Problem 1 - Prealgebra

Question

Each circle below is divided into 8 equal parts. The number below cach circle indicates what fraction of the circle is shaded. Convert each fraction to a decimal. (CIRCLE NOT COPY)

Step-by-Step Solution

Answer

Convert each fraction by dividing the numerator by 8.

Step 1: Understanding the Problem

You need to convert fractions into their decimal form. Each circle is divided into 8 parts and the given fraction represents how many of these parts are shaded.

Step 2: Set Up the Division

To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). For example, if the fraction is \( \frac{3}{8} \), you need to compute \( 3 \div 8 \).

Step 3: Perform the Division

Divide the numerator by the denominator. Continuing with the example \( \frac{3}{8} \): \( 3 \div 8 = 0.375 \). This is the decimal form of the fraction.

Step 4: Repeat for Each Fraction

Perform the division for each fraction given under the circles to find the decimal equivalents. Always ensure you are dividing correctly to get the proper decimal.

Key Concepts

Understanding Numerator and Denominator

Fractions can be quite simple once you understand the basics! A fraction is made up of two parts: the numerator and the denominator. The numerator is the number on top, while the denominator is the number on the bottom. For instance, in the fraction \( \frac{3}{8} \), 3 is the numerator and 8 is the denominator. The numerator tells you how many parts of the whole are being considered, and the denominator tells you into how many equal parts the whole is divided.
Understanding these roles is crucial for converting fractions to decimals. By knowing that the denominator represents division of the whole into equal parts, you can readily proceed with converting them into decimal form by dividing as needed. Remember, the larger the denominator, the smaller each part will be.

Mastering Division of Fractions

The main process for converting a fraction to a decimal is division. When you see a fraction like \( \frac{3}{8} \), you are essentially dealing with division. This fraction can be read as "3 divided by 8." Splitting the quantity (3 in this case) into the number of parts specified by the denominator (8) is what gives you the decimal.When dividing, it’s helpful to set up your division properly. Using long division can clarify the process. It might look complex at first, but with practice, it becomes second nature. Here’s how you set it up:

• Place the numerator under the division symbol.
• The denominator goes outside to the left.

For \( 3 \div 8 \), you would discover the decimal 0.375. Make sure to handle the division carefully, adding zeros when necessary to carry out the division beyond the decimal point.

Decimal Conversion Simplified

Once you’ve mastered the division of a fraction, you're ready for conversion into a decimal. Decimal conversion is straightforward when you carry out the division accurately. With fractions, each division line represents a decimal. If you're working with \( \frac{3}{8} \) and you've noted the result 0.375 from your division, that's your decimal conversion.Here’s a quick way to do it:

• First, remember to arrange fractions correctly for division.
• Second, perform the division carefully to avoid mistakes.
• Lastly, note the decimal always appears after the division, transforming the fraction into an easy-to-use form.

Every decimal represents a part of a whole just like fractions do, but in a way that's sometimes easier to interpret, especially in adding or comparing numbers. Always check your work with different fractions as practice strengthens your skill in conversion.