A common denominator is a shared multiple of the denominators of two or more fractions. When adding or subtracting fractions, it is essential to have a common denominator to combine the fractions accurately.

To find the common denominator for a set of fractions, follow these steps:

- Identify the denominators of the given fractions.
- Find the least common multiple (LCM) of the denominators.
- The LCM will be the common denominator for the fractions.

Find the common denominator for the fractions 1/3 and 2/5.

Step 1: The denominators are 3 and 5.

Step 2: The LCM of 3 and 5 is 15.

Step 3: The common denominator for 1/3 and 2/5 is 15.

Once you have found the common denominator, you can use it to add or subtract the fractions. To do this, follow these steps:

- Express each fraction with the common denominator by multiplying the numerator and denominator by the same value.
- Perform the addition or subtraction on the numerators while keeping the common denominator the same.

Add the fractions 1/3 and 2/5 using the common denominator of 15.

Step 1: Express 1/3 as (1 * 5)/(3 * 5) = 5/15 and 2/5 as (2 * 3)/(5 * 3) = 6/15.

Step 2: 5/15 + 6/15 = 11/15.

The sum of 1/3 and 2/5 using the common denominator 15 is 11/15.

Here are some key points to remember about common denominators:

- A common denominator is necessary for adding or subtracting fractions.
- The common denominator is a multiple of the denominators of the given fractions.
- To find the common denominator, calculate the least common multiple (LCM) of the denominators.
- After finding the common denominator, use it to express the fractions and perform addition or subtraction.

Practice finding common denominators and using them to add or subtract fractions to strengthen your understanding of this concept.

Now that you have learned about common denominators, you can confidently work with fractions and perform operations on them accurately.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

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

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.