Problem 434 Add. $$ \frac{5}{12}+\left(-... [FREE SOLUTION]

Chapter 1: Problem 434

Add. $$ \frac{5}{12}+\left(-\frac{7}{12}\right)+\left(-\frac{11}{12}\right) $$

Short Answer

Expert verified

-\frac{13}{12}

Step by step solution

Identify the common denominator

All fractions involved in this addition problem have the common denominator 12. Hence, there is no need to find a common denominator.

Combine the numerators

Add the numerators of all fractions directly, keeping the denominator common. So, we have: \[ 5 + (-7) + (-11) \]

Simplify the numerator

Perform the addition/subtraction in the numerator: \[ 5 - 7 - 11 = -13 \]

Form the final fraction

Place the simplified numerator over the common denominator: \[ \frac{-13}{12} \]

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Key Concepts

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

Common Denominator

When adding fractions, you need to ensure all fractions have the same denominator. This is known as the common denominator. A common denominator is the same number in the denominator of each fraction. This allows for addition or subtraction to occur directly between the numerators. In our example, all fractions already have the common denominator of 12, simplifying the process. If they didn't, you would need to find the least common multiple (LCM) of the denominators to create equivalent fractions with the same denominator.

Numerator Operation

Once you have a common denominator, you can perform operations on the numerators. In this problem, you need to add the numerators together while keeping the denominator the same. Here, we have the numerators 5, -7, and -11 from the fractions $\frac{5}{12}, -\frac{7}{12}, -\frac{11}{12} $. We perform the addition like this: $ 5 + (-7) + (-11) = -13 $. Make sure to handle negative signs appropriately, as they change the sign of the number being added.

Simplifying Fractions

After performing operations on the numerators, the next step is to simplify the resulting fraction if possible. Simplifying a fraction involves reducing it to its lowest terms. This can be done by finding the greatest common divisor (GCD) and dividing both the numerator and the denominator by this number. In our example, $ \frac{-13}{12} $ is already in its simplest form since 13 is a prime number and doesn't share any common factors with 12. Therefore, the fraction $ \frac{-13}{12} $ is our final answer.

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91影视

Add. $$ \frac{5}{12}+\left(-\frac{7}{12}\right)+\left(-\frac{11}{12}\right) $$

Short Answer

Step by step solution

Identify the common denominator

Combine the numerators

Simplify the numerator

Form the final fraction

Key Concepts

Common Denominator

Numerator Operation

Simplifying Fractions

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