Multiplying a constant and a linear monomial

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Definition

A constant is a quantity which does not change. It is a quantity whose value is fixed and not variable for example the numbers 3, 8, 21π, etc. are constants.

A monomial is a number, or a variable or the product of a number and one or more variables. For example, -5, abc/6, x... are monomials.

A linear monomial is an expression which has only one term and whose highest degree is one. It cannot contain any addition or subtraction signs or any negative exponents.

Multiplying a constant like 5 with a linear monomial like x

gives the result as follows 5 × x = 5x

Example 1

Simplify the expression shown:

13 × 7z

Solution

Step 1:

The constant is 13 and the linear monomial is 7z

Step 2:

Simplifying

13 × 7z = 91z

So, 13 × 7z = 91z

Example 2

Simplify the expression shown:

$\left ( \frac{-5}{11} \right ) \times 9$mn

Solution

Step 1:

The constant is $\left ( \frac{-5}{11} \right )$ and the linear monomial is 9mn

Step 2:

Simplifying

$\left ( \frac{-5}{11} \right ) \times 9mn = \left( \frac{45mn}{11} \right )$

So, $\left (\frac{5}{11} \right) \times 9mn = \left( \frac{45mn}{11} \right)$

Example 3

Simplify the expression shown:

$\left ( \frac{9}{12} \right) \times (3p)$

Solution

Step 1:

The constant is $\left ( \frac{9}{12} \right)$ and the linear monomial is 3p

Step 2:

Simplifying

$\left ( \frac{9}{12} \right) \times (3p) = \left( \frac{9p}{4} \right)$

So, $\left ( \frac{9}{12} \right) \times (3p) = \left( \frac{9p}{4} \right)$