Learn about fractions through these example problems with detailed step-by-step solutions.
Example 1: Identifying Fractions
What fraction of the circle is shaded?
Step 1: Count the total number of equal parts the circle is divided into. There are 4 equal parts. This is the denominator.
Step 2: Count the number of shaded parts. There are 3 shaded parts. This is the numerator.
Step 3: Write the fraction with the numerator over the denominator. The fraction is 3/4.
Step 4: Therefore, 3/4 of the circle is shaded.
Example 2: Equivalent Fractions
Is 1/2 equivalent to 2/4?
Step 1: To check if two fractions are equivalent, you can multiply or divide the numerator and denominator of one fraction by the same non-zero number to see if you get the other fraction.
Step 2: Look at the denominators: 2 and 4. We can multiply 2 by 2 to get 4.
Step 3: Now, multiply the numerator of the first fraction (1/2) by the same number (2). 1 × 2 = 2.
Step 4: The new fraction is 2/4. This is the same as the second fraction.
Step 5: Therefore, 1/2 is equivalent to 2/4.
Example 3: Comparing Like Fractions
Compare the fractions 3/5 and 4/5 using <, >, or =.
Step 1: Check if the fractions have the same denominator. Yes, both fractions have a denominator of 5. These are called like fractions.
Step 2: When comparing like fractions, compare the numerators. The fraction with the larger numerator is the larger fraction.
Step 3: Compare the numerators: 3 and 4. Since 3 < 4, the fraction 3/5 is less than the fraction 4/5.
Step 4: Therefore, 3/5 < 4/5.
Example 4: Adding Like Fractions
Add the fractions 1/8 and 3/8.
Step 1: Check if the fractions have the same denominator. Yes, both fractions have a denominator of 8. These are like fractions.
Step 2: To add like fractions, add the numerators and keep the denominator the same.
Step 3: Add the numerators: 1 + 3 = 4. Keep the denominator 8. The sum is 4/8.
Step 4: Simplify the resulting fraction if possible. Both 4 and 8 are divisible by 4.
4 ÷ 4 = 1
8 ÷ 4 = 2
The simplified fraction is 1/2.
Step 5: Therefore, 1/8 + 3/8 = 4/8 = 1/2.
Practice Mode
Enter your own fraction problem, and get a step-by-step solution.
Note: This basic solver can currently handle simple problems like "add 1/4 and 2/4", "subtract 3/5 from 4/5", or "compare 1/2 and 2/4". Use the format "add fraction1 and fraction2", "subtract fraction1 from fraction2", or "compare fraction1 and fraction2".
Related Concepts
Explore these related mathematical concepts to deepen your understanding of fractions.
Numerator and Denominator
Understanding that the numerator is the number of parts being considered, and the denominator is the total number of equal parts.
Types of Fractions
Learning about proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), and mixed numbers (a whole number and a proper fraction).
Simplifying Fractions
Reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor.
Finding a Common Denominator
A necessary step for adding or subtracting unlike fractions, involving finding the least common multiple (LCM) of the denominators.
