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Chapter 6: Problem 118

What is a proportion? Give an example with your description.

Short Answer

Expert verified
A proportion is a mathematical statement that two ratios are equal. For instance, if 2 apples cost $5, then 3 apples would cost $7.5, written as 2:5 = 3:7.5, or \(a:b = c:d = 2:5 = 3:7.5\).

Step by step solution

01

Definition

A proportion is a statement that two ratios are equal. That is, the ratio of two quantities is equal to the ratio of their corresponding quantities.
02

Concept Clarification

For example, if you have 2 apples and your friend has 4 apples, the ratio of apples you have to the apples your friend has is 2:4 or 2/4. This can also be written as 2:4 = 1:2, meaning the ratio (1/2) is equivalent.
03

More Depth

The general form of a proportion is \(a:b = c:d\). Proportions are insightful in problems requiring 'scaling' or 'resizing'. If you know three of these values, you can find the fourth unknown value.
04

Exercise Solution

Let's set up a proportion to solve the problem. If we have \(a:b = c:d\), suppose we know a=2, b=5 and c=3, we can find d using cross-multiplication, i.e., d = bc/a, so d = 3*5/2, which equals 7.5. In a real-life scenario, this might mean that if 2 apples cost $5, then 3 apples would cost $7.5.

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)

Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

Solve the quadratic equations by factoring. \(3 x^{2}-4 x=15\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-2 x-5\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)
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