# How do I solve a proportion?

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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.

Proportions – What are they??
Proportion = a pair of equal ratios ×3 ×3

How do we tell if something really is a proportion?
Method 1: Put both sides in lowest terms. ÷5 ÷15 ÷5 ÷15

How do we tell if something really is a proportion?
Method 1: Put both sides in lowest terms. The fractions are the same, so it is a true proportion.

How do we tell if something really is a proportion?
Method 2: Find the cross products.

Cross-Product Multiply the numerator of one ratios by the denominator of the other ratio. 3×2=6 6×1=6

The cross products are the same, so it is a true proportion.
If the cross products are equal, the then ratios are equal, and it is a true proportion. 3×2=6 The cross products are the same, so it is a true proportion. 6×1=6

Are these proportions equal?
Method 1 – Lowest Terms ÷2 ÷2

Are these proportions equal?
Method 1 – Lowest Terms No – they are not equal!!

Are these proportions equal?
Method 2 – Cross Products 8×16=128 9×14=126 No – they are not equal!!

Are these proportions equal?
YES – they are equal!!

Are these proportions equal?
YES – they are equal!!

Are these proportions equal?
No – they are not equal!!

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…. Z is the variable

Now, let’s try something harder
When we have a variable, we can still cross-multiply. 10×5 = 50 1×Z = 1Z

Now, let’s try something harder
What do you think we are going to do now? 10×5 = 50 1×Z = 1Z Write the cross products equal to each other.

Now, let’s try something harder
What do you think we are going to do now? 50 = 1Z Write the cross products equal to each other.

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.

Now, let’s try something harder
What do you think we are going to do next? 50 = 1Z 50 ÷ Z = 50 so Z = 50 It is an equation so we are going to do the inverse - DIVIDE.

Solve for the variable:
Let’s try again Solve for the variable: 8×15 = 120 4×X = 4X 4X = 120 120÷4=30 so X = 30

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 = …

Now You TRY

How do I solve a proportion?
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