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Chapter 4: Problem 27

Simplify if possible. $$\frac{-9}{-10}$$

Short Answer

Expert verified
The simplified fraction is \(\frac{9}{10}\).

Step by step solution

01

- Understand the Problem

We need to simplify the fraction \(\frac{-9}{-10}\). This means finding an equivalent fraction that is in its simplest form.
02

- Simplify the Sign

Note that both numerator and denominator are negative: \(\frac{-9}{-10}\). A fraction with both numerator and denominator negative can be simplified by changing both signs to positive. Thus, it becomes \(\frac{9}{10}\).
03

- Check for Further Simplification

The fraction \(\frac{9}{10}\) is already in its simplest form because 9 and 10 have no common factors other than 1. So, no further simplification is needed.

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Key Concepts

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

Negative Fractions
Fractions can have negative signs, but dealing with them is simpler than it seems. When both the numerator and the denominator are negative, their signs can be changed to positive. For example, \(\frac{-9}{-10}\) can be rewritten as \(\frac{9}{10}\). This works because a negative divided by a negative gives a positive result. Remember, the key is to simplify the fraction by balancing positive and negative signs.
Simplest Form
The simplest form of a fraction means it cannot be reduced any further. This occurs when the numerator and denominator have no common factors other than 1. For our fraction \(\frac{9}{10}\), we see that 9 and 10 share no common factors except 1; hence, \(\frac{9}{10}\) is already in its simplest form. Another way to check this is to find the greatest common divisor (GCD) of the numerator and denominator. If it is 1, the fraction is in its simplest form.
Numerator and Denominator
Understanding numerators and denominators is essential in fraction simplification. The numerator, located above the fraction bar, indicates how many parts we have. The denominator, found below the fraction bar, tells us the total number of equal parts. In the fraction \(\frac{-9}{-10}\), -9 is the numerator and -10 is the denominator. When simplifying fractions, dealing only with numbers is easier after addressing any negative signs.

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Most popular questions from this chapter

Determine whether the factorization represents the prime factorization. If not, explain why. $$126=3 \cdot 7 \cdot 3 \cdot 2$$

Multiply or divide the mixed numbers. Write the answer as a mixed number or whole number. $$\left(2 \frac{2}{5}\right)\left(3 \frac{1}{12}\right)$$

Divide. Write the quotient as a mixed number. $$695 \div 34$$

Find the LCM. 42 and 70

Find the LCM. $$21,35,50, \text { and } 75$$
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