In mathematics, a common denominator is a shared multiple of the denominators of two or more fractions. When adding or subtracting fractions with different denominators, it is necessary to find a common denominator in order to perform the operation.

Finding the Common Denominator

To find the common denominator of two or more fractions, you can follow these steps:

Identify the denominators of the fractions.
List the multiples of each denominator.
Find the least common multiple (LCM) of the denominators.

Example

Let's find the common denominator for the fractions 1/4 and 1/3.

Denominators: 4 and 3

Multiples of 4: 4, 8, 12, 16, 20, ... Multiples of 3: 3, 6, 9, 12, 15, 18, ...

The least common multiple of 4 and 3 is 12.

Using the Common Denominator

Once you have found the common denominator, you can rewrite the fractions with equivalent denominators and then perform the addition or subtraction.

For example, with the common denominator of 12, the fractions 1/4 and 1/3 become 3/12 and 4/12, respectively. You can then add them together to get 7/12.

Conclusion

Understanding and finding the common denominator is essential for working with fractions, especially when adding or subtracting them. It allows for the fractions to be combined and manipulated accurately.

◂Math Worksheets and Study Guides Second Grade. Sequencing

Vocabulary/Answer key

Sequencing

The resources above cover the following skills:

Number and Operations (NCTM)

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

Count with understanding and recognize 'how many' in sets of objects.

Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

Connect number words and numerals to the quantities they represent, using various physical models and representations.

Grade 2 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of the base-ten numeration system and place-value concepts

Children develop an understanding of the base-ten numeration system and place-value concepts (at least to 1000). Their understanding of base-ten numeration includes ideas of counting in units and multiples of hundreds, tens, and ones, as well as a grasp of number relationships, which they demonstrate in a variety of ways, including comparing and ordering numbers. They understand multi-digit numbers in terms of place value, recognizing that place-value notation is a shorthand for the sums of multiples of powers of 10 (e.g., 853 as 8 hundreds + 5 tens + 3 ones).

Connections to the Grade 2 Focal Points (NCTM)

Number and Operations: Children use place value and properties of operations to create equivalent representations of given numbers (such as 35 represented by 35 ones, 3 tens and 5 ones, or 2 tens and 15 ones) and to write, compare, and order multi-digit numbers. They use these ideas to compose and decompose multi-digit numbers. Children add and subtract to solve a variety of problems, including applications involving measurement, geometry, and data, as well as nonroutine problems. In preparation for grade 3, they solve problems involving multiplicative situations, developing initial understandings of multiplication as repeated addition.