One Step Equations With Rational Coefficients

One-Step Equations with Rational Coefficients

Presentation

•

Mathematics

•

7th Grade

•

Medium

•

CCSS

6.EE.B.7, 8.EE.C.7B, 3.NF.A.1

Standards-aligned

Courtney Tout

Used 47+ times

FREE Resource

13 Slides • 23 Questions

One-Step Equations with Rational Coefficients

by Courtney Tout

Day 1: Start on Slide 1 End on Slide 18

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

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

Example: 2.4n = 30

Step 1: Rewrite the equation

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

Step 3: Simplify.

Open Ended

Any Questions So Far?

Type response here

Multiple Choice

1.25 = 2.5b

1.2

0.5

1.5

Multiple Choice

1.2h = 10.8

0.11

Multiple Choice

Solve for the variable. 4.9 = 0.7m

-7

Multiple Choice

Solve for the variable. 9 = 0.3n

-30

0.03

-0.03

Multiple Choice

Solve for the variable. 21 = 0.75a

-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

$\frac{2}{1}$

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?

Type response here

Multiple Choice

Solve:

$\frac{1}{3}x=6$

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:

$\frac{3}{4}b=24$

Multiple Choice

Solve:

$20=\frac{1}{5}n$

100

One-Step Equations with Rational Coefficients

by Courtney Tout

Day 1: Start on Slide 1 End on Slide 18

Day 2: Start on Slide 20 End on Slide 35

Show answer

Auto Play

Slide 1 / 36

SLIDE

Similar Resources on Wayground

29 questions

Geometry review

Presentation

•

7th Grade

35 questions

Math Discovery - B - Geometry

Presentation

•

7th Grade

34 questions

Angles - Geometric Word Problems with Expression & Equations

Presentation

•

7th Grade

31 questions

Algebraic Expressions

Presentation

•

6th Grade

31 questions

Simple Probability

Presentation

•

7th Grade

33 questions

Scientific Notation

Presentation

•

7th Grade

27 questions

Mean, Median, Mode, & Range

Presentation

•

7th Grade

32 questions

Metric System

Presentation

•

7th - 8th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

16 questions

Proportional and Non Proportional Relationships in Tables, Graphs, and Equations

Quiz

•

7th Grade

20 questions

Constant of Proportionality

Quiz

•

7th Grade

20 questions

Halloween Trivia

Quiz

•

7th Grade

15 questions

One-Step Equations

Quiz

•

7th Grade

20 questions

Add and Subtract Integers

Quiz

•

6th - 8th Grade

16 questions

Adding and Subtracting Integers

Quiz

•

7th Grade

20 questions

Two-Step Equations Review

Quiz

•

7th Grade

20 questions

Model Algebraic expressions with tiles

Quiz

•

7th Grade