Problem 29 - Prealgebra

Question

Write each decimal as a mixed number. $$5.6$$

Step-by-Step Solution

Answer

The decimal 5.6 as a mixed number is \(5\frac{3}{5}\).

Step 1: Understanding the Decimal

First, identify the whole number and the fractional part of the decimal 5.6. Here, 5 is the whole number and 0.6 is the decimal part.

Step 2: Converting the Decimal Part to a Fraction

Understand that 0.6 can be written as a fraction. The number 6 is in the tenths place, so 0.6 can be expressed as \( \frac{6}{10} \).

Step 3: Simplifying the Fraction

Simplify \( \frac{6}{10} \) by finding the greatest common divisor of 6 and 10, which is 2. Divide both the numerator and the denominator by 2 to get \( \frac{3}{5} \).

Step 4: Writing the Mixed Number

Now, combine the whole number and the simplified fraction. The whole number is 5 and the fractional part is \( \frac{3}{5} \). Therefore, the decimal 5.6 as a mixed number is \( 5\frac{3}{5} \).

Key Concepts

Decimal to Fraction Conversion

When converting a decimal to a fraction, it's essential to understand the positions of the digits after the decimal point. Each position represents a fraction of ten. For example:

• The first position after the decimal is the tenths place, the second is the hundredths place, and so on.
• To convert the decimal part into a fraction, look at the number of places after the decimal point. This indicates what power of ten the denominator will be.
• Take 0.6 as an example. The 6 is in the tenths place, so it can be written as \( \frac{6}{10} \).

Align the denominator with the decimal position: tenths, hundredths, thousandths, etc. This basic conversion lays the groundwork for simplifying fractions next.

Simplifying Fractions

Simplifying a fraction means making it as simple as possible by dividing both the numerator and the denominator by their greatest common divisor (GCD). Here's how to do it:

• Identify the GCD, which is the largest number that can evenly divide both the numerator and the denominator.
• In the fraction \( \frac{6}{10} \), both 6 and 10 can be divided by 2, their GCD.
• Divide both the numerator and the denominator by the GCD: \( \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \).

This process reduces the fraction to its simplest form, making it easier to work with and understand. Simplified fractions are essential for creating mixed numbers without extra complexity.

Mixed Numbers

A mixed number combines a whole number with a fraction. It's a handy way to express quantities greater than one that also include a fractional part. Here's how to form a mixed number:

• Start with the whole number part of your decimal, and the simplified fraction from your converted fractional part.
• In our example, the whole number from 5.6 is 5, and the fractional part is the simplified \( \frac{3}{5} \).
• Write the mixed number as \( 5\frac{3}{5} \), showing that it is composed of a whole number plus a fraction.

Using mixed numbers keeps calculations straightforward when dealing with numbers that have both whole and fractional components. It provides a clear and tidy way to express these values.