7.1: Which One Doesn’t Belong: Comparing Speeds
Which one doesn’t belong? Be prepared to explain your reasoning.
 5 miles in 15 minutes
 3 minutes per mile
 20 miles per hour
 32 kilometers per hour
Let’s revisit equivalent ratios.
Which one doesn’t belong? Be prepared to explain your reasoning.
number of burritos 
cost in dollars 
unit price (dollars per burrito) 


row 1  2  14.00  
row 2  4  
row 3  5  
row 4  10  
row 5  $b$ 
2. What do you notice about the values in this table?
number of burritos 
cost in dollars 
unit price (dollars per burrito) 


row 1  Noah  $b$  $c$  $\frac{c}{b}$ 
row 2  Lin  $2 \boldcdot b$  $2 \boldcdot c$ 
Explain why, if you can buy $b$ burritos for $c$ dollars, or buy $2 \boldcdot b$ burritos for $2 \boldcdot c$ dollars, the cost per item is the same in either case.
number of burritos 
cost in dollars 
unit price (dollars per burrito) 


row 1  14.00  7.00  
row 2  28.00  7.00  
row 3  5  7.00  
row 4  10  7.00 
It takes 4 pounds of apples to make 6 cups of applesauce.
At this rate, how much applesauce can you make with:
How many pounds of apples would you need to make:
pounds of apples  cups of applesauce  

row 1  4  6 
row 2  7  
row 3  10  
row 4  9  
row 5  20 
The table shows different amounts of apples selling at the same rate, which means all of the ratios in the table are equivalent. In each case, we can find the unit price in dollars per pound by dividing the price by the number of pounds.
apples (pounds)  price (dollars)  unit price (dollars per pound)  

row 1  4  10  $10 \div 4 = 2.50$ 
row 2  8  20  $20 \div 8 = 2.50$ 
row 3  20  50  $50 \div 20 = 2.50$ 
The unit price is always the same. Whether we buy 10 pounds of apples for 4 dollars or 20 pounds of apples for 8 dollars, the apples cost 2.50 dollars per pound.
We can also find the number of pounds of apples we can buy per dollar by dividing the number of pounds by the price.
apples (pounds)  price (dollars)  pounds per dollar  

row 1  4  10  $4 \div 10 = 0.4$ 
row 2  8  20  $8 \div 20 = 0.4$ 
row 3  20  50  $20 \div 50 = 0.4$ 
The number of pounds we can buy for a dollar is the same as well! Whether we buy 10 pounds of apples for 4 dollars or 20 pounds of apples for 8 dollars, we are getting 0.4 pounds per dollar.
This is true in all contexts: when two ratios are equivalent, the two unit rates will always be equal.
quantity $x$  quantity $y$  unit rate 1  unit rate 2  

row 1  $a$  $b$  $\frac{a}{b}$  $\frac{b}{a}$ 
row 2  $s \boldcdot a$  $s \boldcdot b$  $\frac{s \boldcdot a}{s \boldcdot b} = \frac{a}{b}$  $\frac{s \boldcdot b}{s \boldcdot a} = \frac{b}{a}$ 