Question

which of the following is the method used to determine whether or not a proportion is true? cross multiplication prorating simplifying inverse operations question 6 (5 points) max and angela are both long - distance runners, but angela runs more than max. for every hour that max spends running, angela spends an hour and a half. write a ratio that compares the time that max spends running to the time that angela spends running. $1\frac{1}{2}$ $\frac{2}{3}$

Explanation:

First Question (Determine method for proportion truth):

To determine if a proportion (like \( \frac{a}{b}=\frac{c}{d} \)) is true, cross - multiplication (checking if \( a\times d = b\times c \)) is the standard method. Prorating is for distributing proportionally, simplifying is for reducing fractions, and inverse operations are for solving equations (not checking proportions).

Step 1: Define the times

Max's running time per hour: Let's take Max's time as \( 1 \) hour (per the problem's "for every hour Max runs..."). Angela's running time for the same comparison is \( 1.5 \) hours (which is \( 1\frac{1}{2} \) or \( \frac{3}{2} \) hours).

Step 2: Form the ratio

The ratio of Max's time to Angela's time is \( \frac{\text{Max's time}}{\text{Angela's time}}=\frac{1}{\frac{3}{2}} \).

Step 3: Simplify the ratio

Using the rule for dividing by a fraction (\( \frac{a}{\frac{b}{c}}=\frac{a\times c}{b} \)), we get \( \frac{1\times2}{3}=\frac{2}{3} \).

Answer:

A. Cross multiplication

Second Question (Ratio of Max's to Angela's running time):