Word Problems of Converting Percent, Fractions, and Decimals

Some GED word problems mix percentages, fractions, and decimals in the same question. The key is fluency: knowing how to convert between all three forms quickly and accurately. Once you can do that, any combination becomes manageable, and these problems often turn out to be simpler than they first appear.

What Are Percent-Fraction-Decimal Word Problems?

These problems involve two or more of the three representations of part-of-a-whole. For example, a problem might tell you that 0.35 of a class passed an exam and ask what fraction that is, or state that \(\color{blue}{\frac{3}{8}}\) of a budget was spent and ask for the decimal and percent. The conversions you need:

• Decimal to Fraction: \(\color{blue}{0.35 = \frac{35}{100} = \frac{7}{20}}\)
• Decimal to Percent: \(\color{blue}{0.35 \times 100 = 35}\)%
• Fraction to Decimal: \(\color{blue}{\frac{3}{8} = 3}\) ÷ \(\color{blue}{8 = 0.375}\)
• Fraction to Percent: \(\color{blue}{0.375 \times 100 = 37.5}\)%
• Percent to Decimal: 60% ÷ \(\color{blue}{100 = 0.60}\)
• Percent to Fraction: 60% = \(\color{blue}{\frac{60}{100} = \frac{3}{5}}\)

How to Solve These Word Problems

Step 1, Identify the given form and the target form

Read the problem. What is given (percent, fraction, or decimal)? What form does the answer need to be in?

Step 2, Convert to the target form

Use the conversion rules above. When in doubt, convert everything to decimals first. They are easiest to compare and calculate with.

Step 3, Solve the question

Apply arithmetic (multiply, compare, add, etc.) using the converted values.

Step-by-Step Summary

1. Read the problem; identify all numbers and their forms (%, fraction, decimal).
2. Convert to a common form (decimals recommended).
3. Perform the required operation (compare, calculate, find percent of a number).
4. Convert the answer to the form the problem requests.

Watch: Converting Between Fractions, Decimals, and Percents

Math with Mr. J covers all conversions in a comprehensive lesson perfect for mixed-form problems:

Worked Examples

Example 1: A school collected 0.35 of its fundraising goal. Write this as a fraction in simplest form and as a percent.

Fraction: \(\color{blue}{0.35 = \frac{35}{100} = \frac{7}{20}}\). Percent: \(\color{blue}{0.35 \times 100 = 35\%}\).
Answer: \(\color{blue}{\frac{7}{20}}\); 35%

Example 2: Express \(\color{blue}{\frac{3}{8}}\) as a decimal and a percent.

Decimal: (color{blue}{3 \div 8 = 0.375}). Percent: \(\color{blue}{0.375 \times 100 = 37.5\%}\).
Answer: 0.375; 37.5%

Example 3: A store sold 0.6 of its inventory. Express this as a fraction and percent. If the store started with 250 items, how many were sold?

Fraction: \(\color{blue}{0.6 = \frac{3}{5}}\). Percent: \(\color{blue}{60\%}\). Items sold: \(\color{blue}{0.6 \times 250 = 150}\).
Answer: \(\color{blue}{\frac{3}{5}}\); 60%; 150 items

Example 4: 40% of a 75-question test is reading questions. Write 40% as a fraction and find the number of reading questions.

Fraction: \(\color{blue}{40\% = \frac{2}{5}}\). Questions: \(\color{blue}{0.40 \times 75 = 30}\).
Answer: \(\color{blue}{\frac{2}{5}}\); 30 reading questions

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More Practice: Fractions and Decimals Video Review

Math Antics reinforces fraction-decimal connections, which are foundational for these mixed-form problems:

Exercises

1. Express 0.24 as a fraction in simplest form and as a percent.
2. A survey found \(\color{blue}{\frac{7}{20}}\) of respondents prefer coffee. Write this as a decimal and a percent.
3. A class scored an average of 85% on a test. Write 85% as a fraction in simplest form and as a decimal.
4. 0.5 of a pizza was eaten. If the pizza was cut into 16 slices, how many slices were eaten? Write the portion as a percent.
5. Convert \(\color{blue}{\frac{5}{8}}\) to a decimal and percent. Is it more or less than 60%?

Answers

1. \(\color{blue}{\frac{6}{25}; 24\%}\)
2. \(\color{blue}{0.35; 35\%}\)
3. \(\color{blue}{\frac{17}{20}; 0.85}\)
4. \(\color{blue}{8 \text{ slices }; 50\%}\)
5. \(\color{blue}{0.625; 62.5\%; \text{ more than } 60\%}\)

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Common Equivalents to Know by Heart

Knowing these pairs saves time on almost every problem.

Comparing Amounts and Finding the Whole

Many word problems do more than ask for a conversion. Here are two types that come up often.

Compare amounts given in different forms

Example: Ana got 4/5 of her quiz right. Ben scored 0.78. Cara scored 82%. Who did best?

• Ana: 4/5 = 0.80
• Ben: 0.78
• Cara: 82% = 0.82

Cara did best, then Ana, then Ben.

Find the whole from a part and a percent

Example: 18 students in a class play soccer. That is 30% of the class. How many students are in the class?

1. Write the percent as a decimal: 30% = 0.30.
2. Part = percent × whole, so 18 = 0.30 × whole.
3. Divide: 18 ÷ 0.30 = 60 students.

Check: 30% of 60 is 0.3 × 60 = 18. It matches.

Find a sale price

Example: A $60 jacket is 25% off. You pay 100% − 25% = 75% of the price, so 0.75 × 60 = $45.

Frequently Asked Questions

How do you convert decimals, fractions and percentages?

To change a fraction to a decimal, divide the top by the bottom: 3/8 = 3 ÷ 8 = 0.375. To change a decimal to a percent, multiply by 100: 0.375 = 37.5%. To change a percent to a fraction, write it over 100 and simplify: 60% = 60/100 = 3/5. Knowing these three moves makes mixed word problems much easier.

How do you solve fraction, decimal and percent word problems?

First decide what the question asks for, then change every number into one form, usually decimals, and do the math. For example, if a store has 80 shirts and 0.25 are blue while 30% are red, there are 0.25 × 80 = 20 blue and 0.30 × 80 = 24 red shirts. Convert the answer back to the form the question wants.

What is 0.375 times 100?

0.375 × 100 = 37.5. Multiplying by 100 moves the decimal point two places to the right. This is how you turn a decimal into a percent, so 0.375 is 37.5%. It is also the decimal form of 3/8, which makes it a handy equivalent to remember for word problems about eighths.

Are there fractions, decimals and percentages word problems for grade 7?

Yes. These problems are a big part of grade 7 math. A typical one: a jacket costs $64 and is marked 3/8 off. Since 3/8 = 0.375, the discount is 0.375 × 64 = $24, so the sale price is $40, which is 62.5% of the original. Working through the exercises builds the same skills.

How do you solve fraction to decimal word problems?

Divide the numerator by the denominator to get the decimal, then use it in the problem. For example, if a runner jogs 5/8 of a mile each day for 4 days, 5/8 = 0.625, so the total is 0.625 × 4 = 2.5 miles. Decimals are especially helpful when you need to compare amounts or use a calculator.

Related Topics

• Word Problems Involving Comparing Percent and Fractions
• Representing Percentage
• Fractional and Decimal Percentages
• Convert Between Fractions and Decimals
• Solving Percentage Word Problems