DIVIDING WHOLE NUMBERS

When we divide a number by another number, we will have the terms dividend, divisor, quotient and remainder. 

Division Algorithm

The sum of the product of quotient & divisor and remainder is equal to dividend.

Dividend  = Quotient x Divisor + Remainder

The number which we divide is called the dividend.

The number by which we divide is called the divisor.

The result obtained is called the quotient.

The number left over is called the remainder.

Dividing Whole Numbers by Whole Numbers

Example 1 :

Divide 300 by 7 and write division algorithm.

Solution :

Use long division to divide 300 by 7.

From the above long division,

dividend = 300

divisor = 7

quotient = 42

remainder = 6

Division algorithm :

300 = 42 x 7 + 6

Dividing Whole Numbers by Fractions

When a whole number is divided by a fraction, keep the whole number as it is, change the division as multiplication and take reciprocal of the fraction.

Example 2 :

Divide 20 by 4/5.

Solution :

20 ÷ 4/5 :

= 20 x 5/4

= 5 x 5/1

= 25

Dividing Whole Numbers by Mixed Numbers 

When a whole number is divided by a mixed number, change the mixed number to an improper fraction and do the same procedure as explained in dividing whole numbers by fractions.

Example 3 :

Divide 26 by 2 3/5.

Solution :

26 ÷ 2 3/5 :

= 26 ÷ 13/5

= 26 x 5/13

= 2 x 5/1 

= 10

Dividing Whole Numbers by Decimals

When a whole number is divided by a decimal, change the decimal to a fraction and do the same procedure as explained in dividing whole numbers by fractions.

How to convert a decimal to a fraction :

If there is one digit after the decimal point, we can write the given decimal number as a fraction by taking denominator 10. If there are two digits after the decimal point, we can write the given decimal number as a fraction by taking denominator 100 and so on.  

Example 4 :

Divide 25 by 0.5.

Solution :

25 ÷ 0.5 :

= 25 ÷ 5/10

= 25 ÷ 1/2

= 25 x 2/1

= 50

Example 5 :

Divide 39 by 0.26.

Solution :

39 ÷ 0.26 :

= 39 ÷ 26/100

= 39 ÷ 13/50

= 39 x 50/13

= 3 x 50/1

= 150

Example 6 :

Divide 7 by 0.02.

Solution :

÷ 0.02 :

= 7 ÷ 2/100

= 7 ÷ 1/50

= 7 x 50/1

= 350

Solving Word Problems

Example 7 :

One pizza can be made in 3/4 hours. How many pizzas can be made in 1 day (24 hours) ?

Solution :

Number of pizzas can be made in 1 day (24 hours) :

= 24 ÷ 3/4

= 24 x 4/3

= 8 x 4/1

= 32

Example 8 :

David can read 5 pages of a book in 10 minutes. How many hours does he need to read the whole book, if the book has 360 pages?

Solution :

Given : David can read 5 pages in 30 minutes.

Number of pages read in 1 hour :

= 5 x 6

= 30 pages

Time taken to read 360 pages :

= 360/30

= 12 hours

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