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Course 3
5-1 Ratios and Proportions
Warm UpWrite each fraction in lowest terms.
1416
1.
972
3.
2464
2.
45120
4.
78
38
18
38
Course 3
5-1 Ratios and Proportions
Problem of the Day
A magazine has page numbers from 1 to 80. What fraction of those page numbers include the digit 5?1780
Course 3
5-1 Ratios and Proportions
Learn to find equivalent ratios to create proportions.
TB P. 216-219
Course 3
5-1 Ratios and Proportions
Vocabulary
ratioequivalent ratioproportion
Course 3
5-1 Ratios and Proportions
A ratio is a comparison of two quantities by division. In one rectangle, the ratio of shaded squares to unshaded squares is 7:5. In the other rectangle, the ratio is 28:20. Both rectangles have equivalent shaded areas. Ratios that make the same comparison are equivalent ratios.
7:5 28:20
Course 3
5-1 Ratios and Proportions
Ratios can be written in several ways. 7 to 5,
7:5, and name the same ratio.
Reading Math
7 5
Course 3
5-1 Ratios and Proportions
Additional Example 1: Finding Equivalent Ratios
Find two ratios that are equivalent to each given ratio.
B.
1854
13
12848
83
A. =927
=9 • 227 • 2
=9 ÷ 927 ÷ 9
927
= Two ratios equivalent
to are and . 927
1854
13
Two ratios equivalent
to are and . 6424
12848
83
=64 • 224 • 2
=64 ÷ 824 ÷ 8
6424
=
6424
=
Multiply or divide the numerator and denominator by the same nonzero number.
Course 3
5-1 Ratios and Proportions
Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.
Course 3
5-1 Ratios and Proportions
Additional Example 2: Determining Whether Two Ratios are in Proportion
Simplify to tell whether the ratios form a proportion.
1215
B. and 2736
327
A. and 218
Since ,
the ratios are in
proportion.
19
= 19
19
=3 ÷ 327 ÷ 3
327
=
19
=2 ÷ 218 ÷ 2
218
=
45=
12 ÷ 315 ÷ 3
1215
=
34=
27 ÷ 936 ÷ 9
2736
=
Since ,
the ratios are not
in proportion.
45 3
4
Course 3
5-1 Ratios and Proportions
Additional Example 3: Earth Science Application
At 4°C, four cubic feet of silver has the same mass as 42 cubic feet of water. At 4°C, would 210 cubic feet of water have the same mass as 20 cubic feet of silver?
4 ÷ 242 ÷ 2
?= 20 ÷ 10210 ÷ 10
221
= 221
442
?= 20210
Since ,
210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver.
221
= 221
Divide.
Course 3
5-1 Ratios and Proportions
Lesson Quiz: Part 1
85
85
= ; yes
Find two ratios that are equivalent to each given ratio.
415
1.
821
2.
1610
3.
3624
4.
Simplify to tell whether the ratios form a proportion.
830
1245
Possible answer: ,
1642
2463
Possible answer: ,
and 32 20
and 28 18
32
149
; no
Course 3
5-1 Ratios and Proportions
Lesson Quiz: Part 2
5. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. What ratio of juice is missing from each bottle? Are the ratios proportional?
864
16128
and ; yes, both equal 1 8
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