# Division of Literals

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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, 18 ÷ 3 means that the number 18 on the left of the division is to be divided by the number 3 on the right side of division sign. In the case Division of Literals also a ÷ b read as ‘a by b’ means that the literal a is to be divided by the literal b and is written as a/b.

Thus, 20 divided by x is written as 20/x and x is divided by 3 is written as x/3. It should be noted that 1/3 of x or x is divided by 3 is also written as x/3

**Examples:**

1. Write each one of the following phrases by using numbers, literals and signs of basic operations:

(i) Quotient of x by 3 is multiplied by y

**Solution :**

We have, quotient of x by 3 = (x/3).(y)

= xy/3

(ii) 3 times x added to 7 by y

**Solution :**

We have, 3 times x = 3x, and 7 by y = 7/y.

∴ 3 times x added to 7 by (divided) y = 3x + 7/y.

(iii) Quotient of x by 4 is added to z

**Solution:**

We have, Quotient of x by 4 = x/4 + z

**Write each of the following phrases by using numbers, literals and signs of basic operations :**

(i) Quotient of z by 6 is multiplied by y.

**Solution :**

We have, Quotient of z by 6 = z/6

:. Quotient of z by 6 is multiplied by y means , z/6 x y = zy/6

(ii) Quotient of x by y added to the product of x and y

**Solution :**

We have, Quotient of x by y = x/y, and product of x and y = xy

∴ Quotient of x by y added to the product of x and y = x/y + xy

(iii) 4 taken away from the quotient of x by 2y.

**Solution :**

We have, Quotient of x by 2y = x/2y

∴ 4 taken away from the quotient of x by 2y = x/2y – 4

**Introduction to Algebra**

• Addition of Literals

• Subtraction of Literals

• Multiplication of Literals

• Division of Literals

• Constants and Variables

• Coefficient

• Addition of Literals

• Subtraction of Literals

• Multiplication of Literals

• Division of Literals

• Constants and Variables

• Coefficient

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