📚 Practice With Worksheets

Continue practicing fraction and mixed-number operations with the worksheets below.

▶️ Learn With Videos

Review common denominators, mixed-number operations, cancellation, and division by a fraction with the videos below.

🛠️ How to Use This Tool

Choose addition, subtraction, multiplication, division, or mixed fraction operations. Then select the problem types and number of questions for your session.

Enter each answer as a simplified fraction, mixed number, improper fraction, or whole number. Leave the whole-number box blank when entering a proper or improper fraction.

Select Check Answer for immediate feedback. After making a valid attempt, use Show Solution to review the complete fraction-operation process.

🧠 Things to Notice

Addition and subtraction require a common denominator, but multiplication and division do not.

Mixed numbers are usually converted to improper fractions before multiplying or dividing. An improper fraction and its equivalent mixed number represent the same value.

Equivalent answers must be expressed in fraction form and reduced to lowest terms. A yellow response means the value may be equivalent, but the form still needs revision.

📘 Vocabulary

Numerator: The number above the fraction bar. It tells how many equal parts are being considered.

Denominator: The number below the fraction bar. It tells how many equal parts make one whole.

Common denominator: A denominator shared by two or more fractions.

Least common denominator (LCD): The least common multiple of the denominators of two or more fractions.

Equivalent fractions: Fractions that have different numerators and denominators but represent the same value.

Proper fraction: A fraction whose numerator is less than its denominator.

Improper fraction: A fraction whose numerator is greater than or equal to its denominator.

Mixed number: A number written as the sum of a whole number and a proper fraction.

Reciprocal: A number formed by interchanging the numerator and denominator of a nonzero fraction.

Cancellation: Simplifying common factors across a multiplication expression before multiplying.

Common factor: A whole number that divides evenly into two or more numbers.

Greatest common factor (GCF): The greatest factor shared by two or more whole numbers.

Lowest terms: A fraction form in which the numerator and denominator have no common factor greater than one.

Regrouping: Renaming one whole as an equivalent fraction when subtracting mixed numbers.

📐 Fraction Operation Rules

The required steps depend on the operation. Use common denominators for addition and subtraction, and simplify products and quotients whenever possible.

Adding Fractions

Rewrite fractions with a common denominator. Add the numerators, keep the common denominator, and simplify.

\[ \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c} \]

When denominators are unlike, first create equivalent fractions using the LCD.

Subtracting Fractions

Rewrite fractions with a common denominator. Subtract the numerators, keep the common denominator, and simplify.

\[ \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c} \]

When subtracting mixed numbers, regroup one whole when the first fractional part is too small.

Multiplying Fractions

Multiply the numerators and multiply the denominators. Convert mixed numbers to improper fractions first.

\[ \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd} \]

Use cancellation before multiplying when a numerator and denominator share a common factor.

Dividing Fractions

Keep the first fraction, change division to multiplication, and multiply by the reciprocal of the second fraction.

\[ \frac{a}{b}\div\frac{c}{d} = \frac{a}{b}\times\frac{d}{c} \]

Simplify the result and rewrite an improper fraction as a mixed number when appropriate.

Always check: The denominator cannot equal zero, and the final fraction should be written in lowest terms.

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