Olympiad Test: Division - 1 - Class 4 MCQ

When we share equally we divide.

After dividing a number, the left over is called remainder.

Explanation:

• Dividing a number: When a number is divided by another number, the result is called the quotient.


• Leftover: The amount that remains after division is called the remainder.


• Example: If we divide 10 by 3, the quotient is 3 and the remainder is 1.


• Usage: The remainder is often used in mathematical operations such as long division and modular arithmetic.


• Importance: Understanding remainders helps in solving various mathematical problems and is a fundamental concept in number theory.

Grouping equally and division

• Definition: Grouping equally refers to dividing a certain quantity or value into equal parts.


• Operation: When we group equally, we perform the operation of division.


• Division: Division is the process of distributing a number into equal parts or groups.


• Example: If we have 12 items and want to group them into 3 equal groups, we would divide 12 by 3 to get 4 items in each group.


• Relationship: Grouping equally and division are related as they both involve distributing a value equally among a certain number of groups or parts.

Explanation:

• Division: Division is the mathematical operation of separating or distributing something into parts. It is the process of finding out how many times one number is contained in another.


• Example: If we have 10 apples and we want to distribute them equally among 2 people, we would perform division to find out that each person gets 5 apples.


• Symbol: The division operation is represented by the symbol "/", or sometimes by the division sign "÷".


• Properties: Division has properties such as the Division Property of Equality and the Division Property of Zero.


• Opposite of Multiplication: Division is the opposite operation of multiplication. If multiplication is combining equal groups to find the total, division is separating a total into equal groups.

When we get remainder it is called imperfect division.

Explanation:

• Divisor: The number that we are dividing by is called the divisor.

By definition, the divisor is the number that divides the dividend. It is the number that tells us how many times the dividend can be divided equally.

• Dividend: The number that is being divided is called the dividend.

The dividend is the total amount that is to be divided into equal parts. It is the number that we are dividing.

• Quotient: The result of division is called the quotient.

The quotient is the answer to a division problem. It is the number of times the divisor divides into the dividend evenly.

• Remainder: The amount left over after division is called the remainder.

If the dividend does not divide evenly by the divisor, then there is a remainder left over.
In this case, the number that we are dividing by is known as the divisor. It is the key element in the division process and determines how many times the dividend is divided to get the quotient.

If 8 ÷ 2 = 4 then 4 is the quotient.

• When any number is divided by one, the answer is the number itself.


• For example, if we have a number x and we divide it by 1, the result will always be x.


• This is because any number divided by 1 is simply that number itself, there is no change in value.


• Dividing by one represents the concept of the whole number being unchanged or undivided.


• So, in this case, if any number is divided by one, it will always result in the original number.

0/x = 0,
where x is any number except 0.

Here Q = 5 and R = 2
Hence Rahul is correct.

Problem:

• 2663 ÷ 7

• Divide 2663 by 7 to get the quotient and remainder.


• 2663 ÷ 7 = 380 with a remainder of 3.


• So, the quotient (Q) is 380 and the remainder (R) is 3.

Answer:

• Q = 380, R = 3

Therefore, the correct answer is A: Q = 380, R = 3.

Detailed

• Step 1: Divide the first digit of the dividend by the divisor: 2 ÷ 4 = 0 (since 2 is less than 4).


• Step 2: Bring down the next digit to create a new dividend: 25.


• Step 3: Divide the new dividend by the divisor: 25 ÷ 4 = 6.


• Step 4: Multiply the quotient obtained in step 1 (0) by the divisor (4) and subtract from the new dividend (25) to get the remainder: 25 - (0 x 4) = 25.


• Step 5: Hence, the quotient is 5 with a remainder of 1.


• Step 6: Therefore, the estimated quotient of 256 ÷ 45 is 5.

Division of 93 by 39

• Dividend = 93


• Divisor = 39


• Quotient = ?


• Remainder = ?

Step 1: Divide the Dividend by the Divisor

• 93 ÷ 39 = 2

Step 2: Multiply the Quotient by the Divisor

• 2 x 39 = 78

Step 3: Find the Remainder

• 93 - 78 = 15

Answer

• Quotient = 2


• Remainder = 15

Therefore, the correct answer is Q = 2, R = 15.

Calculation:

• Given that a dozen has 12 units


• To find the number of dozens in 7044 units, we need to divide 7044 by 12

• 7044 units ÷ 12 = 587 dozens

Answer:

• Option A: 587