A fraction is a way of representing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number).

There are three main types of fractions: proper fractions, improper fractions, and mixed numbers.

**Proper Fraction:**A fraction where the numerator is smaller than the denominator, such as 1/2 or 3/4.**Improper Fraction:**A fraction where the numerator is greater than or equal to the denominator, such as 5/3 or 7/4.**Mixed Number:**A whole number combined with a proper fraction, such as 1 1/2 or 2 3/4.

Equivalent fractions are different fractions that represent the same part of a whole. They have different numerators and denominators, but their values are the same. For example, 1/2, 2/4, and 3/6 are all equivalent fractions.

When adding or subtracting fractions, the denominators must be the same. If they are not, you need to find a common denominator before performing the operation.

When multiplying fractions, simply multiply the numerators and denominators. When dividing fractions, multiply by the reciprocal of the divisor (the fraction you're dividing by).

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. The result becomes the new numerator, with the denominator remaining the same. To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the new fraction, with the same denominator.

- Convert 2 1/2 to an improper fraction.
- Convert 5/3 to a mixed number.
- Add 3/4 and 1/3.
- Multiply 2/3 by 5/8.

Study GuideAdding Fractions Worksheet/Answer key

Adding Fractions Worksheet/Answer key

Adding Fractions Worksheet/Answer key

Adding Fractions

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Compute fluently and make reasonable estimates.

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 5 Focal Points (NCTM)

Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.