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Chapter 6: Problem 17

Convert each decimal fraction to a proper fraction or a mixed number. Be sure to reduce. 16.12

Short Answer

Expert verified
16.12 as a mixed number is 16 \( \frac{3}{25} \).

Step by step solution

01

Understand the Decimal

The decimal 16.12 consists of a whole number, 16, and a decimal fraction, 0.12. Our task is to convert this into a mixed number or a proper fraction.
02

Convert Decimal to Fraction

Take the decimal fraction, 0.12. To convert 0.12 into a fraction, recognize it as 12 over 100, since it represents 12 hundredths. So we write it as \( \frac{12}{100} \).
03

Simplify the Fraction

Simplify \( \frac{12}{100} \) by finding the greatest common divisor of 12 and 100, which is 4. Divide both the numerator and the denominator by 4: \( \frac{12 \div 4}{100 \div 4} = \frac{3}{25} \).
04

Combine Whole Number and Fraction

Combine the whole number 16 with the simplified fraction \( \frac{3}{25} \). This gives us the mixed number 16 \( \frac{3}{25} \).
05

Verify the Solution

To ensure accuracy, convert 16 \( \frac{3}{25} \) back to a decimal: \( 16 + \frac{3}{25} = 16 + 0.12 = 16.12 \). This matches the original decimal.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Fractions
Understanding how to simplify fractions plays a crucial role in many areas of math. The goal is to make the fraction as simple as possible but still equivalent. For example, let's take the fraction \( \frac{12}{100} \).
First, we need to find a number that divides both the numerator (12) and the denominator (100) evenly. This number is called the Greatest Common Divisor (GCD).

When you divide both the top and bottom of a fraction by their GCD, you make the fraction simpler. Here, the GCD of 12 and 100 is 4.
  • Divide 12 by 4, you get 3.
  • Divide 100 by 4, you get 25.
So, \( \frac{12}{100} \) can be simplified to \( \frac{3}{25} \). Always check if the new fraction can be simplified further. If not, then you have your simplest form.
Mixed Numbers
Mixed numbers are essentially a combination of a whole number and a fraction. They鈥檙e used when a number is both greater than 1 plus there is also a fractional part. In our example, 16.12 becomes a mixed number.
First, separate the whole number from the decimal. 16 is the whole number here.

The decimal represents a fraction. Specifically, for 0.12, we already found it converts to \( \frac{3}{25} \).
  • Write the 16 as the whole number.
  • Attach the simplified fraction \( \frac{3}{25} \) next to it.
This makes the mixed number 16 \( \frac{3}{25} \). This helps in situations where it's easier to understand numbers not in strict decimal form.
Greatest Common Divisor
The Greatest Common Divisor, or GCD, is a vital concept when dealing with fractions. It refers to the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.

Finding the GCD helps simplify fractions to their simplest form. To determine the GCD:
  • List the factors of each number. For 12, they are 1, 2, 3, 4, 6, and 12;
  • for 100, they are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
  • The biggest number common to both lists is 4.
So, the GCD of 12 and 100 is 4. Use this number to simplify the fraction \( \frac{12}{100} \) to \( \frac{3}{25} \). Recognizing and applying the GCD makes calculations straightforward and the results more comprehensible.

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Most popular questions from this chapter

Perform the following operations. \(9.26+\frac{1}{4} \cdot 0.81\)

Perform the following operations. \(\frac{1}{20}+3.62 \cdot \frac{3}{8}\)

The decimal digit that appears three places to the right of the decimal point is in the ____________ position.

Write eighty-one and twelve hundredths using digits. 81.12

Write each decimal using digits. Two and one hundred seventy-seven thousandths.
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