GED Mathematical Reasoning: Fractions and Decimal Equivalence

  • The bar in a fraction is another way to denote division. In fact, to change a fraction into a decimal, divide the numerator by the denominator. The easiest way to do this is using a calculator.  Enter the numerator, then press the division key, then enter the denominator.
  • Shown below are some common fraction/decimal equivalencies.
Decimal Fraction Decimal Fraction Decimal Fraction
0.1 \frac{1}{10} 0.375 \frac{3}{8} 0.7 \frac{7}{10}
0.125 \frac{1}{8} 0.4 \frac{2}{5} 0.75 \frac{3}{4}
0.2 \frac{1}{5} 0.5 \frac{1}{2} 0.8 \frac{4}{5}
0.25 \frac{1}{4} 0.6 \frac{3}{5} 0.875 \frac{7}{8}
0.3 \frac{3}{10} 0.625 \frac{5}{8} 0.9 \frac{9}{10}
0.33333… \frac{1}{3} 0.6666… \frac{2}{3}
  • The fractions \frac{1}{3} and \frac{2}{3} are special cases and very commonly used in application problems, so I want to draw your attention to these cases.
  • When you type \frac{1}{3} into the calculator as: one, then the division key, then three, the result showing is: 0.333…. Some simply round this to: .33. Showing on the screen is the decimal version of \frac{1}{3}
  • Similarly, when you type  into the calculator as two, then the division key, then three, the result showing is: 0.666…. It is the decimal version of \frac{2}{3}.
  • You may be wondering: Why is it important to study fraction and decimal equivalencies? For one reason, it can save you time when working word problems. Another reason it is important to be familiar with fraction and decimal equivalency is that it can help you interpret calculator answers.


Example 1

Change \frac{3}{4} into a decimal.


To change \frac{3}{4} into a decimal, we will divide 3 by 4.

The easiest way to do this is using a calculator.  Enter the numerator, then press the division key, then enter the denominator. We’ll press 3, then the division key, then 4. The result is 0.75. So \frac{3}{4} and 0.75 are equivalent.

\frac{3}{4} = 3 \div 4 = 0.75


Example 2

Change 0.275 into a fraction written in lowest terms.


In order to change a decimal into a fraction, we must determine the numerator and denominator.

The numerator of the fraction is the number you see in the decimal. In this case, it is 275. Read the decimal to yourself to determine the denominator. Here’s what I mean: the decimal 0.275 is read as “two hundred seventy five thousands,” therefore the denominator will be 1000. In other words, the denominator of the fraction corresponds to the place value of the last digit on the right.

0.275 = \frac{275}{1000}

After we’ve written the decimal in fraction form, we need to reduce it to lowest terms if possible. In this case, it is possible to reduce the fraction by a factor of 25. When we divide both the numerator and denominator by 25, the result is: \frac{11}{40}. Therefore, the decimal 0.275 is equivalent to the fraction \frac{11}{40}.

\frac{275 \div 25}{1000 \div 25}  = \frac{11}{40}


Example 3

A sweater with an original price of $80 is 50% off. What is the sale price?


We will be talking much more about percents later, but note that taking a discount of 50% is the same as multiplying the original price by 0.50. So to find the sale price of this sweater, we will multiply 0.50 by $80. Of course, this is easy enough to do with a calculator, but if you know that 0.50 is the same as one-half, you’ll likely be able to determine the answer faster than the time it will take you just to find the calculator.

0.50 = \frac{1}{2}

Multiplying one-half times $80 is the same as taking one-half of $80, which a calculation you can probably do in a split second. The answer is $40. So the sale price of the sweater is $40.


Example 4

Marlaine has 20 yards of garden fencing that she would like to cut into three equal sections to use around her flower gardens. How much fencing will she have for each garden? State your answer as a mixed number.


In this example, we need to divide 20 by 3 since 20 yards of fencing is being divided into three equal sections. And we must state our answer as a mixed number.

It’s pretty easy to type 20 divided by 3 into the calculator, but when we do notice the result shown on the screen. It is:  6.666… The question is: How do we write this as a mixed number?

If you know that the fraction equivalent of 0.66666666…. is \frac{2}{3}, then it’s very easy:   6.666…  is equal to 6 and two thirds. Therefore, Marlaine will have 6\frac{2}{3} yards of fencing to surround each of her flower gardens.

You have seen 1 out of 15 free pages this month.
Get unlimited access, over 1000 practice questions for just $29.99. Enroll Now