One-Step Equations with Rational Coefficients

One-Step Equations with Rational Coefficients

by Courtney Tout

​Day 1: Start on Slide 1 End on Slide 18

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​Day 2: Start on Slide 20 End on Slide 35

​Division Problems

• ​3 Ways to write a division problem:

  • ​As a Fraction

  • ​As a Statement

  • ​As a Long Division Problem

​What is a Rational Coefficient?

• ​This is when the coefficient of a variable is a:

  • ​Fraction

  • ​Decimal

• ​When we have rational coefficients it is a ONE-STEP Multiplication Equation.

  • ​to solve for the variable we must use the:

    • ​INVERSE operation : DIVISION

Multiple Select

SELECT ALL THAT APPLY:

Rational Coefficients are coefficients that are:

• Fractions

• Binary

• Decimals

• Invisible

​Review Dividing Decimals

​Top IN Bottom OUT

​

​If your outside number has a decimal make it a whole by moving decimal places.

​

​Then move the same number of spaces inside the division house.

Multiple Choice

Do you need to move the decimal/ re-write the problem before dividing?

• Yes

• No

Multiple Choice

Do you need to move the decimal/ re-write the problem before dividing?

• Yes, because the number outside must be a whole number before we can attempt ANY division.

• No, decimal placement doesn't count when dividing.

​Decimal Coefficients

• ​If the coefficient is a decimal: DIVIDED each side by the coefficient.

​Example: 16 = 0.25n

​Step 1: Write the equation

​

​

​Step 2: Divided both sides by 0.25

​

​

​

​Step 3: Simplify [if needed]

​WRITE THIS IN YOUR JOURNAL!!!!

Multiple Choice

You have the equation:

30 = 0.5n

What do you need to do to get "n" by itself?

• multiply 0.5 to bothsides

• divided 0.5 to both sides

• subtract 0.5 to both sides

• add 0.5 to both sides

Multiple Choice

You have the equation:

30 = 0.5n

You divide $$\frac{30}{0.5}$$  , what should your answer be?

• 30.5

• 6

• 60

• 15

​Example: 2.4n = 30

​Step 1: Rewrite the equation

​

​

​Step 2: Divided both sides by 2.4 to isolate the variable "n"

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​Step 3: Simplify.

Open Ended

Any Questions So Far?

Multiple Choice

1.25 = 2.5b

• 1.2

• 2

• 0.5

• 1.5

Multiple Choice

1.2h = 10.8

• 0.11

• 8

• 9

• 10

Multiple Choice

Solve for the variable. 4.9 = 0.7m 

• 7

• -7

• 2

• 5

Multiple Choice

Solve for the variable. 9 = 0.3n

• 30

• -30

• 0.03

• -0.03

Multiple Choice

Solve for the variable. 21 = 0.75a 

• 28

• -28

• 0.04

• -0.04

STOP HERE​

​

One-Step Equations with Rational Coefficients​

Ms. Tout​

​Invisible Math

• ​Every variable when it is by itself has an invisible 1.

​

​

​

​Example:

• ​x = 1x

• ​b = 1b

• ​m = 1m

​Multiplicative Inverse

​The multiplicative Inverse is where you multiply a fraction by its reciprocal.

​

​When you multiply a fraction by its reciprocal you ALWAYS get 1.

Multiple Choice

What is the recriprocal of 4/5

• 4/5

• 5/4

• 5/1

• 1/5

Multiple Choice

What is the recriprocal of 5

• 5/1

• 1/5

Multiple Choice

Use the Multiplicative Inverse definition to solve:

$$\frac{1}{2}\times\frac{2}{1}=?$$  

• $$\frac{2}{2}=\frac{1}{1}=1$$  

• $$\frac{2}{2}=0$$  

​Fraction Coefficients

• ​If the coefficient is a fraction: MULTIPLY each side by the reciprocal.

​Example:

​Step 1: Write the Equation

​

​

​Step 2: Multiply each side by the reciprocal

​

​

​Step 3: Simplify

​*Remember:

​When you multiply a fraction by its reciprocal it equals 1.

Multiple Choice

You have an equation:

$$\frac{1}{2}x=6$$  

What do you need to do to get "x" by itself?

• add 1/2 to both sides

• divided 6 to both sides

• multiply by the reciprocal on both sides

• add the reciprocal to both sides 

Multiple Choice

You have an equation:

$$\frac{1}{2}x=6$$  

What is the multiplicative inverse or reciprocal of the fraction?

• $$\frac{1}{2}$$  

• 1.2

• 12

• $$\frac{2}{1}$$  

Multiple Choice

You have an equation:

$$\frac{1}{2}x=6$$  

When you multiply by the reciprocal on both sides, what does x = ?

• $$6\ \times\ \frac{1}{2}=\frac{6}{12}$$  

• $$6\times\frac{1}{2}=\frac{6}{2}=3$$  

• $$6\times\frac{2}{1}=\frac{12}{1}=12$$  

• $$6\times\frac{2}{1}=\frac{12}{6}=2$$  

Open Ended

Any Questions So Far?

Multiple Choice

Solve:

$$\frac{1}{3}x=6$$  

• 2

• 18

• 1/2

• The Reciprocal:

  $$\frac{2}{1}$$  

Multiple Choice

To solve the equation below, what should you multiply both sides by?

$$\frac{4}{5}m=\frac{1}{2}$$  

• The Reciprocal

  $$\frac{5}{4}$$  

• The fraction:

  $$\frac{4}{5}$$  

• The Fraction:

  $$\frac{1}{2}$$  

• The Reciprocal:

  $$\frac{2}{1}$$  

Multiple Choice

Solve:  $$\frac{3}{4}v=5$$  

• $$v=\frac{20}{3}=6\ \frac{2}{3}$$  

• $$v=\frac{15}{4}$$  

• $$v=\frac{1}{2}$$  

• $$v=\frac{12}{5}$$  

Multiple Choice

Solve:

$$\frac{3}{4}b=24$$  

• 32

• 36

• 24

• 18

Multiple Choice

Solve:

$$20=\frac{1}{5}n$$  

• 100

• 50

• 4

• 2