1. Ratios compare quantities…

2. Ratios can compare:
Part to Part Quantities
Part to Whole Quantities
Whole to Part Quantities

3. Ratios can be written in three ways…
7 to 4
7 : 4
7/4
The ratios shown above compare the orange uni-fix cubes to the green uni-fix cubes.
If it were asked in reversed, then the ratio of green to orange cubes would be 4 : 7.

4. Ratios can compare three “things” also…
Apples to Oranges to Bananas is 5 : 3 : 2
Bananas to Oranges to Apples is 2 : 3 : 5
Oranges to Apples to Bananas is 3 : 5 : 2
Apples to not Apples is 5 : 5
Bananas to not Bananas is 2 : 8
Oranges to all Fruit is 3 : 10

5. Ratios can be simplified (like fractions)…
The ratio of squares to diamonds is 15 to 20.
By dividing the numerator and denominator
By the GCF, 5, the simplified ratio becomes
3 to 4 (NOT three fourths).
15 = 3

6. Tape Diagrams: Part-Part
There are 11 boys to 16 girls in class, what is the total number of students?

7. Tape Diagram: Part-Whole
There are 16 trucks to 57 vehicles in the parking lot. How many vehicles are not trucks.

10. Using a comparative model, you can see if two quantities are twice as big, three times as big, half the size of the other, etc…

11. Writing ratios with units of measure (yards, miles, liters, centimeters, …)
The Golden Rule: Before you write the ratio of two quantities, the numbers must be in same unit form. For example, meter to meter, feet to feet, gallons to gallons, …
Ratio here is 2 : 1 because both the milk and water are the same unit, gallons.

12. = = 4 feet to 24 inches is NOT 4 : 24
It’s 4 feet to 2 feet, which is 4 : 2…
It can also be 48 inches to 24 inches, 48 : 24.
In every scenario, the simplified ratio would be 2 : 1.
= =

13. 2 gallons to 4 quarts would NOT be 2 : 4…
It would be 2 : 1.
WHY?
There are 4 quarts in 1 gallon.
So, change the 4 quarts to 1 gallon. Then write the ratio.

14. You have to study your conversions to write ratios correctly.
Inches Feet Yards Miles
Cups Pints Quarts Gallons
Ounces Pounds Tons
mm cm m km
ml l kl
mg g kg

15. Inches, Feet, Yards, Miles
How many feet in a mile?
“Five Tomatoes” 

16. Cups, Pints, Quarts, Gallons
In the Gallon Hotel, there are 4 Queen beds. On each bed, there are 2 Pillows, and on each pillow, these are 2 Chocolate mints.

17. Ounces, Pounds, Tons
x x 2000