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Pre-Algebra : Two-Step Equations with Fractions

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Example Questions

Example Question #92 : Two Step Equations

Find the solution for s.

$\frac{3}{6}+\frac{2}{3}s=\frac{3}{5}$ $\displaystyle \frac{3}{6}+\frac{2}{3}s=\frac{3}{5}$

Possible Answers:

$s=\frac{3}{20}$ $\displaystyle s=\frac{3}{20}$

$s=\frac{1}{5}$ $\displaystyle s=\frac{1}{5}$

$s=\frac{18}{15}$ $\displaystyle s=\frac{18}{15}$

$s=\frac{6}{4}$ $\displaystyle s=\frac{6}{4}$

$s=\frac{3}{5}$ $\displaystyle s=\frac{3}{5}$

Correct answer:

$s=\frac{3}{20}$ $\displaystyle s=\frac{3}{20}$

Explanation:

This is a two-step equation. The first step is as follows:

$\frac{3}{6}-\frac{3}{6}+\frac{2}{3}s=\frac{3}{5}-\frac{3}{6}$ $\displaystyle \frac{3}{6}-\frac{3}{6}+\frac{2}{3}s=\frac{3}{5}-\frac{3}{6}$

$\frac{2}{3}s=\frac{3}{5}-\frac{3}{6} \Rightarrow\frac{2}{3}s=\frac{18}{30}-\frac{15}{30}\Rightarrow \frac{2}{3}s=\frac{3}{30}$ $\displaystyle \frac{2}{3}s=\frac{3}{5}-\frac{3}{6} \Rightarrow\frac{2}{3}s=\frac{18}{30}-\frac{15}{30}\Rightarrow \frac{2}{3}s=\frac{3}{30}$

Now we divide both sides by 2/3 as follows:

$\frac{\frac{2}{3}s}{\frac{2}{3}}=\frac{\frac{3}{30}}{\frac{2}{3}}$ $\displaystyle \frac{\frac{2}{3}s}{\frac{2}{3}}=\frac{\frac{3}{30}}{\frac{2}{3}}$

$s=\frac{\frac{3}{30}}{\frac{2}{3}}\Rightarrow s=\frac{3}{30}\cdot \frac{3}{2}$ $\displaystyle s=\frac{\frac{3}{30}}{\frac{2}{3}}\Rightarrow s=\frac{3}{30}\cdot \frac{3}{2}$

$s= \frac{9}{60}=\frac{3}{20}$ $\displaystyle s= \frac{9}{60}=\frac{3}{20}$

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Example Question #151 : Algebraic Equations

$\frac{2}{3}m = 12$ $\displaystyle \frac{2}{3}m = 12$

Possible Answers:

m = 18 $\displaystyle m = 18$

$m = \frac{2}{3}$ $\displaystyle m = \frac{2}{3}$

m = 8 $\displaystyle m = 8$

m = 36 $\displaystyle m = 36$

m = 14 $\displaystyle m = 14$

Correct answer:

m = 18 $\displaystyle m = 18$

Explanation:

To solve the equation,

$\frac{2}{3}m = 12$ $\displaystyle \frac{2}{3}m = 12$

use inverse operations.

Multiply both sides by $\displaystyle 3$ ,

2m = 36 $\displaystyle 2m = 36$

Divide both sides by $\displaystyle 2$ ,

m = 18 $\displaystyle m = 18$

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Example Question #151 : Algebraic Equations

Simplify the following

$\frac{3}{5}x=\frac{9}{5}$ $\displaystyle \frac{3}{5}x=\frac{9}{5}$

Possible Answers:

x=9 $\displaystyle x=9$

x=2 $\displaystyle x=2$

x=10 $\displaystyle x=10$

x=5 $\displaystyle x=5$

x=3 $\displaystyle x=3$

Correct answer:

x=3 $\displaystyle x=3$

Explanation:

This is a two-step problem where you need to isolate x.

The first step is to multiply everything by $\displaystyle 5$ , which gives you:

3x=9 $\displaystyle 3x=9$ because the fives on both sides will cancel.

The next and last step is to divide both sides by $\displaystyle 3$ which gives you a final answer of:

x=3 $\displaystyle x=3$

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Example Question #91 : Two Step Equations

$3\frac{5}{8}+4\frac{1}{2}= ?$ $\displaystyle 3\frac{5}{8}+4\frac{1}{2}= ?$

The answer must be a mixed number.

Possible Answers:

$\frac{65}{8}$ $\displaystyle \frac{65}{8}$

$4\frac{5}{8}$ $\displaystyle 4\frac{5}{8}$

$8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$

$11\frac{7}{8}$ $\displaystyle 11\frac{7}{8}$

Correct answer:

$8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$

Explanation:

The first step to adding mixed numbers is to convert them into improper fractions.

$3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$ $\displaystyle 3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$

$4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$ $\displaystyle 4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$

Next, find the least common multiple of 2 and 8 so that both fractions have the same denominator.

$\frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$ $\displaystyle \frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$

Now that the denominators of both fractions are the same, add the fractions.

$\frac{29}{8}+\frac{36}{8}=\frac{65}{8}$ $\displaystyle \frac{29}{8}+\frac{36}{8}=\frac{65}{8}$

Convert the improper fraction back into a mixed number.

65 divided by 8 is 8 remainder 1, or $8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$ .

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Example Question #91 : Two Step Equations

$3\frac{5}{8}+4\frac{1}{2}= ?$ $\displaystyle 3\frac{5}{8}+4\frac{1}{2}= ?$

The answer must be a mixed number.

Possible Answers:

$\frac{65}{8}$ $\displaystyle \frac{65}{8}$

$4\frac{5}{8}$ $\displaystyle 4\frac{5}{8}$

$8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$

$11\frac{7}{8}$ $\displaystyle 11\frac{7}{8}$

Correct answer:

$8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$

Explanation:

The first step to adding mixed numbers is to convert them into improper fractions.

$3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$ $\displaystyle 3\frac{5}{8}=\frac{[(3\times8)+5]}{8} = \frac{29}{8}$

$4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$ $\displaystyle 4\frac{1}{2}=\frac{[(4\times2)+1]}{2}=\frac{9}{2}$

Next, find the least common multiple of 2 and 8 so that both fractions have the same denominator.

$\frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$ $\displaystyle \frac{9}{2}\times\frac{4}{4}=\frac{36}{8}$

Now that the denominators of both fractions are the same, add the fractions.

$\frac{29}{8}+\frac{36}{8}=\frac{65}{8}$ $\displaystyle \frac{29}{8}+\frac{36}{8}=\frac{65}{8}$

Convert the improper fraction back into a mixed number.

65 divided by 8 is 8 remainder 1, or $8\frac{1}{8}$ $\displaystyle 8\frac{1}{8}$ .

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Pre-Algebra : Two-Step Equations with Fractions

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #92 : Two Step Equations

Example Question #151 : Algebraic Equations

Example Question #151 : Algebraic Equations

Example Question #91 : Two Step Equations

Example Question #91 : Two Step Equations

All Pre-Algebra Resources

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