Transcript 7.1 Ratios and Proportions - Cardinal O'Hara High School

7.1 Ratios and Proportions
• A ratio is a comparison of two quantities
by division.
Dividing a Quantity Into a Given Ratio
• Members of the school band are buying pots of tulips and
pots of daffodils to sell at their fundraiser. They plan to
buy 120 pots of flowers. The ratio number of tulip pots :
number of daffodil pots will be 2 : 3. How many pots of
each type of flower should they buy?
• Let 2x = number of tulip pots
• Let 3x = number of daffodil pots
2x + 3x = 120
5x =120
x = 24
2(24) = 48
3(24) = 72
48 tulip pots, 72 daffodil pots.
Extended Ratio
• An extended ratio compares three (or
more) numbers.
– Ex. a : b : c
Using Extended Ratios
• The lengths of the sides of a triangle are in the
extended ratio 3 : 5 : 6. The perimeter of the triangle
is 98 inches. What is the length of the longest side?
3x + 5x + 6x = 98
14x = 98
x=7
3(7) = 21
5(7) = 35
6(7) = 42
Proportions
• An equation that states two ratios are
equal is called proportion.
• The first and last numbers in a proportion
are the extremes.
• The middle two numbers are the means.
Solving a Proportion
• What is the solution of each proportion?
6 5

x 4
y4 y

9
3
24  5x
3( y  4)  9 y
24
x
5
3 y  12  9 y
x  4.8
12  6y
y2
Properties of Proportions
Writing Equivalent Proportions
x y

6 7
x y

6 7
7x  6 y
x 6

y 7
x 6

y 7
More Practice!!!!!
• Homework – Textbook p. 436 – 437 #10 –
32 even.