8.7 Solve Proportion and Similar Figure Applications
2 min read•june 25, 2024
Proportions are powerful tools for solving real-world problems involving ratios and scaling. They allow us to compare quantities and find unknown values by setting up equations with equivalent fractions. This skill is essential for many practical applications.
From recipe adjustments to indirect measurements, proportions help us tackle a wide range of scenarios. By mastering the techniques of cross-multiplication and algebraic manipulation, we can confidently solve proportions and apply them to real-life situations.
Solving Proportions
Clearing fractions in proportions
Top images from around the web for Clearing fractions in proportions
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Fractions View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Fractions View original
Is this image relevant?
1 of 3
Top images from around the web for Clearing fractions in proportions
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Fractions View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials View original
Is this image relevant?
OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: Fractions View original
Is this image relevant?
1 of 3
Proportions equate two ratios expressed as fractions (32=64)
Cross-multiply terms to clear fractions multiply numerator of first by denominator of second ratio and vice versa
Set resulting cross-multiplied terms equal to each other
Isolate variable using algebra techniques combine like terms, divide both sides by variable's coefficient
Solve 4x=23 for x cross-multiply x⋅2=4⋅3, simplify 2x=12, divide by 2 x=6
Applying Proportions
Proportions for real-world ratios
Proportions solve problems with or scaling
Identify known and unknown quantities (variable) in problem
Set up with ratios comparing same types of quantities
Solve proportion for unknown variable using cross-multiplication and algebra
Recipe 2 cups flour per 3 cups sugar, 9 cups sugar available, find flour needed let x be flour, set up 32=9x, cross-multiply and solve 2⋅9=3⋅x, 18=3x, x=6, need 6 cups flour
Use to solve real-world problems involving ratios and rates
Similar triangles for indirect measurement
Similar triangles have same shape, different sizes congruent , proportional corresponding sides
Find unknown lengths identify similar triangles, set up proportion with corresponding side ratios, solve for unknown length
6-foot person casts 4-foot shadow, nearby tree casts 12-foot shadow, find tree height let x be tree height, set up 46=12x, cross-multiply and solve 6⋅12=4⋅x, 72=4x, x=18, tree is 18 feet tall
extends to other shapes beyond triangles, maintaining proportional relationships between corresponding parts
Scale and Ratio Applications
is a ratio that relates measurements on a model or map to actual measurements
Use ratios to convert between scaled representations and real-world dimensions
Apply proportions to solve problems involving maps, blueprints, and models