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Grade 6 Operations on Fractions

Interactive step-by-step solver for understanding operations on fractions and solving related problems.

Grade 6 Operations on Fractions
Back to Grade 6 Chapter 5: Decimals
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Step-by-Step Learning

Learn about operations on fractions through these example problems with detailed step-by-step solutions.

Example 1: Adding Fractions with Like Denominators

Calculate the value of \(\frac{3}{5} + \frac{1}{5}\).

Step 1: Check if the denominators are the same. Here, both fractions have a denominator of 5.
Step 2: Add the numerators: \(3 + 1 = 4\).
Step 3: Keep the denominator the same: \(\frac{4}{5}\).
Step 4: Check if the fraction can be simplified. Since 4 and 5 have no common factors, \(\frac{4}{5}\) is in its simplest form.
Step 5: Therefore, \(\frac{3}{5} + \frac{1}{5} = \frac{4}{5}\).
Adding Fractions: Expression: \(\frac{3}{5} + \frac{1}{5}\) Add numerators: \(3 + 1 = 4\) Result: \(\frac{4}{5}\)

Example 2: Subtracting Fractions with Unlike Denominators

Calculate the value of \(\frac{3}{4} - \frac{2}{3}\).

Step 1: The denominators are different (4 and 3). Find the least common denominator (LCD).
Step 2: The LCD of 4 and 3 is \(4 \times 3 = 12\).
Step 3: Convert each fraction to an equivalent fraction with denominator 12:
  • \(\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)
  • \(\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)
Step 4: Subtract the numerators: \(9 - 8 = 1\).
Step 5: Keep the denominator: \(\frac{1}{12}\).
Step 6: The fraction \(\frac{1}{12}\) is already in its simplest form.
Step 7: Therefore, \(\frac{3}{4} - \frac{2}{3} = \frac{1}{12}\).
Subtracting Fractions: Expression: \(\frac{3}{4} - \frac{2}{3}\) Convert to common denominator: \(\frac{9}{12} - \frac{8}{12}\) Result: \(\frac{1}{12}\)

Example 3: Multiplying Fractions

Calculate the value of \(\frac{2}{5} \times \frac{3}{7}\).

Step 1: Multiply the numerators: \(2 \times 3 = 6\).
Step 2: Multiply the denominators: \(5 \times 7 = 35\).
Step 3: Write the product as a fraction: \(\frac{6}{35}\).
Step 4: Check if the fraction can be simplified. Since 6 and 35 have no common factors, \(\frac{6}{35}\) is in its simplest form.
Step 5: Therefore, \(\frac{2}{5} \times \frac{3}{7} = \frac{6}{35}\).
Multiplying Fractions: Expression: \(\frac{2}{5} \times \frac{3}{7}\) Multiply numerators and denominators: \(2 \times 3 = 6\), \(5 \times 7 = 35\) Result: \(\frac{6}{35}\)

Practice Mode

Enter your own problem related to operations on fractions, and get a step-by-step solution.

Note: This basic solver can currently handle addition and subtraction of fractions with like or unlike denominators (e.g., Calculate 2/3 + 1/3; Calculate 3/4 - 1/2) and multiplication of fractions (e.g., Calculate 2/5 * 3/4).

Related Concepts

Explore these related mathematical concepts to deepen your understanding of operations on fractions.

Fractions

A fraction represents a part of a whole, written as \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator.

Common Denominator

To add or subtract fractions, they must have the same denominator, often found using the least common multiple (LCM).

Simplifying Fractions

Divide the numerator and denominator by their greatest common divisor (GCD) to simplify a fraction.

Multiplication of Fractions

Multiply numerators together and denominators together, then simplify the result if possible.