A proportion is a statement that two ratios are equal. In other words, when two ratios are set equal to each other, they form a proportion. Equivalent fractions are fractions that represent the same value even though they may look different. To find equivalent fractions, you can multiply or divide both the numerator and the denominator by the same number.

For example, the fractions 1/2 and 2/4 are equivalent because if you multiply the numerator and denominator of 1/2 by 2, you get 2/4. Similarly, if you divide the numerator and denominator of 2/4 by 2, you get 1/2.

To work with proportions and equivalent fractions, follow these steps:

- Identify the given ratios or fractions.
- Set up the proportions by equating the two ratios.
- Cross-multiply and solve for the missing value.
- To find equivalent fractions, multiply or divide both the numerator and denominator by the same number.

Remember, proportions and equivalent fractions are important concepts in mathematics and are used in various real-life applications such as cooking, scaling drawings, and understanding financial ratios.

Practice working with proportions and equivalent fractions to strengthen your understanding of these concepts.

.Study GuideProportions/Equivalent Fractions Worksheet/Answer key

Proportions/Equivalent Fractions Worksheet/Answer key

Proportions/Equivalent Fractions Worksheet/Answer key

Proportions/Equivalent Fractions

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.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Connecting ratio and rate to multiplication and division

Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.