Problem 27 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ -\frac{3}{4} $$

Step-by-Step Solution

Answer

-0.75

Step 1 - Understand the fraction

The fraction given is \( -\frac{3}{4} \). It represents a negative part of a whole.

Step 2 - Divide the numerator by the denominator

To convert the fraction \( \frac{3}{4} \) into a decimal, divide 3 by 4.

Step 3 - Perform the division

When you divide 3 by 4, you get 0.75. Therefore, \( \frac{3}{4} = 0.75 \).

Step 4 - Add the negative sign

The original fraction was negative, so add the negative sign to the decimal. This gives \( -0.75 \).

Key Concepts

fractions to decimals

Converting fractions to decimals is a helpful math skill that allows you to express ratios in a different format. A fraction tells you how many parts of a whole you have. To convert it to a decimal, you perform a division. For instance, for the fraction \(\frac{3}{4}\), you divide the numerator (3) by the denominator (4). By performing the division, we get 0.75. This means that \(\frac{3}{4}\) is the same as 0.75 in decimal form. So, anytime you're converting fractions to decimals, just remember—divide the top number by the bottom number, and you'll get your decimal!

numerator and denominator

A fraction consists of two main parts: the numerator and the denominator. The numerator is the top number and shows how many parts you have. The denominator is the bottom number and signifies how many equal parts the whole is divided into. For example, in the fraction \(\frac{3}{4}\), 3 is the numerator and 4 is the denominator.
Understanding these two components is crucial for performing various operations with fractions, including converting them into decimals. If you want to find what part of the whole a fraction represents in decimal form, you need to divide the numerator by the denominator. In our example, dividing 3 by 4 gives you 0.75.
Without knowing what the numerator and denominator represent, working with fractions would be quite confusing. So always remember: the numerator is the parts at hand, and the denominator is how many parts make a whole.

negative numbers

Understanding negative numbers is essential, especially when they appear in fractions. Negative numbers represent values less than zero and are found left of zero on the number line. For instance, -1, -2, and -3 are all negative numbers.
When converting a negative fraction to a decimal, you follow the same steps as with positive fractions, but you must keep the negative sign in your final result. In our example, we began with the fraction \(-\frac{3}{4}\). By converting the positive part \(\frac{3}{4}\) to the decimal 0.75 and then attaching the negative sign, we get the final result of -0.75.
Negative numbers can make calculations seem more challenging, but as long as you remember to add the negative sign in the end, the steps remain the same! Just don't forget: a negative number simply represents a value less than zero.