Consumer Math Unit 1

Multi-Step Equations

4 Steps to Follow to solve an equation:

1. Distribute

2. Combine Like Terms

3. Move your variable to one side of the equation (add or subtract)

4. SADMEG

Multiple Choice

What is the first thing you should do to simplify an equation?

• add

• Distributive Property

• Combine like terms

• divide

Distributive Property

Multiple Select

Which of the following equations require you to use the Distributive Property first?

Select all that apply.

• 6x-8=7(x+2)

• 7n-5=3

• 2(a-9)=9a+1

• 4-9y=8+4y-2

Multiple Choice

Let's Practice using the Distributive Property.

6(x-3)

• x-18

• 6x+18

• 6x-18

• 6x-9

Once you distribute, check to see if you have like terms, on the same side of the equal sign. Here are some examples of like terms:

• 5x and -6x

• -6 and 3 ***Remember that constants (regular numbers) are like terms with each other.***

• 7m and m

Multiple Select

Check the boxes that show like terms.

• 5 and -8

• 4n and -8x

• -9 and 9x

• 1 and 7

• 6y and 8y

Multiple Choice

Let's practice combining like terms.

7x-8+3x-1

• 10x-9

• 21x+8

• 4x+9

• 10x+9

Once you distribute and combine like terms, make sure variables are on one side and constants (regular numbers) are on the other side. Use inverse operations to move terms to the other side.

Multiple Select

If we wanted to move variables to one side, what operations could we do to accomplish this?

(2 answers)

7x-8=-5x+3

• Subtract 7x from both sides

• Add 8 to both sides

• Subtract 3 from both sides

• Add 5x to both sides

Here is an example of how to solve a Multi-Step equation. See if you can follow the steps that are written on the side.

Multiple Choice

$$Simplify:\ \ -3\left(2x\ -\ 5\right)$$  

• $$9x$$  

• $$-6x\ +\ 15$$  

• $$-6x\ -5$$  

• $$-6x-15$$  

Multiple Choice

$$Simplify:\ 5\left(3x\ -\ 1\right)\ -8+x$$  

• $$20x-45$$  

• $$11x-8$$  

• $$16x-9$$  

• $$16x-13$$  

Special Cases of Linear Equations

Special Case for Equations (No Solution)

If the variables drop out and you are left with a false statement, then the equation has NO SOLUTION!

ex. If you solve the equation and all that is left is -2 = 6 would mean the equation has no solution.

Special Case for Equations (Infinite Solutions)

If the variables drop out and you are left with a TRUE statement, then the equation has INFINITE SOLUTIONS!

ex. If you solve the equation and all that is left is 6 = 6 would mean the equation has infinite solutions.

Multiple Choice

$$Solve:\ 3x\ -9\ =2x\ +6\ +\ x$$  

• No Solution

• Infinite Solutions

Multiple Choice

$$Solve:\ -\left(4-y\right)\ =y\ -5+1$$  

• No Solution

• Infinite Solutions

Metric & US Conversions

In technical work, you must sometimes convert between units.

The image to the right shows relative size between units.

Metric & U.S. Conversions

• In the U.S. system, the acre is the basic unit of land area.

• Historically, the acre was the ground that a yoke of oxen could plow in one day.

• 1 acre = 43, 560 ft²

• 1 mile² = 640 acres

• 1 km² = 247.11 acres

Multiple Choice

How many full cups are in a 2-L soft drink bottle?

1 L = 1.0567 quarts

2 pint = 1 quart

1 pint = 2 cups

• 10 full cups

• 8 full cups

• 6 full cups

• 12 full cups

Multiple Choice

How many inches is 9 meters?

1 meter = 39.37 inches

• 0.2286 inches

• 0.2286 meters

• 354.33 inches

• 354.33 meters

Multiple Choice

How many kilograms does 60 lb of sheet metal weigh?

1 kilogram = 2.2046 pounds

• 132.28 kg

• 132.28 lbs

• 27.22 kg

• 27.22 lbs

Rounding Decimals

​

Multiple Choice

Round 8.27 to the tenths place.

• 8.2

• 8.3

• 8

• 8.27

Multiple Choice

Round 45.835 to the hundredths place.

• 45.8

• 45.84

• 45.83

• 45.835

Multiple Choice

Round 3.712 to the nearest whole number (ones).

• 3.7

• 3

• 4

• 3.71

Multiple Choice

How much longer is the adult crocodile than the baby crocodile?

• 20.7m longer

• 2.72m longer

• 2.072 longer

• 0.72m longer

Multiple Choice

How far did he walk altogether?

• 20.37km

• 23.07km

• 23.37km

• 27.37km

Multiple Choice

• $2467.5

• $24.675

• $246.75

Fill in the Blanks

Dividing Decimals

Steps to Dividing with Decimal

• Step 1: Move the decimal point in the divisor to make it a whole number.

• Step 2: Move the decimal point in the dividend the same number of spaces.

• Step 3: Divide

• Step 4: Line up your decimals

Multiple Choice

0.15 ÷ 0.03

• 0.5
• 0.05
• 5
• 0.15

Multiple Choice

1.8 ÷ 0.2

• 9
• 90
• 0.9
• 0.09

Multiple Choice

2.8 ÷ 4

• 7
• 0.7
• 0.07
• 70

Multiple Choice

Corrine has 10 pounds of trail mix to divide into 8 bags. How much trail mix will go in each bag? 

• 0.125 trail mix
• 12.5 pounds
• 1.25 pounds
• 12.5 trail mix