GOSEA 7 - Solving Proportions

GOSA 7

Solving Proportions

It can not be stressed enough how important proportions are to Geometry.

By continuing to the next slide and completing this lesson, you testify that you are the student who is enrolled in GOSA at BCHS with Mrs. Haley and that you are doing the lesson for yourself and no one else.

The last two lessons have focused on solving equations.

Lesson 5 covered one-step equations.

Lesson 6 covered two-step and multi-step equations.

This lesson will cover a special type of equation called a proportion.

What is a proportion?

A proportion is an equation (mathematical statement containing two expressions joined by an equals sign) in which two ratios (also known as fractions) are set equal to each other.

True, False or Conditional?

Proportions can be classified as true statements, false statements, or conditional statements.

True Proportions

False Proportions

Conditional Proportions

How can you tell if a proportion is true or false?

Many math students do not enjoy working with fractions and do not know how to determine if two fractions are equal or not (even with the help of a calculator).

How can you tell if a proportion is true or false? (continued)

It can be determined if two fractions are equal or not with simple multiplication known as "cross multiplication".

Cross Multiplication is simply done by multiplying across the equals sign.

Cross Multiplication

Cross multiplication is done by multiplying the top of one fraction (numerator) by the bottom of the other fraction (denominator).

We do NOT cross multiply here!!!

Cross Multiplication can only take place when two fractions are joined by an equals sign, not a multiplication sign.

We do NOT cross multiply here!!!

When two fractions are joined by a multiplication symbol, the top numbers (numerators) are multiplied together to get a new numerator; the bottom numbers (denominators) are multiplied together to get a new denominator.

The new fraction is then reduced.

Because the proportion could be true or false depending on the value of x, we say the proportion is CONDITIONAL. 

In many Geometry problems, it will be your job to solve conditional proportions.

While some of the answers may be easy to find "in your head", you will be required to show work on HOW you found your answer.

You will not get to show work here on these problems, but know that you will have to show work on written assignments.

Because this equation has division acting on the variable, we will undo the division with multiplication to solve the equation.

Because this equation is a proportion, the type of multiplication we will do will be cross multiplication.

I failed to mention some things in Lessons 5 and 6 when solving equations!!!

*Don't lose your equals sign. It goes on every line.

*Only one equals sign per line.

*Show work going down your paper, not across.

​*Write solutions to equations as "x = 2" not as "2".

(Use whatever variable is in the problem. )

​*You may have to find a couple of values in a problem before finding the answer needed. Always circle the FINAL answer (the information being asked for in the problem).

Multiple Choice

Which is the correct next step in solving  $$\frac{m}{5}=\frac{9}{15}$$  ?

• m = 3

• $$m\cdot15=5\cdot9$$  

• $$m\cdot9\ =5\cdot15$$  

• $$m\cdot5=9\cdot15$$  

Multiple Choice

Which is the correct next step in solving  $$\frac{4}{k}=\frac{7}{9}$$  ?

• $$4+9=k+7$$  

• $$k\cdot9=4\cdot7$$  

• $$k\cdot7=4\cdot9$$  

• $$k\div7=4\div9$$  

Multiple Choice

Which is the correct next step in solving  $$\frac{8}{12}=\frac{c}{26}$$  ?

•   $$12\cdot c=8\cdot26$$  

•   $$8\cdot c=12\cdot26$$  

• $$8\cdot12=c\cdot26$$  

• $$12\div c=26\div8$$  

Multiple Choice

Which shows the correct work for solving   $$\frac{5}{20}=\frac{4}{a}$$  ?

• $$5\cdot4=20\cdot a$$ $$20=20a$$   $$\frac{20}{20}=\frac{20a}{20}$$   

• $$5\cdot a=20\cdot4$$   $$5a=80$$   $$\frac{5a}{80}=\frac{80}{80}$$  

• $$20\cdot4=5\cdot a$$   $$80=5a$$   $$\frac{80}{5}=\frac{5a}{5}$$  

Multiple Choice

$$\frac{x+2}{4}=\frac{7}{8}$$  Which work is correct for this solving this proportion?

• $$\left(x+2\right)8=4\cdot7$$   $$8\left(x+2\right)=28$$   $$8x+16=28$$   $$8x+16-16\ =\ 28\ -\ 16$$   $$8x=12$$  

• $$\left(x+2\right)8=4\cdot7$$   $$8\left(x+2\right)\ =\ 28$$   $$8x\ +\ 2\ =\ 28$$   $$8x\ +\ 2-2\ =\ 28\ -\ 2$$   $$8x=26$$  

Keep doing this assignment until you make a 100. That is the only way you will get the 100 for Geometry in the Fall.​