A ratio is a comparison of two or more quantities. It is often written as a fraction or using a colon (:). For example, if you have 3 red marbles and 5 blue marbles, the ratio of red marbles to blue marbles can be written as 3:5 or 3/5. Ratios are used to compare the sizes of two or more quantities.

To write a ratio, simply compare two quantities using a colon or as a fraction. For example, if you have 4 apples and 6 oranges, the ratio of apples to oranges can be written as 4:6 or 4/6, which can be simplified to 2:3 by dividing both parts of the ratio by their greatest common factor.

Ratios that represent the same comparison are called equivalent ratios. Equivalent ratios can be found by multiplying or dividing both parts of the ratio by the same number. For example, the ratios 2:3 and 4:6 are equivalent because 2 * 2 = 4 and 3 * 2 = 6.

Ratios can also be written as fractions. For example, a ratio of 2:3 can be written as the fraction 2/3. This is especially useful when solving problems involving ratios using fraction operations.

Ratios are used in many real-life situations, such as cooking (measuring ingredients), finance (calculating interest rates), and map reading (scale drawings). Understanding ratios is important for solving various problems in these areas.

When studying ratios, it's important to understand the following concepts:

- How to write ratios using a colon or as a fraction
- Finding equivalent ratios by multiplying or dividing both parts of the ratio
- Converting ratios to fractions and vice versa
- Applying ratios to real-life situations

Practice solving problems involving ratios and try to relate them to everyday situations to reinforce your understanding of the concept.

Remember that ratios are used to compare quantities and are an important aspect of mathematics and everyday life.

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.