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

Building On
6.EE.2.c

Write, read, and evaluate expressions in which letters stand for numbers.

Addressing
7.NS.1.d

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

7.NS.2.c

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.A

No additional information available.