Solving Proportions

Solving ProportionsA proportion is an equation showing that two ratios are equal.

Solving ProportionsA proportion is an equation showing that two ratios are equal.

Ex) Consider the following stick figures:

Solving ProportionsA proportion is an equation showing that two ratios are equal.

Ex) Consider the following stick figures:

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

Solving ProportionsIn a proportion, there will always be a rule that relates the first ratio to the second by multiplication or division.

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.

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

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.

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.

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 =

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)

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)

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)

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.

Solving ProportionsEx) Solve:

.12,1512

7560

.5:1575

60

nSo

bydividedarelefttheontermsTheRULE

n

Solving ProportionsEx) Solve:

.12,1512

7560

.5:1575

60

nSo

bydividedarelefttheontermsTheRULE

n

Solving ProportionsEx) Solve:

.12,1512

7560

.5:1575

60

nSo

bydividedarelefttheontermsTheRULE

n

Solving ProportionsEx) Solve:

.12,1512

7560

.5:1575

60

nSo

bydividedarelefttheontermsTheRULE

n

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?

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

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?

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 =

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

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.

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 =

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)

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)

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)

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.

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.