Fraction, Decimal, and Percent Word Problems

Real-world math rarely asks you to work with fractions alone, or decimals alone, or percents alone. A recipe might call for $\frac{3}{4}$ cup of flour while the bag label shows the weight in decimals. A store might advertise 25% off an item priced at $39.99. These situations require you to move fluidly between fractions, decimals, and percents, sometimes within a single problem.

This page brings together the conversion skills and arithmetic you have built and puts them to work in practical, multi-step word problems.

Strategy for Mixed-Form Problems

When a problem mixes fractions, decimals, and percents, follow this approach:

1. Read the full problem before computing anything.
2. Identify what form is most convenient for the calculation. Percents are easy for “what percent” questions. Decimals are handy for multiplication and money. Fractions work well for exact portions.
3. Convert all numbers to the same form before combining them.
4. Solve step by step, showing your work at each stage.
5. Check that your answer makes sense in context.

Worked Examples

Example 1: Shopping with a Coupon

A jacket costs $85.00. The store offers a 20% discount, and you also have a coupon for an additional $\frac{1}{10}$ off the discounted price. What is the final price?

Step 1: Find the 20% discount amount.

$85.00 \times 0.20 = 17.00$

Step 2: Subtract to get the discounted price.

$85.00 - 17.00 = 68.00$

Step 3: Apply the $\frac{1}{10}$ coupon to the discounted price.

$68.00 \times \frac{1}{10} = 6.80$

Step 4: Subtract the coupon savings.

$68.00 - 6.80 = 61.20$

The final price is $61.20.

Example 2: Recipe Scaling

A cookie recipe calls for $\frac{2}{3}$ cup of sugar. You want to make 1.5 batches. How much sugar do you need?

Step 1: Multiply the amount by the scaling factor.

$\frac{2}{3} \times 1.5$

Step 2: Convert 1.5 to a fraction: $1.5 = \frac{3}{2}$.

$\frac{2}{3} \times \frac{3}{2} = \frac{6}{6} = 1$

You need exactly 1 cup of sugar.

Example 3: Survey Data Interpretation

A company surveyed 240 employees about commuting. The results showed that $\frac{3}{8}$ drive alone, 0.25 carpool, and the rest use public transit. How many employees use each method?

Step 1: Convert everything to the same form. Using decimals:

$\frac{3}{8} = 0.375$

Step 2: Find the public transit fraction.

$1 - 0.375 - 0.25 = 0.375$

Step 3: Calculate the number of employees for each method.

• Drive alone: $240 \times 0.375 = 90$ employees
• Carpool: $240 \times 0.25 = 60$ employees
• Public transit: $240 \times 0.375 = 90$ employees

Check: $90 + 60 + 90 = 240$. The numbers add up correctly.

Example 4: Measurement Conversion

A board is 6.75 feet long. A carpenter cuts off $\frac{1}{3}$ of the board. What percent of the original board remains?

Step 1: If $\frac{1}{3}$ is cut off, then $\frac{2}{3}$ remains.

Step 2: Convert $\frac{2}{3}$ to a percent.

$\frac{2}{3} \approx 0.6667 = 66.67\%$

About 66.67% of the original board remains.

To find the remaining length: $6.75 \times \frac{2}{3} = \frac{6.75 \times 2}{3} = \frac{13.50}{3} = 4.50$ feet.

Example 5: Tip Calculation

A restaurant bill is $47.50. You want to leave a tip of $\frac{1}{5}$ of the bill. Your friend says that is the same as a 20% tip. Are they correct, and what is the tip amount?

Step 1: Convert $\frac{1}{5}$ to a percent.

$\frac{1}{5} = 0.20 = 20\%$

Yes, your friend is correct.

Step 2: Calculate the tip.

$47.50 \times 0.20 = 9.50$

The tip is $9.50, making the total $57.00.

Practice Problems

Work through each problem and check your answer.

Problem 1: A shirt originally costs $45.00. It is marked down by 30%, and then you use a coupon for an additional $\frac{1}{4}$ off the sale price. What do you pay?

Problem 2: A tank holds 50 gallons of water. It is currently 0.6 full. After using $\frac{1}{5}$ of the water in the tank, how many gallons remain?

Problem 3: In a class of 32 students, $\frac{5}{8}$ passed the first exam. Of those who passed, 75% scored above 80. How many students scored above 80?

Problem 4: A recipe calls for 2.5 cups of flour. You only want to make $\frac{2}{5}$ of the recipe. How many cups of flour do you need?

Problem 5: A phone battery is at 85%. After browsing for a while, the battery drops by $\frac{1}{4}$ of its current charge. Then you charge it back up by 0.10 of the full battery capacity. What percent is the battery at now?

Key Takeaways

• Real-world problems often mix fractions, decimals, and percents in a single scenario.
• Convert to a common form before doing arithmetic. Decimals are usually easiest for multiplication and money; fractions are best for exact portions.
• Always re-read the question after solving to make sure you answered what was actually asked.
• Multi-step problems require careful order of operations: apply each discount, fraction, or percent in the correct sequence.
• Check your answer for reasonableness. If a discounted price is higher than the original, something went wrong.

Return to Arithmetic for more foundational math topics.