Division of Literals

Division of literals obeys all operation of division of numbers.

In arithmetic, we have studied that the division sign ‘÷’ read as ‘by’ between two numbers means that the number on the left of the division sign is to be divided by the number on the right.

For example:

15 ÷ 3 means that the number 15 on the left of the division sign is to be divided by the number 3 on the right of division sign.

In the case of literal numbers also x ÷ y read as ‘x by y’ means that the literal x is to be divided by the literal y and is written as x/y.

Thus 25 divided by a is written as 25/a and y divided by 5 written as y/5. It should be noted that 1/5 of y or y divided by 5 is also written as y/5.

Similarly, x divided by 10 is x/10. Quotient of 5 by z is 5/z.

Examples on Division of Literals:

Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction, multiplication and division:

1. Quotient of x by 4 is added to y.

Solution: We have,

Quotient of x by 4 = x/4

Therefore, quotient of x by 4 added to y = x/4 + y

2. Quotient of z by 6 is multiplied by y.

Solution: We have,

Quotient of z by 6 = z/6

Therefore, quotient of z by 6 is multiplied by y = z/6 × y = zy/6

3. Quotient of x by y added to the product of x and y.

Solution: We have,

Question of x by y = x/y

And product of x and y = xy

Therefore, quotient of x by y and to product of x and y = x/y + xy.

4. 100 taken away from the quotient of 5m by 2x.

Solution: We have,
Quotient of 5m by 2x = 5m/2x.

Therefore, 100 taken away from the quotient of 5m by 2x = 5m/2x - 100

5. Product of 4 and a divided by the difference of 5 and a.

Solution: Product of 4 and a = 4a

Difference of 5 and a = (5 - a)

Thus, we have 4a ÷ (5 - a)

or, 4a/(5 - 4)

6. Express the share of each child algebraically if x apples were equally distributed among four children.

Solution: Total number of Apple = x

Number of children = 4

Therefore, each children gets x ÷ 4 = x/4 apples.

7. Quotient of x by 2 subtracted from 10 less than x

Solution: We have,

Quotient of x by 2 = x/2

10 less than x = (x - 10)

Thus, we have (x - 10) - x/2

Properties of Division of Literals

For any literal number a

(i) a ÷ a = 1

(ii) 0 ÷ a = 0

(iii) a ÷ 1 = a

Division of literals is neither commutative nor associative.

Algebra Page

6th Grade Page

From From Division of Literals to HOME PAGE to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Fundamental Geometrical Concepts | Point | Line | Properties of Lines

    Apr 18, 24 02:58 AM

    Point P
    The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

    Read More

  2. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 18, 24 02:15 AM

    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  3. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Apr 18, 24 01:36 AM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More

  4. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 18, 24 12:31 AM

    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  5. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More

Literal Numbers - Worksheets

Worksheet on Addition of Literals

Worksheet on Subtraction of Literals

Worksheet on Multiplication of Literals

Worksheet on Division of Literals

Worksheet on Powers of Literal Numbers