Transcript unit-1-ratio-and-rate

Unit 1
Ratios and Unit
Rates
How do we use ratios
and unit rates to solve
real-world math
problems?
•Ratio
•Rates
CCSS: 6.RP.2; 3b
Ratio
• Compares two numbers or quantities
by division
• part to part
• part to whole
• whole to part
Ratio
2 to 5
•Ratio form
2:5
•Fraction form
2
5
•Word form
Equivalent Ratios
• Write the ratio as a fraction
• Mult or div the numerator and
denominator by the same
nonzero number
• Write the result as a fraction
Equivalent Ratios
• Use cross products to
determine if ratios
(fractions) are equivalent
Equivalent Ratios
• Proportions – two ratios
are equivalent
• Two ratios form a proportion
if their cross products are
equal
Proportion
“equal fractions”
• Words
3 : 12 = 5 : 20
• fraction 3 = 5
12
20
cross products 3 x 20 = 12 x 5
60
= 60
Ratio
proportion
Percent
“%”
a ratio that compares
a number to 100.
Ratio
as a percent of a number
• Use a proportion part =
whole
• in words
is =
of
• Find the part….What is?
%
100
%
100
•Ratio
•Rates
CCSS: 6.RP.2; 3b
Rate
as a percent
• Use a proportion part =
whole
• in words
is =
of
%
100
%
100
• Find the part of 100….What %?
Rates
• A ratio that compares two
quantities with different
units of measure
Unit rate
Unit price “$”
•Unit rate
•Unit $
unit cost or unit price
CCSS: 6.RP.2; 3b
Unit Rate
• Compare two quantities
with different units of
measure
• Has 1 unit as its second
term, or denominator
Unit Rate
40 breaths in 1 minute
55 miles per hour
32 miles on 1 gallon
80 words per minute
Unit Cost (price)
$ 5.50 per hour
$ 1.75 per lb
$ 14.00 for 1 book
$ 4.00 for 1 ticket
Key Concepts
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Ratios
Unit Rates
Proportional Relationships
Percent and percentage problems
Measurement conversions (metric and
standard)
• Ordered pairs in all quadrants of the
coordinate plane
Vocabulary
• Comparison
• Equivalent
• Fractional
representation
• Per
• Rate
• Unit price
• Unit rate
• Equivalent ratio
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Percent
Rate
Transform units
quadrants
coordinate plane
coordinates
Absolute value
Origin