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Question

# Write two different proportions using each set of numbers. Use cross products to justify your answer. A. $1.80,$1.20, 14, 21 B. 1, 3.5, 31.50, 9.0 C. 11.7, 8424, 0.02, 14.4

Solution

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#### Part A.

Determine the proportion of the given values.

\begin{align*} \dfrac{1.80}{1.20} &= \dfrac{21}{14} && \text{Write a proportion}\\ 1.80 \cdot 14 &= 1.20 \cdot 21 && \text{Cross-multiply}\\ 25.2 &= 25.2 && \text{Simplify}\\ \\ \dfrac{14}{21} &= \dfrac{1.20}{1.80} && \text{Write a proportion}\\ 14 \cdot 1.80 &= 21 \cdot 1.20 && \text{Cross-multiply}\\ 25.2 &= 25.2 && \text{Simplify} \end{align*}

#### Part B.

Determine the proportion of the given values.

\begin{align*} \dfrac{1}{3.5} &= \dfrac{9.0}{31.50} && \text{Write a proportion}\\ 1 \cdot 31.50 &= 3.5 \cdot 9.0 && \text{Cross-multiply}\\ 31.50 &= 31.50 && \text{Simplify}\\ \\ \dfrac{31.50}{9.0} &= \dfrac{3.5}{1} && \text{Write a proportion}\\ 31.50 \cdot 1 &= 9.0 \cdot 3.5 && \text{Cross-multiply}\\ 31.50 &= 31.50 && \text{Simplify} \end{align*}

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