Question 1

What is the least common denominator (LCD) of the fractions in the equation $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10}$$?

Accepted Answer

$$70$$

Question 2

After multiplying both sides of the equation $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10} by$$ $$70$$, what is the resulting equation?

Accepted Answer

$$50 + 14b = 49$$

Question 3

What is the value of $$b in $$the equation $$50 + 14b = 49$$?

Accepted Answer

$$b = -\frac{1}{14}$$

Question 4

Which property is used when multiplying both sides of an equation by the LCD to clear fractions?

Accepted Answer

Distributive Property

Question 5

If you substitute $$b = -\frac{1}{14}$$ back into the original equation $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10}$$, what should the result be?

Accepted Answer

$$\frac{7}{10}$$

Question 6

Which of the following steps is NOT necessary when solving $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10}$$?

Accepted Answer

Factoring the left side

Question 7

What is the first step in solving an equation with fractions such as $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10}$$?

Accepted Answer

Multiply both sides by the LCD

Question 8

Which of the following real-world scenarios could be modeled by the equation $$\frac{5}{7} + \frac{b}{5} = \frac{7}{10}$$?

Accepted Answer

Mixing two solutions with different concentrations to achieve a target concentration

Question 9

After clearing fractions and simplifying, you have $$50 + 14b = 49. $$What is the next step to solve for $$b$$?

Accepted Answer

Subtract $$50$$ from both sides

Question 10

Which of the following is a common mistake when solving equations with fractions?

Accepted Answer

Not multiplying every term by the LCD

Question 11

Suppose you have the equation $$\frac{a}{4} + \frac{2a}{5} = 3. $$What is the LCD you should use to clear the fractions?

Accepted Answer

$$20$$

Question 12

If you solve $$\frac{3}{8} + \frac{x}{2} = 1$$, what is the value of $$x$$?

Accepted Answer

$$\frac{5}{8}$$

Solving Linear Equations with Fractions: Step-by-Step Guide

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