Solving Problems with Rational Numbers

Student Summary

We can apply the rules for arithmetic with rational numbers to solve problems.

In general, a−b=a+-ba - b = a + \text- b.

If a−b=xa - b = x, then x+b=ax + b = a. We can add -b\text- b to both sides of this second equation to get that x=a+-bx = a + \text- b.

Remember: The distance between two numbers is independent of the order, while the difference depends on the order.

And when multiplying or dividing:

  • A positive number multiplied or divided by a negative number always has a negative result.

  • A negative number multiplied or divided by a positive number always has a negative result.

  • A negative number multiplied or divided by a negative number always has a positive result.

Visual / Anchor Chart

Standards

Building On
6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = q for cases in which p, q, and x are all nonnegative rational numbers.

Addressing
7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Building Toward
7.EE.4.a

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers.