Equivalent Ratios
What does it mean for a ratio to be equivalent to another?
Equivalent means equal. Equivalent ratios are equal to each other just like fractions can be equivalent to each other.
Make a double number line.
Label the top line blue water, the bottom line yellow water, and label each tick mark as an increase by 1 from 0 - 10.
Dividing by 2 is like multiplying by what unit fraction?
1 / 2
If one batch of fruit punch needs 4 parts cranberry juice, 3 parts apple juice, and 2 parts grape juice, how many total parts are there in one batch of the punch?
Is the ratio 24 : 9 equivalent to 8 : 3?
Yes! 24 : 9 is three times the size of 8 : 3.
Use the lines you made to solve this problem.
How much yellow water should be used for 11 mL of blue water?
33 mL of yellow water.
How much money per 1 hour would you make if you made $90 for 5 hours of work?
What unit fraction would you have to multiply by to get to that unit rate?
$18 for 1 hour of work
If we have a ratio of 5 sneakers : 6 boots, how many people are wearing sneakers in a room of 55 people?
5 sneakers : 6 boots : 11 people
_________ : ___________ : 55 people
11 x 5 = 55 so...
5 x 5 = 25 people wearing sneakers
Is the ratio 5 : 4 equivalent to 22 : 6?
No! 22 is not a multiple of 5 and 6 is not a multiple of 4.
Some equivalent ratios would be 10 : 8, 15 : 12, 20 : 16 etc.
Andre ran 2 km in 15 minutes, and Jada ran 3 km in 20 minutes. Solve each ratio for the unit rate as mins per 1 km to compare them. Did they run at the same speed?
Ratios:
2 km : 15 mins
Both divided by 2 = 1 km : 7 1/2 mins
3 km : 20 mins
Both divided by 3 = 1 km : 6 2 /3 mins
How much would you be paid at that same rate of $18 per hour if you worked for 12 hours?
$18 * 12 hours = $216
If we use the fruit punch ratio again...
4 parts cranberry, 3 parts apple, and 2 parts grape for a total of 9 parts...
... how many parts of each do we need for 6 batches of fruit punch? How many parts do we need in total?
4 x 6 = 24 parts cranberry
3 x 6 = 18 parts apple
2 x 6 = 12 parts grape
9 total parts x 6 batches = 54 total parts