## Division

Category : 5th Class

### Division

Division: distribution of a quantity into some parts such that each of the parts contains equal amount is called division.

Dividend: The number which is divided. Divisor: The number by which other number is divided.

Quotient: Number of times by which the divisor is multiplied to get equal to dividend.

Remainder: The number which is left after subtraction

Divide 4575 by 20 .
\begin{align} & \underset{\text{Divisor}\,\leftarrow 20)4575(228\to \text{Quotient}}{\mathop{\overset{\text{Dividend}}{\mathop{\uparrow }}\,}}\, \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{-40}{057} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{-40}{175} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{-160}{\underline{015}}\to \text{Remainder} \\ \end{align}

Divide 25689 by 23 and find remainder.

\begin{align} & 23)25689(1116 \\ & \underline{-23} \\ & \,\,\,026 \\ & \underline{-23} \\ & \,\,\,038 \\ & \underline{-23} \\ & \,\,\,\,159 \\ & \underline{-138} \\ & \,\,\,\,\underline{021} \\ \end{align}

How to Perform Division

Consider first digit of the dividend from left.

Condition 1:  When the first digit is greater than or equal to the divisor:

Step 1: Multiply the divisor by a number such that the product is closest to the number but not greater.

Step 2: Write the multiplier in the quotient side and the product below the number and subtract.

Step 3: Bring down the second digit of the dividend and write it right to the difference.

Step 4: Now compare the formed number with the divisor. If the number is greater than divisor, follow the above steps. If the number is smaller than the divisor multiply the divisor by 0 and follow above steps. Continue the process till all the digits of the dividend is brought down.

Condition 2: When the first digit is smaller than the divisor, Step 1: Multiply the divisor by 0 and follow the above steps.

Note: If the number formed by first two digits of the dividend is also smaller than divisor, multiply the divisor by 0 and follow the above steps.

Word Problems Based on Division

Arwin types 66 words in a minute, the average number of letter in a word is 6. If he types for 10 hours, how many times can he type the word "mathematics"?

(a) 21600 times

(b) 19200 times

(c) 15200 times

(d) 25200 times

(e) None of these

Explanation

Arwin types 66 words in a minute and the average number of letter in a word is 6 Therefore, total number of letters he types in a minute $=66\times 6=396$ Thus, in 10 hours he can type $=396\times 60\times 10$ letters = 237600 letters The word "mathematics" contains 11 letters. Therefore, total number of times he can type the word "mathematics" $=\frac{237600}{11}=21600.$

There are 72575 mangoes. They are to be packed into boxes. If each box contains 25 mangoes, find the number of required boxes.

(a) 2225

(b) 3000

(c) 2903

(d) 7125

(e) None of these

Explanation

Total number of mangoes = 72575

Number of mangoes in one box = 25

Therefore, total number of boxes $=\frac{72575}{25}=2903$

• Addition, subtraction and multiplication always starts from right and gees to left.
• When we add 1 to n digit highest number we get n+1 digit smallest number (n is a natural number).
• Product of two numbers is an add number.
• Product of two even numbers is an even number.
• Product of a add number and an even number is an even number.

• Addition is the sum numbers.
• When any number is added by 6, the number does net get change.
• Subtraction is the difference of two numbers.
• When 8 is subtracted from a number, the number remains same.
• Multiplication is the short cut method of repeated addition.
• When a number is multiplied by B, the number gets 8.
• When a number is multiplied by 1, the number does net get changed.
• Division is the method ff distribution if a quantity into some equal parts.
• When a number is divided by 1, the number does not get changed.

Find the sum of A, B and C when A = 96545, B = 225, and C = 1002?

(a) 97770

(b) 97772

(c) 77792

(d) 47772

(e) None of these

Explanation

A + B + C = 96545 + 225 + 1002 = 97772.

In a school, number of boys is 645 more than that of girls. If there are 2563 girls in the school, find the total number of students in the school?

(a) 5771

(b) 3208

(c) 4568

(d) 4786

(e) None of these

Explanation

Number of girls in the school = 2563

Number of boys in the school = 2563 + 645 = 3208

Total number of students in the school = 2563 + 3208 = 5771.

There are two sets of question paper. Set A contains 25 objective questions and 60 subjective questions. Set B contains 35 objective question and 50 subjective question.

Jack: Both the sets of question paper has contained equal number of questions.

Codi: Total number of subjective questions is equal to the total number of objective questions. Who is correct?

(a) Jack

(b) Codi

(c) Both are correct

(d) Both are partially incorrect

(e) None of these

$\underline{\frac{\begin{matrix} \begin{matrix} 4 \\ + \\ \end{matrix} & \begin{matrix} 6 \\ 2 \\ \end{matrix} & \begin{matrix} 8 \\ 0 \\ \end{matrix} & \begin{matrix} 9 \\ 6 \\ \end{matrix} & \begin{matrix} 8 \\ 4 \\ \end{matrix} \\ \end{matrix}}{\begin{matrix} 4 & 8 & 8 & 6 & 2 \\ \end{matrix}}}$

Look the above sum carefully and find in which one of the following columns from right there is a mistake?

