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
- Guided Lesson
- We work on the same skills as the lesson, but we add simplifying
- 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.
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)
The expressions seem to be the most challenging for students at this level.
Math Skill Quizzes
If you or your students have trouble with these, review the single step algebra sheets.