Pre-Algebra Workbook 7: Decimals & Percent

Line up the decimal points, add as with whole numbers, and then place the decimal point in the answer directly below the others.

Line up the decimal points:

$$\begin{array}{r} 3.45 \\ +\;2.70 \\ \hline \end{array}$$

Add column by column:

• Hundredths: $5 + 0 = 5$
• Tenths: $4 + 7 = 11$ (write $1$ in the tenths place and carry $1$)
• Ones: $3 + 2 + 1 = 6$

So

$$3.45 + 2.70 = 6.15$$

The correct choice is C. $6.15$.

Line up the decimal points. You can write $5.2$ as $5.20$ so both numbers have the same number of decimal places, then subtract.

Rewrite $5.2$ as $5.20$ to match decimal places:

$$\begin{array}{r} 5.20 \\ -\;3.75 \\ \hline \end{array}$$

Subtract starting from the hundredths place:

• Hundredths: need to subtract $5$ from $0$ so borrow from the tenths.
• After borrowing: tenths become $1$ hundredths become $10$
• Hundredths: $10 - 5 = 5$
• Tenths: now $1 - 7$ borrow from the ones: ones become $4$ tenths become $11$
• Tenths: $11 - 7 = 4$
• Ones: $4 - 3 = 1$

So

$$5.20 - 3.75 = 1.45$$

The correct choice is B. $1.45$.

To round to the nearest tenth, look at the hundredths digit. If it is $5$ or more, round the tenths digit up by $1$ otherwise leave it the same.

In $4.376$

• The tenths digit is $3$
• The hundredths digit is $7$

Since $7 \ge 5$ round the tenths digit up from $3$ to $4$

So $4.376$ rounded to the nearest tenth is $4.4$

The correct choice is D. $4.4$.

Line up the decimal places by writing each number with three decimal digits if needed (for example, $0.5$ as $0.500$), then compare digit by digit from left to right.

Rewrite each decimal with three digits after the decimal point:

• $0.45 = 0.450$
• $0.5 = 0.500$
• $0.405$ stays $0.405$
• $0.495$ stays $0.495$

Now compare:

$$0.405 < 0.450 < 0.495 < 0.500$$

The greatest value is $0.5$

The correct choice is B. $0.5$.

Read $0.6$ as "six tenths" and write it as $\dfrac{6}{10}$ then simplify by dividing the numerator and denominator by their greatest common factor.

Write $0.6$ as a fraction:

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

The greatest common factor of $6$ and $10$ is $2$ so divide numerator and denominator by $2$

$$\dfrac{6}{10} = \dfrac{6 \div 2}{10 \div 2} = \dfrac{3}{5}$$

So $0.6$ as a fraction in simplest form is $\dfrac{3}{5}$

The correct choice is C. $\dfrac{3}{5}$.

Convert the fraction to an equivalent fraction with denominator $100$ or divide $3 \div 20$ to get the decimal.

Find an equivalent fraction with denominator $100$

$$\dfrac{3}{20} = \dfrac{3 \times 5}{20 \times 5} = \dfrac{15}{100}$$

As a decimal, $\dfrac{15}{100} = 0.15$

So $\dfrac{3}{20}$ as a decimal is $0.15$

The correct choice is A. $0.15$.

To convert a decimal to a percent, multiply by $100$ and attach the percent symbol.

Multiply $0.37$ by $100$

$$0.37 \times 100 = 37$$

Attach the percent symbol:

$$0.37 = 37\%$$

So $0.37$ as a percent is $37\%$

The correct choice is B. $37\%$.

First find $25\%$ of $40$ to get the discount, then subtract that amount from the original price.

Find $25\%$ of $40$

$$25\% = 0.25, \quad 0.25 \cdot 40 = 10$$

So the discount is $$10$

Subtract the discount from the original price:

$$40 - 10 = 30$$

So the sale price is $$30$

The correct choice is C. $$30$.

Percent increase = $\dfrac{\text{amount of increase}}{\text{original amount}} \times 100\%$ Find the increase, divide by $50$ then multiply by $100$

Find the amount of increase:

$$65 - 50 = 15$$

Use the percent increase formula:

$$\text{Percent increase} = \dfrac{15}{50} \times 100\%$$

Simplify $\dfrac{15}{50}$

$$\dfrac{15}{50} = \dfrac{3}{10} = 0.3$$

Now multiply by $100\%$

$$0.3 \times 100\% = 30\%$$

So the percent increase is $30\%$

The correct choice is D. $30\%$.

Convert $18\%$ to a decimal and multiply by $35$ to find the tip amount.

Convert $18\%$ to a decimal:

$$18\% = 0.18$$

Multiply by the bill amount:

$$0.18 \cdot 35 = 6.3$$

So the tip should be $$6.30$

The correct choice is B. $$6.30$.