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:

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• 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: \(\color{blue}{3 &\text{ div }; 8 = 0.375}\). 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

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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Frequently Asked Questions

What is the easiest way to convert between all three forms?

Use decimals as a “hub.” Convert everything to a decimal first: divide the fraction, or divide the percent by 100. Once you have a decimal, multiply by 100 for the percent, or place over a power of 10 and simplify for the fraction.

How do I simplify a fraction from a decimal like 0.375?

Write it as \(\color{blue}{\frac{375}{1000}}\), then find the GCF of 375 and 1000 (= 125), and divide: 375 ÷ \(\color{blue}{125 = 3}\); 1000 ÷ \(\color{blue}{125 = 8}\). So \(\color{blue}{0.375 = \frac{3}{8}}\).

Why is it helpful to convert to decimals when comparing?

Decimals have a uniform place-value structure. You can compare 0.625 and 0.60 by looking at the hundredths digit, which is much faster than finding a common denominator for \(\color{blue}{\frac{5}{8}}\) and \(\color{blue}{\frac{3}{5}}\).

Related Topics

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