## Multiplication and Division of Rational Numbers

#### Aligned To Common Core Standard:

**Grade 7 Number Systems** - 7.NS.A.2c

What are common strategies to multiply and divide rational numbers?
A rational number is a number that can be written as a normal fraction, like a ratio. For example:
5 = 5/1
1.75 = 7/4
.001 = 1/1000
0.111… = 1/9
So, a rational number looks like:
P/ Q
But remember, Q cannot be zero.
**Multiplication** - So, if you are looking to multiply rational numbers, the first tip to do it successfully is multiplying the tops and bottoms with each other separately. Like this:
(a/b) x (c/d) = (ac/bd)
1/2 x 2/5 = (1 x 2) / (2x5) = 2/10 = 1/5
**Divide** - When it comes down to dividing the rational numbers. First, you need to flip the second number or make it a reciprocal and then multiply like below: (A/B) / (C/D)
A/B x D/C = AD/BC
1/2 divided by 1/6
Reciprocal of the second fraction = 6/1
Hence, 1/2 x 6/1 = (1 x 2) / (6x1) = 6/2 = 3
Often times student uses some pictorial or visual aid that can help them understanding the problem much better.

### Printable Worksheets And Lessons

- Equations and Equivalence
Step-by-step Lesson- Find the equivalent fractions and complete
an equation.

- Guided Lesson
- We work on the same skills as the lesson, but we add simplifying
expressions.

- Guided Lesson
Explanation - I worked hard to keep this one to a single page.
It took some effort.

- Practice Worksheet
- We work hard on all three major skills of this section.

- Matching Worksheet
- This is a cool way to match up the various skills we worked on.
See how you like it.

- Division of Rational (Fractional) Expressions Worksheet Five Pack - Some of these quotients might take you some time to come up with.

#### Homework Sheets

Fraction equivalence, completing operations, and simplifying expressions.

- Homework 1 - Reduce all the fractions to see which fraction is equivalent to it.
- Homework 2 - In order to get a positive product from a negative number, we know that the equation must follow this pattern: negative × negative = positive (Our answer must be negative.)
- Homework 3 - Simplify the expression: 5(4t + 7)

#### Practice Worksheets

The expressions seem to be the most challenging for students at this level.

- Practice 1 - What integer would make this sentence true?
- Practice 2 - Simplify the expressions.
- Practice 3 - Which of the following fractions is equivalent to 9/17?

#### Math Skill Quizzes

If you or your students have trouble with these, review the single step algebra sheets.