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Chapter 3: Problem 20

Subtract and simplify. $$ \frac{9}{10}-\frac{3}{100} $$

Short Answer

Expert verified
\(\frac{87}{100}\)

Step by step solution

01

Find Common Denominator

The denominators are 10 and 100. To subtract the fractions, a common denominator is needed. The least common denominator (LCD) of 10 and 100 is 100.
02

Convert Fractions

Convert each fraction to have the common denominator. For the first fraction, \(\frac{9}{10}\), multiply both the numerator and the denominator by 10 to get \(\frac{90}{100}\). The second fraction, \(\frac{3}{100}\), already has the common denominator.
03

Subtract the Fractions

Now that both fractions have the same denominator, subtract the numerators: \(\frac{90}{100} - \frac{3}{100} = \frac{90 - 3}{100} = \frac{87}{100}\).
04

Simplify the Result

In this case, \(\frac{87}{100}\) is already in its simplest form because the greatest common divisor of 87 and 100 is 1.

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Key Concepts

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

Common Denominator
When you want to subtract fractions, you need to make sure that the fractions share a common base鈥攖he denominator. This makes it possible to directly compare and work with the fractions. If the denominators are different, like in the problem \(\frac{9}{10} - \frac{3}{100}\), it's essential to find a common denominator first.
Initially, check the denominators of each fraction. Here, they are 10 and 100. A multiple that both denominators can fit into evenly is necessary. In this problem, the smallest number they both can divide into is 100. This number is called the Least Common Denominator (LCD). Finding the LCD is the next step in making the fractions suitable for subtraction.
Subtracting Fractions
Once both fractions share a common denominator, they can be subtracted. Start by adjusting the fractions to the shared baseline. In this exercise, \(\frac{9}{10}\) becomes \(\frac{90}{100}\) by multiplying both its numerator and denominator by 10. The fraction \(\frac{3}{100}\) already fits the common denominator of 100.
Now, with both fractions possessing the same denominator, you can proceed. Subtract their numerators while keeping the denominator constant: \(\frac{90}{100} - \frac{3}{100} = \frac{90 - 3}{100} = \frac{87}{100}\). By handling them this way, the subtraction is straightforward and manageable.
Least Common Denominator (LCD)
Identifying the Least Common Denominator (LCD) is critical for smoothly subtracting fractions. The LCD of two numbers is the smallest multiple that both original denominators can divide by without leaving a remainder. In essence, finding the LCD allows you to express multiple fractions consistently and comparably.
For example, between denominators 10 and 100, the LCD is 100. Why? Because it is the smallest number divisible by both 10 and 100. Once discovered, convert each fraction to match this base. In this exercise, \(\frac{9}{10}\) transformed into \(\frac{90}{100}\) to fit the LCD framework, making the subtraction easier.

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Most popular questions from this chapter

Subtract and simplify. $$ \frac{5}{6}-\frac{1}{6} $$

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