Expressions with Rational Numbers

Student Summary

We can represent sums, differences, products, and quotients of rational numbers (and combinations of these) with numerical and algebraic expressions. 

Sums:

12+-9\frac12 + \text-9

-8.5+x\text-8.5 + x

Differences:

12-9\frac12 - \text-9

-8.5x\text-8.5 - x

Products:

(12)(-9)(\frac12)(\text-9)

-8.5x\text-8.5x

Quotients:

12÷-9\frac12\div\text-9

-8.5x\frac{\text-8.5}{x}

We can write the product of two numbers in different ways.

  • By putting a little dot between the factors, like this: -8.5x\text-8.5\boldcdot x.
  • By putting the factors next to each other without any symbol between them at all, like this: -8.5x\text-8.5x.

We can write the quotient of two numbers in different ways as well.

  • By writing the division symbol between the numbers, like this: -8.5÷x{\text-8.5}\div{x}.
  • By writing a fraction bar between the numbers, like this: -8.5x\frac{\text-8.5}{x}.

When we have an algebraic expression like -8.5x\frac{\text-8.5}{x} and are given a value for the variable, we can find the value of the expression. For example, if xx is 2, then the value of the expression is -4.25, because -8.5÷2=-4.25\text-8.5 \div 2 = \text-4.25.

Visual / Anchor Chart

Standards

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Addressing
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