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Pre-Algebra : One-Step Equations with Decimals

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Example Questions

Example Question #151 : One Step Equations

Evaluate: 0.06x = 3

Possible Answers:

0.2

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate , divide both sides by 0.06 .

$\frac{0.06x}{0.06} = \frac{3}{0.06}$

x=50

If dividing by decimals is difficult, multiply the numerator and denominator by 100 to get whole numbers to divide.

$\frac{3\cdot 100}{0.06\cdot 100}=\frac{300}{6}$

Next factor the numerator to find a common factor to cancel out.

$=\frac{300}{6}=\frac{6\cdot 50}{6}=50$

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Example Question #152 : One Step Equations

Solve: 1.04x = -3.12

Possible Answers:

$\frac{1}{3}$

2.08

-4.16

$-\frac{1}{3}$

Correct answer:

Explanation:

To determine the value of the unknown variable, isolate the term by dividing both sides by 1.04 .

$\frac{1.04x}{1.04} = \frac{-3.12}{1.04}$

x=-3

If dividing by decimals is difficult, you can convert each decimal into an integer by multiplying each number by 100 or moving the decimal to the right two places.

$\\1.04\times 100 x=-3.12\times 100\\ 104x=-312$

Now divide,

$\frac{104x}{104}=\frac{-312}{104}=\frac{-3\cdot 104}{104}=-3$

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Example Question #341 : Algebraic Equations

Solve: 0.33x = 66

Possible Answers:

200

$\frac{1089}{50}$

$\frac{20000}{11}$

Correct answer:

200

Explanation:

To solve for the unknown variable, divide both sides by 0.33 .

$\frac{0.33x }{0.33}= \frac{66}{0.33}$

x=200

If dividing by decimals is difficult, you can convert the decimal into an integer by multiplying the decimal number by 100 or moving the decimal to the right two places.

${0.33x \times 100 }= 66 \times 100$

33x=6600

Now divide each side by 33 and then factor the numerator to simplify the fraction.

$\frac{33x}{33}=\frac{6600}{33}$

$x=\frac{200\cdot 33}{33}=200$

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Example Question #41 : One Step Equations With Decimals

Solve: 0.15x = 15

Possible Answers:

2500

2.25

100

225

Correct answer:

100

Explanation:

Divide 0.15 on both sides of the equation.

$\frac{0.15x}{0.15} = \frac{15}{0.15}$

x=100

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Example Question #343 : Algebraic Equations

Solve: 0.04x = 0.8

Possible Answers:

0.02

200

0.2

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To solve for , divide both sides by 0.04 .

$\frac{0.04x }{0.04}= \frac{0.8}{0.04}$

$\frac{0.8}{0.04} = \frac{80}{4}$

x=20

If dividing by decimals is difficult, just multiply both decimals by 100 to get integers.

$\frac{0.8\times 100}{0.04\times100} = \frac{80}{4}$

When you multiply by 100 you move the decimal two spaces to the right.

From here factor the numerator and cancel like terms.

$\frac{80}{4}=\frac{20\cdot 4}{4}=20$

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Example Question #46 : One Step Equations With Decimals

Solve: 0.3 + x = 0.03

Possible Answers:

2.7

-2.7

-2.07

2.07

-0.27

Correct answer:

-0.27

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract 0.3 from both sides to isolate the .

0.3 + x -0.3= 0.03-0.3

Add a placeholder if necessary.

x= 0.03 - 0.30 = -0.27

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Example Question #42 : One Step Equations With Decimals

Solve: 0.35 = 0.02+x

Possible Answers:

0.33

0.55

3.7

0.15

0.37

Correct answer:

0.33

Explanation:

To isolate the unknown variable, subtract 0.02 on both sides of the equation.

0.35- 0.02= 0.02+x- 0.02

x=0.33

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Example Question #48 : One Step Equations With Decimals

Solve for : 0.2x = 0.3

Possible Answers:

$\frac{3}{2}$

0.6

$\frac{1}{10}$

Correct answer:

$\frac{3}{2}$

Explanation:

Isolate the variable by dividing both sides by 0.2 .

$\frac{0.2}{0.2}x = \frac{0.3}{0.2}$

The fraction can be solved by moving the decimal on both the denominator and numerator one unit to the right.

The answer is: $\frac{3}{2}$

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Example Question #49 : One Step Equations With Decimals

Solve and express the answer as a fraction: 0.9x = 8

Possible Answers:

$\frac{80}{9}$

$\frac{8}{90}$

$\frac{9}{80}$

$\frac{36}{5}$

$\frac{18}{25}$

Correct answer:

$\frac{80}{9}$

Explanation:

To solve for the unknown variable, divide both sides by 0.9 .

$\frac{0.9x}{0.9} = \frac{8}{0.9}$

Converting 0.9 to a fraction will become $\frac{9}{10}$ .

When eight divides by this fraction, it is similar to multiplying its reciprocal.

$\frac{8}{0.9} = 8\times \frac{10}{9} = \frac{80}{9}$

The answer is: $\frac{80}{9}$

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Example Question #43 : One Step Equations With Decimals

Solve: 1.25x = 5

Possible Answers:

6.25

3.25

Correct answer:

Explanation:

Divide 1.25 on both sides of the equation to isolate the unknown variable.

$\frac{1.25x}{1.25} = \frac{5}{1.25}$

x=4

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Pre-Algebra : One-Step Equations with Decimals

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #151 : One Step Equations

Example Question #152 : One Step Equations

Example Question #341 : Algebraic Equations

Example Question #41 : One Step Equations With Decimals

Example Question #343 : Algebraic Equations

Example Question #46 : One Step Equations With Decimals

Example Question #42 : One Step Equations With Decimals

Example Question #48 : One Step Equations With Decimals

Example Question #49 : One Step Equations With Decimals

Example Question #43 : One Step Equations With Decimals

All Pre-Algebra Resources

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