# Multiplication and Division of Rational Numbers Worksheets

A rational number is a value that is created by dividing two integers, where the denominator is not equal to zero. We have mastered the use of multiplication and division with basic integers, but what happens when those values are presented as fractions? When we are using these operations with these types of numbers there are simple patterns and almost tricks that we can use to get an accurate and reliable product or quotient. In this section we will explore how to tackle these types of problems with ease and consistency. You should focus on mastering how to perform the multiplication operation first. Division follows the same path, but with one little twist. When dividing, we begin by finding the reciprocal of one of the values. These worksheets and lesson will progress towards understanding the use of these operations in great detail.

### Aligned Standard: Grade 7 Number Systems - 7.NS.A.2c

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - A few advanced expressions make their way in here.
- Quiz 2 - What integer would make this sentence true?
- Quiz 3 - Test out how you did with this topic.

### What Strategies Are Used to Multiply and Divide Rational Numbers?

A rational number is a number that can be written as a normal fraction of two integers, like a ratio.

Common examples of rational numbers include: 5 = 5/1, 1.75 = 7/4, 0.001 = 1/1000, 0.111...= 1/9.

So, a rational number looks like this, in variable form: P/ Q.

But remember, Q cannot be zero.

What happens when we put these values through multiplication and division operations? They follow a common pattern in each case that we can use to our advantage to manipulate the outcomes reliably.

**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).

In action it would appear like this: 1/2 x 2/5 = (1 x 2) / (2 x 5) = 2/10 = 1/5. We placed the numerator together as a product over the product of the denominators. When you get your final value, make sure to simplify (reduce) the value.

**Division** - 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. It follows the form of rearrangement highlighted here: (A/B) / (C/D) would become: A/B x D/C = AD/BC.

Putting this to use to solve the problem: 1/2 divided by 1/6.

Step 1) Find the reciprocal of the second fraction. The reciprocal of 1/6 = 6/1.

Step 2) Treat it like a multiplication problem: 1/2 x 6/1 = (1 x 2) / (6 x 1) = 6/2 = 3.

Often student uses some pictorial or visual aids that can help them understanding the problem much better. The key with multiplication is to align the numerators and denominators. When dividing rationale fractions, we flip the second fraction and then treat it as a multiplication problem from there.