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What divided by 5 equals 5?

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  • Last Updated : 31 Aug, 2022
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In mathematics division is also known as repetitive subtraction and division is basically the process of dividing a larger number into equivalent groups of smaller sizes. Any division expression in mathematics is represented as the formulae of the numerator divided by the denominator, where the numerator is the larger number which is split into the denominator of smaller sizes. However, the numerator may or may not be equal to or larger than the denominator also this operation of division can be considered as the opposite of the multiplication operation.

Division Operation

Every operation of division between any two numbers ‘A’ and ‘B’ comprises various elements which are obtained as a result of the division operation between these two, for example, some of the elements are the parts of the division operation are the Quotient, Dividend, Remainder, and Divisor respectively, and in order to understand all of these four elements which are also known as divisional elements we can study the following division which takes place between the numbers 110 and 7. Here 110 which is a numerator is also known as dividend and 7 which is the denominator is also known as divisor respectively.

Division Problems

 

Divident = Divisor x Quotient + Remainder

From the above Division it is clear that,

110 = 7 x 15 + 5

Terminology used in Division Operation

Divisor: The number which represents the denominator in the division operation is known as a divisor which is also referred to as a number of groups in which the dividend is split into, for example, if we divide 10 toffees among 2 children, then 2 is considered to be the division divisor of this operation.

Quotient: The answer that is obtained on the division of the numerator by the denominator is known as the quotient and it is basically the result that may or may not be of the same category of the integer or whole numbers to which the numerator or denominator belong. For example, if we split 10 toffees among 2 children then each child will get 5 toffees here 5 is the Quotient.

Dividend: Dividend is also known as the numerator which is a number that we split into the equal group, for example in the above problem division of 10 toffees among 2 children 10 is the dividend of this problem.

Remainder: Sometimes the numerator may not be completely divided by the denominator in that case we obtain a remainder that is not equivalent to zero. However, in the case of perfect division among the numerator and denominator, the remainder may be equal to zero. Therefore the remainder is equivalent to the value that is left out as residue upon the division of the numerator by the denominator. For example on the division of 10 toffees among 2 children both of the children will get equal toffees which are equivalent to 5 hence the remaining toffees will be equal to zero, therefore, the remainder is zero.

Solving Division Equations 

For carrying out the division process between the dividend and the divisor, we use the denominator as the divisor and the numerator as the dividend respectively. The dividend is written inside the brackets and the divisor is written outside it.

Step 1: Now starting from left to right the dividend is divided from the divisor and then the respective quotient and the remainders are obtained. So the process is first we extract the left-most digit of the dividend and check whether it is completely divided by the divisor and what is the multiplicative factor of it in case the dividend’s first digit is smaller than the divisor value then the first two digits are considered in the first step of the division process.

Step 2: The quotient of the division of the left-most digit of the dividend by the divisor is written on the top of the brackets line and is noted as 1the quotient’s first digit. 

Step 3: Now the first digit which is the left-most digit of the dividend is subtracted from the product obtained from the multiplication of the divisor and the quotient digit, this difference is noted down and this difference is used for successive division operation.

Step 4: Now the Dividend’s next digit is taken into consideration which is equivalent to 6 in this case

Step 5: We repeat the same steps from step 2 until we obtain the remainder on successive division of all the digits of the dividend by the divisor and in case the remainder is smaller than the divisor because in case the remainder is smaller it cannot be divided by the divisor.

See the illustration below, which illustrates the division process in the above phases.

Division Problem 2

 

What divided by 5 equals 5?

Solution:

Let us assume the number which on division by 5 gives us 5 to be x.

Now, 

x/5 = 5 

On solving for x, we get, 

=> x = 5×5

=> x = 25

Therefore, 25 when divided by 5 gives us 5. 

Solved Examples on Division

Example 1: If a divided by 2 gives you 10. Solve for a?

Solution:

a ÷ 2 = 10

Taking 2 on the right-hand side, 

a = 2 × 10

a = 20 

Example 2: If a/b is 15, what is b/a? 

Solution:

a/b = 15

Now, reciprocating the fraction, we get,

b/a = 1/15 

Example 3: What is obtained on the division of 30 by 15? 

Solution:

On the division of 30 by 15, we get,

30/15 = 2 

Example 4: If a/6 = 4/3, solve for a.

Solution:

We have,

=> a/6 = 4/3

Taking 6 on RHS, we have,

a = (4 x 6)/3 

a = 8

Example 5: What divided by 10 gives 2?

Solution:

Let 10/x = 2 

=> 10 = 2x 

=> x = 5

5 divided by 10 gives 2

Example 6: Find the GCD of (3,2).

Solution:

GCD (2,3) = HCF of (2,3)

Since 2 and 3 are not divisible by each other and have no common factors 

Therefore, upon division by each other, they yield the greatest common divisor = 1

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