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.
