Basic Algebra/Working with Numbers/Dividing Rational Numbers

Lesson

Dividing rational numbers covers a general area of equations. For an equation that is such has only to have a numerator and denominator that are both rational numbers. In turn, one will come out with a quotient that fits the terms applied to a "rational number". Given the fact that you already understand rational numbers, you will understand this unit. If, on the other hand, you have no clue what a rational number is, then you should do some research concerning this subject so that you can understand the explanation of dividing such numbers that follows this text.

Anyway, dividing rational numbers, sometimes worded "quotients of rational expressions", is simply dividing a rational number by a rational number. For instance, look at the example problems, dividing rational numbers is very easy. If you have a fraction dividing another fraction then you simply flip the dividend and, by multiplying, one will come out with exactly the same number. The knowledge of expressing how this works is beyond the scope of this lesson. But, it works every time. You are still dividing, but you have switched your means of doing so. When you come to more complicated problems that have unknown variables the same method works. So if you have a fraction of 7 over 5 divided by 3 over 4, you will simply flip the 3 over 4 and multiply the fractions instead of dividing. This is a method that will be used again and again in math, so know it well. Look at the examples given and, although this is easy, make sure you know it.

Example Problems

Example 1

${\frac {2}{7}}\div {\frac {14}{16}}$

${\frac {2}{7}}\times {\frac {16}{14}}$ (Change the division to multiplication and flip the fraction on the right.)

${\frac {1}{7}}\times {\frac {16}{7}}$ (Reduce fractions with any common factors on top and on bottom.)

${\frac {1\times 16}{7\times 7}}$ (Multiply the tops and bottoms together.)

${\frac {16}{49}}$ (Simplify)

${\frac {14}{2}}\div {\frac {14}{2}}$

${\frac {14\times 2}{2\times 14}}=$

${\frac {28}{28}}=1$

${\frac {31}{2}}=15.5$

${\frac {77}{9}}=8.{\overline {55}}$

${\frac {12}{6}}=2$

${\frac {36}{8}}=4.5$

${\frac {55}{3}}=18.{\overline {33}}$

Practice Games

put links here to games that reinforce these skills

Practice Problems

Note: Use parentheses for the repeating part, ex. ${\frac {1}{9}}=0.{\overline {1}}=$0.(1)

1

${\frac {59}{7}}=$

2

${\frac {46}{5}}=$

3

${\frac {97}{4}}=$

4

${\frac {73}{4}}=$