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Pre-Algebra
7-1 Ratios and Proportions7-1 Ratios and Proportions
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
7-1 Ratios and Proportions
Warm UpWrite each fraction in lowest terms.
Pre-Algebra
7-1 Ratios and Proportions
1416
1.
972
3.
2464
2.
45120
4.
78
38
18
38
Pre-Algebra
7-1 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
Pre-Algebra
7-1 Ratios and Proportions
Today’s Learning Goal Assignment
Learn to find equivalent ratios
to create proportions.
Pre-Algebra
7-1 Ratios and Proportions
BrainPOP Videoshttp://www.brainpop.com/math/
ratioproportionandpercent/proportions/
http://www.brainpop.com/math/ratioproportionandpercent/ratios/
Pre-Algebra
7-1 Ratios and Proportions
Relative density is the ratio of the density of a substance to the density of water at 4°C. The relative density of silver is 10.5. This means that silver is 10.5 times as heavy as an equal volume of water.
The comparisons of water to silver in the table are ratios that are all equivalent.
42 g31.5 g21 g10.5 gSilver
4 g3 g2 g1 gWater
Comparisons of Mass of Equal Volumesof Water and Silver
Pre-Algebra
7-1 Ratios and Proportions
Ratios can be written in several ways. A colon is
often used. 90:3 and name the same ratio.
Reading Math
90 3
Pre-Algebra
7-1 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.
Pre-Algebra
7-1 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 by the same nonzero number.
Pre-Algebra
7-1 Ratios and Proportions
Try This: Example 1
Find two ratios that are equivalent to each given ratio.
B.
1632
24
6432
42
A. =816
=8 • 216 • 2
=8 ÷ 416 ÷ 4
816
= Two ratios equivalent
to are and . 816
1632
24
Two ratios equivalent
to are and . 3216
6432
42
=32 • 216 • 2
=32 ÷ 816 ÷ 8
3216
=
3216
=
Multiply or divide the numerator by the same nonzero number.
Pre-Algebra
7-1 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.
Pre-Algebra
7-1 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
Pre-Algebra
7-1 Ratios and Proportions
Try This: Example 2
Simplify to tell whether the ratios form a proportion.
1449
B. and 1636
Since ,
the ratios are in
proportion.
15
= 15
15
=3 ÷ 315 ÷ 3
315
=
15
=9 ÷ 945 ÷ 9
945
=
27
=14 ÷ 749 ÷ 7
1449
=
49=
16 ÷ 436 ÷ 4
1636
=
Since ,
the ratios are not
in proportion.
27 4
9
315
A. and 945
Pre-Algebra
7-1 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
Pre-Algebra
7-1 Ratios and Proportions
Try This: Example 3
At 4°C, two cubic feet of silver has the same mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver?
?= 10 ÷ 5105 ÷ 5
221
221
= 221
221
?= 10105
Since ,
105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver.
221
= 221
Pre-Algebra
7-1 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