on a bench. How many benches are required for 432 students to sit?

(a) 108

(b) 109

(c) 107

(d) All of these

(e) None of these

Explanation Total number of required benches  How many times 7 can be taken away from 8764?

(a) 1253

(b) 1252

(c) 1254

(d) 1270

(e) None of these There are 3 trays of eggs and each tray contains 20 eggs. How many trays are required if 10 eggs are arranged in each tray?

(a) 6

(b) 5

(c) 7

(d) 8

(e) None of these

Explanation The required number of trays . The number of chairs in a room is 25 and same number of chairs are there in 25 such rooms. How many equal number of chairs can be arranged in equal number of rows outside from both the rooms?

(a) 24

(b) 25

(c) 26

(d) 27

(e) None of these

Explanation

Total number of chairs = 25 x 25 = 625. Therefore, 25 chairs can be arranged in 25 number of rows. There are 6 fruit baskets in a hall. If one basket contains 34 fruits then how many number of 2 times bigger than the baskets are required for the same quantity of fruits?

(a) 1

(b) 2

(c) 3

(d) 4

(e) None of these

Explanation Total number of fruits = 34 x 6 = 204. The capacity of fruit basket that can contain 2 times bigger than the basket = 34 x 2 = 68. Hence, the number of baskets . If a mini bus can carry 28 children, then how many mini buses will be needed to carry 392 children?

(a) 14

(b) 23

(c) 32

(d) 41

(e) None of these

Explanation The required number of buses = 392 - 28 =14 buses. • Division means equal distribution.
• The symbol of division is horizontal line and two dots .
• Divided number is called dividend and denoted by capital letter "D".
• The number which divides the dividend is called Divisor denoted by 'D'.
• The number of times that the division has been carried out is called the quotient denoted by 'Q'.
• The number which is left after the division is called remainder denoted by 'R'.
• The division should be continued till the remainder is either ‘0’ or less than the divisor (d).
• Number divided by itself gives the quotient.
• Number divided by 1 is the number itself.
• If a number divides 0 then the result is always 0.
• A number cannot be divided by 0. • Division is the inverse process of multiplication.
• The symbol of division is also known as obelus.
• Another name of obelus is dagger. The symbol of dagger is
• Highest common factor was first found by successive common division method and laterally accepted.
• The galley method for division was also known as batello or scratch method for division.

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