It is an equation stating that two ratios are equal.
A. Ratio
B. proportion
C. base
D. rate
The correct answer and explanation is:
The correct answer is B. proportion.
A proportion is an equation that shows two ratios or fractions are equal. For example, if two ratios such as ab\frac{a}{b} and cd\frac{c}{d} are set equal, the equation ab=cd\frac{a}{b} = \frac{c}{d} represents a proportion.
Proportions are commonly used in mathematics, particularly in solving problems related to scale, rates, or similar figures. They are based on the fundamental concept that if two ratios are equal, then their cross-products will also be equal. This property is known as the cross-multiply rule, and it can be written as: a×d=b×ca \times d = b \times c
This rule allows for solving for unknown values in the proportion. For example, if we are given the proportion 34=x8\frac{3}{4} = \frac{x}{8}, we can solve for xx by cross-multiplying: 3×8=4×x⇒24=4x⇒x=63 \times 8 = 4 \times x \quad \Rightarrow \quad 24 = 4x \quad \Rightarrow \quad x = 6
Proportions are extremely useful in various real-world applications. In cooking, for instance, if a recipe for 2 servings requires 1 cup of sugar, and a person wants to make 6 servings, they can set up a proportion to find the required amount of sugar: 12=x6\frac{1}{2} = \frac{x}{6}
Solving this proportion gives x=3x = 3, meaning 3 cups of sugar are needed. Proportions also play a critical role in fields such as finance, chemistry, and physics, where relationships between quantities need to be understood and manipulated efficiently.