Worked Examples

Complete step-by-step solutions to common fraction problems. Each example shows every step of the calculation process, from the initial problem through to the final simplified answer.

Converting Fractions

26 2/3 as an Improper Fraction

Convert the mixed number 26 2/3 into an improper fraction. Shows how to multiply the whole number by the denominator and add the numerator.

Convert 9/20 to Decimal

Learn how to convert the fraction 9/20 to decimal form using the division method, with explanation of place values and rounding.

Adding Fractions

Adding 1/2 + 1/4

Add fractions with different denominators by finding the least common denominator, converting both fractions, then adding and simplifying.

Dividing Fractions

Dividing 8/1 ÷ 1/2

Divide fractions using the multiply-by-reciprocal method. Shows how to flip the second fraction and multiply, then simplify the result.

Finding Reciprocals

Reciprocal of 5/9

Find the reciprocal of 5/9 by swapping the numerator and denominator. Includes explanation of when reciprocals are useful in mathematics.

Reciprocal of 53/17

Calculate the reciprocal of 53/17 and convert between improper fraction and mixed number forms of both the original and reciprocal.

Working with Mixed Numbers

Simplify 7 3/4 + 6 1/2

Add mixed numbers by converting to improper fractions, finding a common denominator, adding, then converting back to mixed number form.

How These Examples Help

Each worked example on this site follows the same clear structure to help you understand not just what the answer is, but how to arrive at it systematically.

1

Problem Statement

Every example begins with a clear statement of the problem, showing exactly what needs to be calculated or converted.

2

Method Selection

The appropriate method is identified and explained, with brief context on why this approach is used for this type of problem.

3

Step-by-Step Solution

Each calculation step is shown individually with explanations. No steps are skipped, even simple arithmetic.

4

Multiple Answer Formats

The final answer is presented in multiple formats where applicable: simplified fraction, mixed number, decimal, and percentage.

5

Related Examples and Tools

Each example suggests similar problems and links to relevant calculators for further practice and exploration.

Using Examples for Learning

These worked examples serve multiple purposes depending on your needs:

  • Homework Verification: Check your work against complete solutions
  • Method Learning: See the standard approach for each type of problem
  • Test Preparation: Practice with realistic problems before exams
  • Quick Reference: Look up how to solve specific fraction problems
  • Teaching Aid: Use as examples when explaining fractions to others

Each example shows one standard method for solving the problem. In mathematics, there may be multiple valid approaches to the same problem, especially for more complex calculations. Different curricula may prefer different methods or notation styles.

If you need to work through a problem that isn't shown here, try using the relevant calculator and following its step-by-step output. The calculators handle any valid input values and show complete working for every calculation.

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