Comparison

Comparison is the process of determining the similarities and differences between two or more objects, numbers, or quantities. In mathematics, comparison is often used to compare the value of numbers, fractions, decimals, and percentages.

Methods of Comparison

There are several methods to compare numbers and quantities:

Using the greater than (>), less than (<), or equal to (=) symbols to compare two numbers. For example, 5 > 3, 7 < 10, 4 = 4.
Using the concept of ordering. Numbers can be ordered from least to greatest or greatest to least.
Using visualization tools such as number lines or bar models to help compare quantities.

Comparing Fractions

When comparing fractions, it's important to have a common denominator. If the denominators are the same, the fraction with the greater numerator is larger. If the denominators are different, the fractions can be compared by finding a common denominator and then comparing the numerators.

Comparing Decimals and Percentages

Decimals and percentages can be compared by looking at their numerical values. For decimals, the number with more decimal places is greater. For percentages, their numerical values can be directly compared, keeping in mind that percentages are always out of 100.

Study Guide

Here are some key points to remember when studying comparison:

Understand the symbols for comparison: >, <, =.
Learn how to order numbers from least to greatest and greatest to least.
Practice comparing fractions with common denominators and different denominators.
Compare decimals based on the number of decimal places.
Remember that percentages can be directly compared based on their numerical values.

By mastering the skill of comparison, you'll be able to make informed decisions and analyze numerical information more effectively.

◂Math Worksheets and Study Guides Sixth Grade. Ratio

The resources above cover the following skills:

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.