Problem 6
Question
For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 1.8 $$
Step-by-Step Solution
Verified Answer
\(\frac{9}{5}\)
1Step 1: Express the Decimal as a Fraction
First, write the decimal number as a fraction. Since 1.8 has one decimal place, it can be written as \(\frac{18}{10}\).
2Step 2: Simplify the Fraction
Next, simplify the fraction \(\frac{18}{10}\). Find the greatest common divisor (GCD) of 18 and 10. The GCD is 2.
3Step 3: Divide Numerator and Denominator by GCD
Divide both the numerator and the denominator by the GCD (2). So, \(\frac{18 \div 2}{10 \div 2} = \frac{9}{5} \).
Key Concepts
simplifying fractionsgreatest common divisor (GCD)fraction simplification
simplifying fractions
One of the key concepts in your exercise is simplifying fractions. Simplifying a fraction means reducing it to its lowest form.
To do this, both the numerator (the top number) and the denominator (the bottom number) should be divided by their greatest common divisor (GCD).
For example, in the fraction \(\frac{18}{10}\), we know that both 18 and 10 can be divided by their common factor, which is 2.
When we divide both by 2, we get \(\frac{9}{5}\), which is the simplified form. Simplifying fractions makes them easier to work with, so it’s a good skill to master.
To do this, both the numerator (the top number) and the denominator (the bottom number) should be divided by their greatest common divisor (GCD).
For example, in the fraction \(\frac{18}{10}\), we know that both 18 and 10 can be divided by their common factor, which is 2.
When we divide both by 2, we get \(\frac{9}{5}\), which is the simplified form. Simplifying fractions makes them easier to work with, so it’s a good skill to master.
greatest common divisor (GCD)
The greatest common divisor (GCD) is the largest positive integer that divides two or more numbers without leaving a remainder. It's crucial for fraction simplification.
Finding the GCD helps you reduce a fraction to its simplest form. Here's a simple way to find the GCD:
Finding the GCD helps you reduce a fraction to its simplest form. Here's a simple way to find the GCD:
- List the factors of each number.
- Find the highest number that appears in both lists.
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 10: 1, 2, 5, 10
fraction simplification
Fraction simplification involves converting a fraction into its simplest form.
This process makes fractions easier to read and work with. Let’s go through the steps using your example \(\frac{18}{10}\):
1. Identify the GCD of the numerator and the denominator (which is 2 in this case).
2. Divide both the numerator and the denominator by the GCD:
\(\frac{18}{10} \rightarrow \frac{18 \div 2}{10 \div 2} = \frac{9}{5}\)
Now you have a simplified fraction.
This method can be used for any fractions, regardless of the complexity.
Knowing how to simplify fractions is a fundamental math skill that’s useful in more advanced topics.
This process makes fractions easier to read and work with. Let’s go through the steps using your example \(\frac{18}{10}\):
1. Identify the GCD of the numerator and the denominator (which is 2 in this case).
2. Divide both the numerator and the denominator by the GCD:
\(\frac{18}{10} \rightarrow \frac{18 \div 2}{10 \div 2} = \frac{9}{5}\)
Now you have a simplified fraction.
This method can be used for any fractions, regardless of the complexity.
Knowing how to simplify fractions is a fundamental math skill that’s useful in more advanced topics.
Other exercises in this chapter
Problem 5
For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 1.2 $$
View solution Problem 5
For exercises 1-12, simplify. $$ \frac{54}{28} $$
View solution Problem 6
For exercises 1-12, simplify. $$ \frac{72}{64} $$
View solution Problem 6
For exercises 1-80, evaluate. $$ 100-7^{2} $$
View solution