Writing and Solving Proportions
Write proportions as equal ratios and solve for unknown values using cross-multiplication in Grade 7 math real-world applications.
Key Concepts
New Concept Proportions are equations stating that two ratios are equal, frequently used to solve mathematical problems involving similar figures and scale drawings. What's next Next, you'll explore worked examples on setting up and solving proportions with similar triangles. Soon, we'll tackle indirect measurement problems using shadows and scale drawings with blueprints and maps.
Common Questions
What is a proportion?
A proportion is an equation stating that two ratios are equal, written as a/b = c/d. Proportions are used to find unknown values when two ratios have a known relationship. Cross-multiplication (a × d = b × c) is the standard method for solving proportions.
How do you solve a proportion with a missing value?
Set up the proportion with the unknown variable in one of the four positions. Cross-multiply to create a single equation: if a/b = c/x, then ax = bc. Divide both sides by the coefficient of x to isolate the variable and find the missing value.
What are real-world applications of proportions?
Proportions appear in everyday situations: scaling recipes (if 2 cups makes 24 cookies, how many cups for 36 cookies?), unit conversions (miles to kilometers), map reading (1 inch = 50 miles), and calculating discounts or tax rates on different purchase amounts.