Fractions
Free lessons and practice worksheets for fractions — worked examples, common mistakes, and step-by-step solutions.
- 01Fractions3 min read
Adding Fractions
Adding fractions combines two or more fractional quantities to find their total sum. When fractions have the same denominator, the numerators add directly, but different denominators require finding a common denominator first. The process follows the fundamental principle that fractions represent parts of equal-sized wholes.
- 02Fractions3 min read
Dividing Fractions
Dividing fractions follows a counterintuitive rule: multiply by the reciprocal of the divisor. The operation 2/3 ÷ 4/5 becomes 2/3 × 5/4, yielding 10/12 or 5/6. This "invert and multiply" method transforms division into multiplication, making calculations straightforward.
- 03Fractions3 min read
Fraction / Decimal / Percent
Fractions, decimals, and percentages represent identical mathematical values in different formats. The fraction 3/4 equals the decimal 0.75, which equals 75 percent. Converting between these forms requires understanding that fractions represent division, decimals show place value positions, and percentages express parts per 100.
- 04Fractions3 min read
Fraction Representations
Fraction representations display the same mathematical value in different visual or numerical forms. A fraction like 3/4 can appear as a shaded portion of a circle, a point on a number line at 0.75, or as the decimal 0.75. These multiple representations help connect abstract fraction concepts to concrete visual understanding.
- 05Fractions3 min read
Fraction Word Problems
Fraction word problems combine real-world scenarios with fractional calculations, requiring students to identify the fractional relationship within a context. These problems typically involve finding a fraction of a quantity, determining what fraction represents a given situation, or combining fractions in meaningful contexts. The key skill lies in translating words into mathematical operations, particularly recognizing when 'of' indicates multiplication.
- 06Fractions3 min read
Introduction to Fractions
A fraction represents equal parts of a whole, written as one number over another with a line between them. The top number (numerator) shows how many parts are selected, while the bottom number (denominator) shows how many equal parts the whole is divided into. For example, 3/4 means 3 out of 4 equal parts.
- 07Fractions3 min read
Multiplying Fractions
Multiplying fractions follows a straightforward rule: multiply the numerators together and multiply the denominators together, then simplify the result. This operation appears in CCSS standards starting in grade 4 with whole number multiplication and expanding to full fraction multiplication in grade 5. The process differs from adding fractions because no common denominator is needed.
- 08Fractions3 min read
Subtracting Fractions
Subtracting fractions involves finding the difference between two fractional quantities by working with their numerators and denominators. The process requires a common denominator when the fractions have different bottom numbers, following the same principle as addition but removing rather than combining parts. This operation appears throughout mathematics, from basic arithmetic in elementary grades to advanced algebra and calculus.