solving proportions
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Solving Proportions. Solving Proportions. A proportion is an equation showing that two ratios are equal. . Solving Proportions. A proportion is an equation showing that two ratios are equal. Ex) Consider the following stick figures:. Solving Proportions. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/1.jpg)
Solving Proportions
![Page 2: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/2.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
![Page 3: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/3.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
![Page 4: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/4.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
![Page 5: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/5.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
In the first figure, the ratio of the height of the head to the height of the body is 1:3.
![Page 6: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/6.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
In the first figure, the ratio of the height of the head to the height of the body is 1:3. The second figure is twice as big; we could write the ratio of the head to the body as 2:6.
![Page 7: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/7.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
In the first figure, the ratio of the height of the head to the height of the body is 1:3. The second figure is twice as big; we could write the ratio of the head to the body as 2:6.
1:3 = 2:6
![Page 8: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/8.jpg)
Solving ProportionsA proportion is an equation showing that two ratios are equal.
Ex) Consider the following stick figures:
In the first figure, the ratio of the height of the head to the height of the body is 1:3. The second figure is twice as big; we could write the ratio of the head to the body as 2:6.
1:3 = 2:6 This is a proportion.
![Page 9: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/9.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
![Page 10: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/10.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
![Page 11: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/11.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
![Page 12: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/12.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
The first figure is still in the ratio 1:3, but the second figure is now in the ratio 5:6.
![Page 13: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/13.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
The first figure is still in the ratio 1:3, but the second figure is now in the ratio 5:6. These ratios are not equal.
![Page 14: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/14.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
The first figure is still in the ratio 1:3, but the second figure is now in the ratio 5:6. These ratios are not equal.
1:3 ≠ 5:6
![Page 15: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/15.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
The first figure is still in the ratio 1:3, but the second figure is now in the ratio 5:6. These ratios are not equal.
1:3 ≠ 5:6 These ratios do not form a proportion.
![Page 16: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/16.jpg)
Solving ProportionsNow let’s multiply the height of the first figure’s head by 5, but still only multiply the height of the body by 2.
The first figure is still in the ratio 1:3, but the second figure is now in the ratio 5:6. These ratios are not equal.
1:3 ≠ 5:6 These ratios do not form a proportion.
We can say that the second figure’s head is out of proportion.
![Page 17: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/17.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division.
![Page 18: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/18.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
![Page 19: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/19.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
![Page 20: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/20.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule.
![Page 21: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/21.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
![Page 22: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/22.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
3:7 =
![Page 23: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/23.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
3:7 = (x 3)
![Page 24: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/24.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
3:7 = 9: (x 3)
![Page 25: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/25.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
3:7 = 9:21 (x 3)
![Page 26: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/26.jpg)
Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division. In the proportion 1:3 = 2:6, the terms on the left are multiplied by 2 to equal the terms on the right.
Ex) Solve the following proportion:
3:7 = 9:n
Since it’s a proportion, there must be a rule. The terms on the left are being multiplied by 3.
3:7 = 9:21 (x 3)
So, n = 21.
![Page 27: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/27.jpg)
Solving ProportionsEx) Solve:
.12,1512
7560
.5:1575
60
nSo
bydividedarelefttheontermsTheRULE
n
![Page 28: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/28.jpg)
Solving ProportionsEx) Solve:
.12,1512
7560
.5:1575
60
nSo
bydividedarelefttheontermsTheRULE
n
![Page 29: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/29.jpg)
Solving ProportionsEx) Solve:
.12,1512
7560
.5:1575
60
nSo
bydividedarelefttheontermsTheRULE
n
![Page 30: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/30.jpg)
Solving ProportionsEx) Solve:
.12,1512
7560
.5:1575
60
nSo
bydividedarelefttheontermsTheRULE
n
![Page 31: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/31.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
![Page 32: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/32.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
![Page 33: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/33.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule?
![Page 34: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/34.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 =
![Page 35: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/35.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
![Page 36: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/36.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
![Page 37: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/37.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 =
![Page 38: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/38.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 = (x 30.5)
![Page 39: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/39.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 = 91.5 : (x 30.5)
![Page 40: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/40.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 = 91.5 : 61 (x 30.5)
![Page 41: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/41.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 = 91.5 : 61 (x 30.5)
So, n = 61.
![Page 42: Solving Proportions](https://reader036.vdocuments.us/reader036/viewer/2022081507/56815db4550346895dcbe22c/html5/thumbnails/42.jpg)
Solving ProportionsEx) The ratio of the length to the width of a widescreen TV is 3:2. If the screen is 91.5 cm long, what is its width?
Solve the following proportion:
3 : 2 = 91.5 : n
What is the rule? 91.5 ÷ 3 = 30.5
So, the rule is that the terms on the left are multiplied by 30.5.
3 : 2 = 91.5 : 61 (x 30.5)
So, n = 61.
The width of the TV screen is 61 cm.