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4 2 5 1 3 0011 0010 1010 1101 0001 0100 1011 Proportions How do I solve a proportion?

Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Page 1: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

ProportionsHow do I solve a

proportion?

Page 2: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Proportions – What are they??

• Proportions are a way to relate information.

• They compare two ratios.

Page 3: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Proportions – What are they??

Proportion = a pair of equal ratios

5 15=10 30

×3×3

Page 4: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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How do we tell if something really is a

proportion?

Method 1: Put both sides in lowest terms.

5 15=10 30

÷5÷5

÷15÷15

Page 5: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

How do we tell if something really is a

proportion?

Method 1: Put both sides in lowest terms.

1 1=2 2

The fractions are the same, so it

is a true proportion.

Page 6: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

How do we tell if something really is a

proportion?

Method 2: Find the cross products.

6 2=3 1

Page 7: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011Cross-Product

Multiply the numerator of one ratios by the

denominator of the other ratio.

6 2=3 1 6×1=6

3×2=6

Page 8: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011Cross-Product

If the cross products are equal, the then ratios are

equal, and it is a true proportion.

6 2=3 1 6×1=6

3×2=6 The cross products are the same, so it is a true proportion.

Page 9: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Are these proportions equal?

Method 1 – Lowest Terms

148=9 16

÷2÷2

Page 10: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Are these proportions equal?

Method 1 – Lowest Terms

78=9 8

No – they are not equal!!

Page 11: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Are these proportions equal?

Method 2 – Cross Products

148=9 16

8×16=1289×14=126

No – they are not equal!!

Page 12: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Are these proportions equal?

611=22 12

YES – they are equal!!

Page 13: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Are these proportions equal?

93=4 12

YES – they are equal!!

Page 14: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Are these proportions equal?

2010=15 35

No – they are not equal!!

Page 15: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Now, let’s try something harder

Sometimes, we will only know 3 of the 4 values in a

proportion. The missing value is a VARIABLE. Take a

look….51 =

10 ZZ is the variable

Page 16: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Now, let’s try something harder

When we have a variable, we can still cross-multiply.

51 =10 Z

10×5 = 501×Z = 1Z

Page 17: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Now, let’s try something harder

What do you think we are going to do now?

51 =10 Z

10×5 = 501×Z = 1Z

Write the cross products equal to each other.

Page 18: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Now, let’s try something harder

What do you think we are going to do now?

50 = 1ZWrite the cross products

equal to each other.

Page 19: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Now, let’s try something harder

What do you think we are going to do next?

50 = 1ZIt is an equation so we are

going to do the inverse - DIVIDE.

Page 20: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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0011 0010 1010 1101 0001 0100 1011

Now, let’s try something harder

What do you think we are going to do next?

50 = 1Z

It is an equation so we are going to do the inverse -

DIVIDE.

50 ÷ Z = 50 so Z = 50

Page 21: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Let’s try againSolve for the variable:

8×15 = 1204×X = 4X

4X = 120

120÷4=30

so X = 30

84 =15 X

Page 22: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Here are some steps:1.) Cross multiply.

2.) Write the cross-products equal to each other.

3.) Divide the number by itself by the number with the variable.

4.) Write your answer as x = …

Page 23: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Now You TRY

1.) 415=30 Q

3.) S16=20 10

2.) 11M=10 2

Page 24: Proportions How do I solve a proportion?. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios

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Summarize

Answer the EQ:

How do I solve a proportion?