Textbook Problem

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For problems 1-8, answer true or false.

When solving an equation that involves fraction, the equation can be cleared of all the fraction by multiplying both sides of the equation by least common multiple of all the denominators in the problem.

To determine

True or false.

Explanation of Solution

L.C.M:

Least common multiple of the number of values is a factor, which is completely divisible by all the number of values.

Calculation:

Given,

In solving an equation that involves fractions, the equation can be cleared of all the fractions by multiplying both sides of the equation by the least common multiple of all denominators in the problem.

The above statement is true.

Because, the least common multiple of any number of values, which can be expressed or factored by having each one of the value as a factor for which LCM was found.

Thus, when the LCM of all the denominators of a equation is multiplied on the both sides, each denominator divides the multiplied LCM exactly and thereby all the denominators will become $1$

Example:

$\frac{2x}{3}-\frac{x}{4}=\frac{2}{7}$

The LCM of the denominator $\mathrm{3,\; 4}$ and $7$ is $84$, thus multiplying $84$ on both sides we have,

$84\left(\frac{2x}{3}-\frac{x}{4}\right)=84·\frac{2}{7}$

Apply the distributive property of multiplication over subtraction,

$84\left(\frac{2x}{3}\right)-84\left(\frac{x}{4}\right)=84·\frac{2}{7}$

Now, factorize the LCM $84$, multiplied with each term according to its denominator