Textbook Problem

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For problems 1-48, determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. (Objective 1 and 2)

$\frac{n}{4}-\frac{5}{6}=\frac{5}{12}$

To determine

Whether the given problem is an equation or an expression.

Explanation of Solution

Approach:

Solving an equation is to find the value of the unknown(s) involved in the equation, such a value is said to be the solution of the equation and which on substitution it should satisfy the equation.

In solving equations which contains fractional terms, the following given steps need to be followed.

STEP 1:

Find the LCM of all the denominators in the equation.

STEP 2:

Multiply the obtained LCM on both sides of the equation.

STEP 3:

Clear all the denominators in the equation by the application of the distributive property and associative property of multiplication.

STEP 4:

Combine the terms of the unknown variables of the equation to be on one side (Left) of the equation and the constants on the other side (Right)

STEP 5:

Focus to obtain the value of the unknown by simplification.

Calculation:

Given,

$\frac{n}{4}-\frac{5}{6}=\frac{5}{12}$

The above problem is an equation since, $\frac{n}{4}-\frac{5}{6}$ and $\frac{5}{12}$ are related by the “equal to” sign.

Thus, let us solve the equation.

$\frac{n}{4}-\frac{5}{6}=\frac{5}{12}$

First clear the expression of all fractions by multiplying the LCM of all the denominator $4$ and $6$ which is $12$ on both side.

$12\left(\frac{n}{4}-\frac{5}{6}\right)=12\left(\frac{5}{12}\right)$

Apply the distributive property to the left side,

$12\left(\frac{n}{4}\right)-12\left(\frac{5}{6}\right)=12\left(\frac{5}{12}\right)$

$4·3\left(\frac{n}{4}\right)-6·2\left(\frac{5}{6}\right)=12\left(\frac{5}{12}\right)$

$3\left(4·\frac{n}{4}\right)-\left(2\right)\left(6·\frac{5}{6}\right)=12\left(\frac{5}{}\right)$