Download I. What is a ratio? - Perry Local Schools

I. What is a ratio?
A. A ratio is a comparison of 2 quantities. B. A ratio is a relationship between two numbers. It tell us for every amount of one thing, how much there is of another thing.
C. For example, suppose I have 10 pairs of socks for every pair of shoes. The ratio of socks to shoes would be 10 to 1
•
The ratio of shoes to socks would be 1 to 10 •
II. Writing Ratios
A.
The order of the words in the problem is the order you must write the numbers
What is the ratio of stars to stripes on the American Flag? Since stars come first, we write the number of stars first in the ratio. So we would have the ratio 50 stars to 13 stripes B.
•
•
•
There are 3 ways to write ratios
Word to 50 to 13
Colon : 50:13
Fraction 1st number is the numerator 50/13
Tip ­ Always write the ratio in words first to help you keep the numbers in order
A.
stars to stripes is 50 to 13, 50:13, and 50/13
Important Caution: Sometimes, the number you need for a ratio is not directly given. B.
You may need to find the number first before you write the ratio.
Example: There are 20 students in the class. 13 are girls. Write a ratio of boys to girls.
The number of boys is not given. How would we find that number? _________________
So, the number of boys = ________
Ratio of boys to girls (boys:girls) ______________, ______________, ______________
1
2
III. Reading Ratios ­ All three forms are read the same way, “ ___ to ___”
So for the ratio that compares stars to stripes, we would say
50 to 13 fifty to thirteen •
50:13 fifty to thirteen •
50 / 13 fifty to thirteen •
IV. PRACTICE ­ Please write ratios in all three forms for each of the following.
1. There are 9 horses and 4 elephants in a circus. Write the ratio of elephants to horses.
2. There are 5 cars and 6 vans in a parking lot. Write the ratio of vans to cars.
3. A soccer team played 25 games and won 17.
a. What is the ratio of the number of wins to the number of losses?
b. What is the ratio of the number of games won to the number of games played? 4. A class of 30 students has 13 girls. What is the ratio of girls to boys?
3
V. Simplifying Ratios
Anytime we are dealing with ratios, we should reduce them to simplest form.
A.
B.
Since we can write a ratio in fraction form, it is easy to reduce a ratio just like a fraction. That means we can divide by any form of 1 (a number over itself)
C.
Example: There are 5 stars and 10 circles. Write the ratio of stars to circles.
stars to circles = 5:10 In fraction form this is 5/10 ÷ 5/5 = 1/2 So stars to circles is 5:10 which equals 1:2 in lowest terms (1 to 2, 1/2)
IMPORTANT DIFFERENCES ­ When a ratio is in fraction form, we can handle it almost the same as D.
we would handle a fraction. There are a few important differences between fractions and ratios written in fraction form.
Ratios that look like improper fractions can NOT be written as mixed numbers or whole numbers. •
Ratios compare 2 numbers, so if you wrote them as mixed numbers or whole numbers you would not be able to see the 2 numbers you are comparing. To make orange paint, you need 3 drops of red for every 2 drops of yellow. The ratio of red to yellow is 3:2 or 3/2. We can NOT say 3/2 = 1 ½ because we cannot see how much red or how much yellow we need.
Fractions are only allowed to have whole numbers as numerators or denominators. But ratios compare •
any two numbers, so the numerator or denominator could be a decimal, a fraction, a mixed number or a whole number.
A recipe calls for 1 ½ cups of flour for every 2 eggs used. Write a ratio of flour to eggs. flour:eggs 1 ½ : 2 , 1 ½ / 2, 1 ½ to 2
4
VI. More practice. Write the ratio all 3 ways in lowest terms!
5. In the following diagram, what is the ratio of shaded squares to white squares?
10. A real horse is 1.7 meters high. A statue of the horse is 3 meters high. What is the ratio of the height of the horse to the height of the statue?
5
VII. Types of Ratios ­ We will learn about 2 of the 3 types of ratios this year
A.
Part to Part Ratio ­ Compares one part of a set to another part of the set
Example (use the picture at the right):
•
What is the ratio of boys to girls? 4:1 4 to 1 4/1
•
What other part to part ratio could we write?
__________________________________________________
B.
Part to Whole Ratio ­ Compares a part of a set to the whole set
Example: The ratio of girls to all students in the picture is 1:5 1to 5 1/5
Write the ratio all 3 ways. Be sure to write it in lowest terms! Then tell what type of ratio you have (part to part OR part to whole). You may want to use your own paper for this.
P
U
R
M
A
W
A
S A
Y A
D
N
O
M
N
O
TE
E
L
P
M
O
C
17. 17 blue marbles, 10 violet marbles, 8 red marbles, and 16 yellow marbles
Write the ratio of red marbles to violet marbles
18. 10 black marbles and 4 blue marbles
Write the ratio of blue marbles to all marbles
19. 10 black marbles, 12 blue marbles, 7 brown marbles, and 19 white marbles
Write the ratio of blue marbles to black marbles
6