Proportions
Transcript of Proportions
42510011 0010 1010 1101 0001 0100 1011
ProportionsHow do I solve a
proportion?
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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
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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
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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.
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How do we tell if something really is a
proportion?
Method 2: Find the cross products.
6 2=3 1
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Multiply the numerator of one ratios by the
denominator of the other ratio.
6 2=3 1 6×1=6
3×2=6
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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.
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Are these proportions equal?
Method 1 – Lowest Terms
148=9 16
÷2÷2
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Are these proportions equal?
Method 1 – Lowest Terms
78=9 8
No – they are not equal!!
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Are these proportions equal?
Method 2 – Cross Products
148=9 16
8×16=1289×14=126
No – they are not equal!!
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Are these proportions equal?
611=22 12
YES – they are equal!!
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Are these proportions equal?
93=4 12
YES – they are equal!!
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Are these proportions equal?
2010=15 35
No – they are not equal!!
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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
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Now, let’s try something harder
When we have a variable, we can still cross-multiply.
51 =10 Z
10×5 = 501×Z = 1Z
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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.
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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.
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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.
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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
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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
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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 = …
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Now You TRY
1.) 415=30 Q
3.) S16=20 10
2.) 11M=10 2
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Summarize
Answer the EQ:
How do I solve a proportion?