Proportion
A proportion is a statement that two ratios are equal. In other words, it expresses the equality of two ratios. The general form of a proportion is:
a/b = c/d
Where a, b, c, and d are numbers or algebraic expressions, and b and d are not zero.
Key Concepts:
- Ratios: A ratio is a comparison of two quantities. For example, if there are 3 boys and 5 girls in a class, the ratio of boys to girls is 3:5.
- Proportional Relationships: When two ratios are equal, they form a proportional relationship. If a/b = c/d, then a is directly proportional to b and c is directly proportional to d.
- Cross Products Property: In a proportion a/b = c/d, the cross products ad and bc are equal. This property can be used to solve proportions.
How to Solve Proportions:
- Cross Multiplication: To solve a proportion a/b = c/d, you can cross multiply by multiplying a by d and b by c. Set the resulting products equal to each other and solve for the unknown.
- Equivalent Fractions: You can also solve proportions by finding an equivalent fraction. Multiply or divide both parts of the ratio by the same number to find a new ratio that is equivalent to the given one.
Example:
Find the value of x in the proportion 3/5 = x/15.
Solution: Using cross multiplication, we get 3 * 15 = 5x. Simplifying, we have 45 = 5x. Dividing both sides by 5, we find that x = 9.
Study Guide:
- Understand the concept of ratios and how they are used to compare quantities.
- Learn to recognize proportional relationships and how to express them in the form of a proportion.
- Practice solving proportions using cross multiplication and finding equivalent fractions.
- Work on real-world problems that involve proportional reasoning, such as scaling and map problems.
- Review the cross products property and how it can be used to solve proportions.
Proportions are an important concept in mathematics and have many applications in everyday life. Understanding how to work with proportions will help you solve various types of problems involving comparisons and scaling.
.◂Math Worksheets and Study Guides Seventh Grade. Rational and Irrational Numbers
Study Guide
Rational and Irrational Numbers 
Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Connections to the Grade 7 Focal Points (NCTM)
Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.