Problem 61 - Prealgebra

Question

Write each decimal as an equivalent proper fraction or mixed number. 0.18

Step-by-Step Solution

Answer

0.18 = \( \frac{9}{50} \)

Step 1: Understanding the Decimal

Understand that the decimal 0.18 represents a fraction of a whole number, where 18 is in the hundredths place.

Step 2: Express as a Fraction

Write 0.18 as a fraction with denominator 100: \( \frac{18}{100} \). This is because '0.18' means 18 hundredths.

Step 3: Simplify the Fraction

Simplify \( \frac{18}{100} \) by finding the greatest common divisor (GCD) of 18 and 100, which is 2. Divide both the numerator and the denominator by 2: \( \frac{18 \div 2}{100 \div 2} = \frac{9}{50} \).

Step 4: Verify the Fraction

Check if \( \frac{9}{50} \) can be simplified further. Since 9 and 50 have no other common divisors, \( \frac{9}{50} \) is in its simplest form.

Key Concepts

Simplifying Fractions

The process of simplifying fractions is crucial to making calculations easier and results clearer. When you have a fraction like \(\frac{18}{100}\), the aim is to reduce it to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator.

• First, identify the GCD, which is the largest number that divides both the numerator and the denominator without leaving a remainder. For \(\frac{18}{100}\), the GCD is 2.
• Next, divide both the numerator and the denominator by the GCD: \(\frac{18 \div 2}{100 \div 2} = \frac{9}{50}\). This step reduces the fraction to its simplest form, making it easier to interpret and use.

Ensuring your fraction is fully simplified helps avoid errors in calculations, particularly when dealing with multiple fractions at once. It's a handy skill that can make dealing with decimals and fractions much less intimidating!

Equivalent Fractions

Understanding equivalent fractions is key to converting decimals to fractions and back again. Equivalent fractions are different fractions that represent the same value. For instance, \(\frac{18}{100}\) and \(\frac{9}{50}\) are equivalent because they compute to the same decimal value—0.18.

• To find equivalent fractions, you can either multiply or divide both the numerator and the denominator by the same non-zero number. This changes their appearance but not their value.
• In this exercise, we initially represented 0.18 as \(\frac{18}{100}\) before simplifying it to \(\frac{9}{50}\). Both fractions represent the same portion of a whole.

Grasping this concept allows for greater flexibility in solving problems, as it gives you the ability to move between different representations of the same number with ease.

Mixed Numbers

While the exercise specifically dealt with converting a decimal into a fraction, it’s useful to know what mixed numbers are, especially when dealing with numbers greater than one. A mixed number contains both a whole number and a fraction, like 1 3/4.

• When converting a decimal to a mixed number, start by separating the whole number part from the fractional part. For example, converting 2.75: the whole number is 2, and 0.75 becomes \(\frac{3}{4}\).
• Add these components together to get the mixed number form: 2 3/4.

Understanding mixed numbers is important when dealing with real-world measurements, such as in cooking or construction, where quantities don't always come in whole numbers. It's also a basic skill that complements the process of fraction simplification and finding equivalents.