Transcript Lesson 7-1: Ratios and Proportions

Lesson 7-1: Ratios and
Proportions
Learning Goal: Write and solve
basic and extended ratios
Wastepaper Basketball
• 2 volunteers shoot 10 times
• 1 volunteer to record successes and
failures
Analysis of basketball stats
• Write ratio of successes : failures
• If the ratio stays true and 50 shots are
made, how many successes and
failures can be expected?
Analysis of basketball stats cont.
• Write ratio of successes : attempts
• How many attempts should it take
you to make 12 shots?
Notes: Ratios and Proportions
• Ratio – a comparison of two
quantities by division
– Can be written a : b, a to b, or a/b
– Usually write a and b with the same
units so you can simplify
Example 1
A bonsai tree is 18in wide and stands
2 ft tall. What is the ratio of the width
of the bonsai to its height?
Example 2
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 of
tulips to daffodils will be 2 : 3. How
many pots of each type of flower
should they buy?
Notes: Extended Ratios
• Extended Ratio – compares 3 or
more numbers
– a:b:c
• Example 3: The lengths of the sides
of a triangle are in the extended ratio
4 : 7 : 9. The perimeter is 60cm.
What are the lengths of the sides?
Proportions
• Proportion – an equation that sets 2
ratios equal to each other
• Extremes– first and last numbers
• Means – middle 2 numbers
Example 4: Solve each proportion
9=a
2 14
15 = 3
m+1
m
Does order matter?
• If you flip a proportion (the reciprocal)
is it still true? Yes!
• If you switch the means is the
proportion still true? Yes!
• If you add one to both sides of the
proportion is the proportion still true?
Yes!
Equivalent Proportions
7-1 Homework
• Heading: 7-1 pg 459 #13, 14,
16, 19, 20, 22, 23, 32, 38, 39
• Work must be shown to receive
credit
• Due Tuesday, February 10th