Multiplicative property of equality with integers calculator

Addition and multiplication properties in R

Commutative property of addition

a + b = b + a

Commutative property of multiplication

a x b = b x a

Associative property of addition

(a +b ) + c = a + (b + c)

Associative property of multiplication

(a x b) x c = a x ( b x c)

Distributive property

a x (b + c) = a x b + ax  c

Special Products in Algebra

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 - 2ab + b2

a2 -b2 = (a + b)(a-b)

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Using the Multiplicative Property of Equality with One-Step Linear Equations Involving Whole Numbers

Step 1: Find what number can be multiplied on the side of the equation with the variable in order to cancel the coefficient. This will result in the variable being by itself.

Step 2: Multiply both sides of the equation by the number found in step 1.

Step 3: Simplify the result.

Using the Multiplicative Property of Equality with One-Step Linear Equations Involving Whole Numbers - Vocabulary and Equations

One-Step Linear Equations: A one-step linear equation is a linear equation that can be solved in one step. Linear equations have no exponents on the variables, other than an implied exponent of 1.

Multiplicative Property of Equality: The multiplicative property of equality states that if you multiply (or divide, which is the same as multiplying by a reciprocal fraction) both sides of an equation by the same non-zero number, the truth of the equation does not change. That is, if A= B, then AC = BC where C is a non-zero number.

Whole Number: A whole number is a positive number which can be written without any fraction or decimal parts. Whole numbers are also called the counting numbers along with the number 0.

We will use the steps above and these definitions to use the multiplicative property of equality to solve one-step linear equations involving whole numbers in the following two examples.

Example Problem 1: Using the Multiplicative Property of Equality with One-Step Linear Equations Involving Whole Numbers

Use the multiplicative property of equality to determine the value of x if 3x = 36.

Step 1: Find what number can be multiplied on the side of the equation with the variable in order to cancel the coefficient.

The side of the equation with the variable is 3x. We want a number that when multiplied by 3 results in 1 (thus canceling the 3 and leaving the x by itself). Dividing by 3 would cancel our 3 out, and dividing is the same as multiplying by a reciprocal fraction. So we can multiply by {eq}\dfrac{1}{3} {/eq}.

Step 2: Multiply both sides of the equation by the number found in step 1.

We need to multiply both sides of the equation by {eq}\dfrac{1}{3} {/eq}.

{eq}\dfrac{1}{3}\cdot 3x = \dfrac{1}{3}\cdot 36 {/eq}

Step 3: Simplify the result.

To simplify, complete the multiplication on each side of the equation. Remember that whole numbers can be thought of as fractions with a denominator of 1, and to multiply fractions, we multiply the numerators together and the denominators together.

{eq}\begin{align} \dfrac{1}{3}\cdot 3x {}& = \dfrac{1}{3}\cdot 36\\ \dfrac{1}{3}\cdot\dfrac{3}{1}x & = \dfrac{1}{3}\cdot\dfrac{36}{1}\\ \dfrac{3}{3} x & = \dfrac{36}{3}\\ x & = 12 \end{align} {/eq}

The solution to the equation is x = 12.

Example Problem 2: Using the Multiplicative Property of Equality with One-Step Linear Equations Involving Whole Numbers

Use the multiplicative property of equality to determine the value of p if 36 = 4p.

Step 1: Find what number can be multiplied on the side of the equation with the variable in order to cancel the coefficient.

In order to cancel the 4, we need to multiply by {eq}\dfrac{1}{4} {/eq}.

Step 2: Multiply both sides of the equation by the number found in step 1.

Multiplying, we have

{eq}\dfrac{1}{4}\cdot 36 = \dfrac{1}{4}\cdot 4p {/eq}

Step 3: Simplify the result.

Completing the multiplication and simplifying the fractions, we have

9 = p

The solution to the equation is p = 9.

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