- Properties of Real Numbers
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- Identifying Like Terms
- Combining like terms: Whole number coefficients
- Introduction to properties of addition
- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

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# Multiplying a constant and a linear monomial

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, 21…π, 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*

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

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

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