(a) First

(b) Second

(c) Third

(d) Fourth

(e) None of these

Subtract 5896 from the difference between 98456 and 2999

(a) 45897

(b) 48796

(c) 89561

(d) 48963

(e) None of these

Explanation

Difference between 98456 and 2999 = 98456 - 2999 = 95457

Now subtract 5896 from 95457

Thus 95457-5896=89561

If B = 456, find the value of A in the equation A - 2B = 3B

(a) 912

(b) 1368

(c) 456

(d) 2280

(e) None of these

Explanation

Given B = 456, Therefore, $2B=2\times 456=912,$and $3B=3\times 456=1368$ Now put the value of 2B and 3B in the equation Thus A - 912 = 1368, A = 912 + 1368 A =2280

lf A - B = 255, B - C = 275, C - D = 250 then find A - D

(a) 840

(b) 780

(c) 260

(d) 275

(e) None of these

Which one of the following is not true about the subtraction?

(a) When a number is subtracted from two times of itself result is the number itself

(b) When a number is subtracted from the least whole number, the result is not a whole number

(c) When two negative integers, are subtracted from each other the result may be positive or negative integer

(d) Subtraction is the method by which difference between two numbers is found

(e) None of these

A question paper contains 30 questions. Questions from 1 to 17 are of 4 marks each and questions from 18 to 30 are of 5 marks each. Jack solves Q1, Q2, Q5, Q6, Q15, Q18, Q27 and Q,30 whereas Codi solves all thequestions. Find the difference between marks of Codi and Jack.

(a) 133

(b) 98

(c) 90

(d) 100

(e) None of these

Which one of the following is the product of 2795 and 630?

(a) 2754602

(b) 1760850

(c) 2457860

(d) 2546380

(e) None of these

Explanation

$2795\times 630=1760850$

Arwin types 40 words in a minute. He types 8 hours in a day. How many words would he type if he works from Monday to Saturday?

(a) 19200 words

(b) 91200 words

(c) 115200 words

(d) 95200

(e) None of these

John has a collection of 150 maths book. Each book has 225 number of pages. If each of the page contains 5 questions and John takes 3 minutes to solve one question, how much time does John take to solve all the questions contained by 100 such books?

(a) 625 hours

(b) 525 hours

(c) 520 hours

(d) 775 hours

(e) None of these

There are 75 bulbs in a house. Each bulb consumes 60 joule energy each second. 50 bulbs was replaced by 50 power saver. If one power saver consumes 10 joule energy in a second, find the total amount of energy now save in a day(1 kilo joule = 1000 joule).

(a) 388800 kilo joule

(b) 43200 kilo joule

(c) 129600 kilo joule

(d) 216000 kilo joule

(e) None of these

Divide 45648 by 24 and find the quotient.

(a) 190

(b) 1902

(c) 1901

(d) 1900

(e) None of these

Explanation

\begin{align} & 24)45648(1902 \\ & \frac{\,\,\,\,-24}{216} \\ & \frac{-216}{00048} \\ & \frac{\,\,\,-48}{\underline{00\,\,\,}} \\ \end{align} Quotient = 1902

An ant is climbing on a pole. If height of the pole is 700 m and the ant cover 5 cm in 1  second, find the time taken by the ant to reach on the  top of the pole.

(a) 4 hour 30 minute

(b) 4 hour 53 minute

(c) 3 hour 23 minute

(d) 5 hour 53 minute

(e) None of these

Explanation

Height of the pole $=700\times 100cm=70000cm$ Total time taken by the ant to reach on the top of the pole $=\frac{70000}{5}=14000$second

When A is divided by 42, the remainder is 33. If A = 414615, find the quotient.

(a) 9870

(b) 9874

(c) 9872

(d) 9873

(e) None of these

When X is divided by Y, the quotient and remainder are Z and R respectively. Which one of the following is not true?

(a) If Z is two times of Y then R < Y

(b) $Y\times \text{(Z+1)}>X$

(c)$X+R=Y\times Z+2R$

(d) $2Z\times 2Y=2Z$

(e) None of these

Zack wants to multiply two numbers such that their product is 4083936. For this, he selects first number 456 and other number 7896. He finds the product is not same as he wants. Therefore, he replaces 7896 by one of the following numbers. Choose which one is this?

(a) 8056

(b) 8956

(c) 5896

(d) 5796

(e) None of these

If A = 2510, B = 2650 and C = 2512, which one of the following is greatest?

(a) $A\times B$

(b) $B\times C$

(c) $A\times C$

(d) $A\times A$

(e) None of these

Find the sum of 25486 and 3562.

(a) 28056

(b) 28956

(c) 25896

(d) 29048

(e) None of these