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Chapter 2: Problem 16

Find a decimal equivalent for each fraction or mixed number. \(\frac{9}{12}\)

Short Answer

Expert verified
0.75

Step by step solution

01

Simplify the Fraction

Identify the greatest common divisor (GCD) of the numerator and the denominator. For \(\frac{9}{12}\) the GCD is 3. Divide both the numerator and the denominator by 3 to simplify the fraction: \(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)
02

Convert the Simplified Fraction to a Decimal

Divide the numerator by the denominator: \(\frac{3}{4} = 0.75\)

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Key Concepts

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

Simplifying Fractions
Simplifying fractions makes them easier to work with by reducing them to their smallest form. To do this, you need to find a common factor for both the numerator (top number) and the denominator (bottom number). A fraction is simplified when you cannot divide the numerator and denominator evenly by any number other than 1.
Say you have the fraction \(\frac{9}{12}\). Notice that both 9 and 12 can be divided by 3. After dividing, the fraction simplifies to \(\frac{3}{4}\).
  • Identify a common factor shared by both numbers.
  • Divide both numerator and denominator by this common factor.
Simplifying fractions can help when performing further calculations, like conversion to decimal or comparing fractions.
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that can divide both the numerator and denominator of a fraction without leaving a remainder. Finding the GCD is the key to simplifying fractions effectively.
For the fraction \(\frac{9}{12}\), we need to figure out the largest number that can evenly divide both 9 and 12. The divisors of 9 are 1, 3, and 9, while the divisors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common divisor of 9 and 12 is 3.
  • List the factors of both the numerator and denominator.
  • Identify the largest number common to both lists.
Once the GCD is found, use it to simplify the fraction by dividing both the numerator and denominator by this number. In our example, dividing 9 and 12 by 3 gives us \(\frac{3}{4}\).
Fraction to Decimal
Converting a fraction to a decimal involves a simple division. You divide the numerator (top number) by the denominator (bottom number).
Starting with the simplified fraction \(\frac{3}{4}\), we divide 3 by 4. This gives us 0.75. Converting fractions to decimals is an important skill for various math problems and real-world applications.
  • Ensure the fraction is simplified.
  • Divide the numerator by the denominator using long division or a calculator.
For example, \(\frac{3}{4}\) when divided results in 0.75. Thus, \(\frac{9}{12}\) in decimal form is 0.75 because \(\frac{9}{12}\) simplifies to \(\frac{3}{4}\).

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Most popular questions from this chapter

Tell the nearest tenths of a centimeter that each given measurement is between. For example, 3.66 is between 3.6 and 3.7 \(1.01 \mathrm{cm}\)

Find a decimal equivalent for each fraction or mixed number. \(\frac{376}{20,000}\)

Of the 560 students at Roosevelt Middle School, 240 participate in after- school sports. Of the 720 students at King Middle School, 300 participate in after-school sports. a. In which school does the greater number of students participate in sports? b. In which school does the greater fraction of students participate in sports?

Prove It! Write a convincing argument to show that \(\frac{3}{4}\) of a fruit bar is not a fair trade for \(\frac{3}{5}\) of a fruit bar.

Find each quantity without using a calculator. \(7.7 \div 1,000\)
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