2. Def: Ratio means fraction. The ratio of “a” to “b” is just the fraction:
3. Example: The ratio of dogs to cats in a pet store is 3 to 5. Mathematically, this means: In English, this means: For every 3 dogs, there are 5 cats!
4. BIG NOTE: This DOES NOT MEAN there are only 3 dogs and 5 cats. It COULDMEAN there are 3 dogs and 5 cats. -OR- There might be 6 dogs and 10 cats. -OR- There might be 9 dogs and how many cats? ………15 cats -OR- There might be 12 dogs and how many cats? ………. 20 cats And, so on….
5. SAMPLE PROBLEM #1 The ratio of the number of men to women in a store is 5 to 7, if there are 35 women in the store, how many men are there?
6. First let’s THINK!!!! Since the ratio is 5 to 7, that mean for every 5 men there are 7 women. So if there are: 5 men there are 7 women 10 men there are 14 women 15 men there are 21 women 20 men there are 28 women 25 men there are 35 women Thus, our answer is 25 men.
7. Mathematical Method If you notice, every time I get a group of 5 men I get a group of 7 women. So the question is: How many groups of women must I have if there are 35 women? ……….. 5 This means I must have 5 groups of men as well…
9. Since we need 5 groups of women to get 35, we must need 5 groups of men. Create Equivalent Fractions! Multiply by a form of1. # of men There are 25 men in the store! # of women Form of 1. Notice 5 was the number of groups needed,
10. Sample Problem #2: YOU TRY The ratio of hats to scarves in a clothing store is 8 to 3. How many scarves are in the store if there are 104 hats?
11. Solution: # of hats There are 39 scarves in the store # of scarves Form of 1: The number of groups needed was 13.
