Problem 59 - Algebra 1: Concepts and Skills

Question

Write the fraction or mixed number as a decimal. (Skills Review pp. 763,767) $$ \frac{56}{20} $$

Step-by-Step Solution

Answer

The fraction \(\frac{56}{20}\) can be written as a decimal as 2.8.

Step 1: Simplify the Fraction

The first task is a simplification, looking at the fraction, both the numerator 56 and denominator 20 have a common factor which is 4. So the fraction can be simplified as: \(\frac{56 ÷ 4}{20 ÷ 4}\) = \(\frac{14}{5}\)

Step 2: Divide

To convert the fraction into decimal, the numerator (14) needs to be divided by the denominator (5). This results in 2.8.

Key Concepts

Fraction Simplification

Fraction simplification is an important step to make fractions easier to work with. By simplifying a fraction, we reduce the numbers on the top (numerator) and bottom (denominator) to their smallest possible form while keeping the same value. For simplifying, find the greatest common factor (GCF) of both the numerator and denominator.
For example, in the fraction \( \frac{56}{20} \), the GCF is 4. By dividing both the numerator and the denominator by 4, you simplify the fraction to \( \frac{14}{5} \).

• Identify the GCF by listing out factors of both numbers.
• Divide both the numerator and the denominator by this GCF.
• Ensure that the new fraction cannot be further simplified.

Simplification helps in keeping numbers smaller, making them more manageable for further calculations.

Division

After simplifying a fraction, the next step is often to convert it to a decimal. This process involves division. The fraction \( \frac{14}{5} \) means you need to divide 14 (numerator) by 5 (denominator).
Performing division gives the decimal form of the fraction. In this example:

• Divide 14 by 5, which equals 2 with a remainder of 4.
• To continue, write the remainder as a decimal (0.8 in this case).
• The result becomes 2.8 when combined.

Division transforms fractions into decimals, useful for clearer understanding or when a decimal is required.

Numerator and Denominator

Understanding the terms numerator and denominator is key to working with fractions. The numerator is the number on top, representing how many parts of a whole you have. The denominator is the bottom number, showing the total number of equal parts that make up the whole.
In \( \frac{56}{20} \):

• 56 is the numerator, indicating the number of parts considered.
• 20 is the denominator, signaling total parts needed to make a whole.

After simplification, the new fraction \( \frac{14}{5} \) still maintains this basic structure but in a simpler form. Remember, any operation on a fraction involves these two components, maintaining the balance between what a part is and how many parts make up the whole. Understanding this helps in accurately performing fraction-related calculations, providing a foundation for more complex math operations.