Pre-Algebra : Two-Step Equations with Fractions

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #92 : Two Step Equations

Find the solution for s.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

\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:

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

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

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

 

Example Question #151 : Algebraic Equations

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

Possible Answers:

\displaystyle m = 18

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

\displaystyle m = 8

\displaystyle m = 36

\displaystyle m = 14

Correct answer:

\displaystyle m = 18

Explanation:

To solve the equation,

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

use inverse operations.

Multiply both sides by \displaystyle 3,

\displaystyle 2m = 36

Divide both sides by \displaystyle 2,

\displaystyle m = 18

Example Question #151 : Algebraic Equations

Simplify the following

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

Possible Answers:

\displaystyle x=9

\displaystyle x=2

\displaystyle x=10

\displaystyle x=5

\displaystyle x=3

Correct answer:

\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:

\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:

\displaystyle x=3

Example Question #91 : Two Step Equations

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

The answer must be a mixed number.

Possible Answers:

\displaystyle \frac{65}{8}

\displaystyle 4\frac{5}{8}

\displaystyle 8\frac{1}{8}

\displaystyle 11\frac{7}{8}

Correct answer:

\displaystyle 8\frac{1}{8}

Explanation:

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

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

\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.

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

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

\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 \displaystyle 8\frac{1}{8}.

Example Question #91 : Two Step Equations

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

The answer must be a mixed number.

Possible Answers:

\displaystyle \frac{65}{8}

\displaystyle 4\frac{5}{8}

\displaystyle 8\frac{1}{8}

\displaystyle 11\frac{7}{8}

Correct answer:

\displaystyle 8\frac{1}{8}

Explanation:

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

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

\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.

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

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

\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 \displaystyle 8\frac{1}{8}.

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