Pre-Algebra - One-Step Equations

Solve for .

$\frac{x}{-0.9}=-3.1$

Explanation

$\frac{x}{-0.9}=-3.1$ Multiply both sides by . When multiplying decimals, first multiply normally and then count the number of decimal places in the problem. We have . So starting from the right, we shift two places to the left to get a decimal of . Since we are multiplying with negative numbers, we need to determine if the answer is negative. There are two negative numbers and that means the answer is positive.

Solve:

Explanation

Divide by on both sides of the equation.

$\frac{2.02x}{2.02}=\frac{ -0.202}{2.02}$

Decimals may be written as fractions.

$-0.202=-\frac{202}{1000}; 2.02=\frac{202}{100}$

Dividing by a fraction is the same as multiplying by its reciprocal:

Substitute and solve.

$x=-\frac{202}{1000}\times\frac{100}{202}$

Solve for .

Explanation

Divide both sides by . Both decimals each have one decimal place so the expression becomes: $\frac{1.5}{0.3}=\frac{15}{3}$ .

Solve:

$\frac{1089}{50}$

$\frac{20000}{11}$

Explanation

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

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

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.

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

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

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

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

Solve:

$\frac{1}{4}$

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

$\frac{0.6x }{0.6}= \frac{24}{0.6}$

Decimals may be written as fractions.

$0.6=\frac{6}{10}$

Dividing by a fraction is the same as multiplying by its reciprocal:

Substitute and solve.

$x=\frac{24}{1}\times\frac{10}{6}$

$x=\frac{240}{6}=\frac{6\cdot 40}{6}$

The six in the numerator and in the denominator cancel out and we are left with the final answer,

Solve for .

Explanation

Divide both sides by . The denominator has less decimal places than the numerator so we just shift one decimal place for top and bottom: $\frac{4.12}{0.2}=\frac{41.2}{2}$ .