Problem 443 Subtract. $$ -\frac{23}{u}-\... [FREE SOLUTION]

Chapter 1: Problem 443

Subtract. $$ -\frac{23}{u}-\frac{15}{u} $$

Short Answer

Expert verified

$ \frac{-38}{u} $

Step by step solution

Identify the denominators

Notice that both fractions $ -\frac{23}{u} $ and $ -\frac{15}{u} $ have the same denominator, which is $ u $. This means you can combine them into a single fraction.

Combine the fractions

Since both fractions have the same denominator, combine the numerators by subtraction: $ -\frac{23}{u} - \frac{15}{u} = \frac{-23 - 15}{u} $.

Simplify the numerator

Subtract the numerators: $ -23 - 15 = -38 $. So, the fraction simplifies to $ \frac{-38}{u} $.

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Key Concepts

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

Introduction to Subtracting Fractions

When you subtract fractions, the first step is to check if the denominators鈥攖he numbers at the bottom of the fractions鈥攁re the same. If the denominators match, you can subtract the numerators鈥攖he numbers at the top of the fractions鈥攅asily. In our exercise, we start with the fractions $-\frac{23}{u}-\frac{15}{u}$. Since both fractions share the same denominator, which is $u$, we can proceed to subtract the numerators directly. This simplifies the process significantly.

Combining fractions becomes straightforward when the denominators are the same. Look out for this feature to make subtraction easier.

Understanding Common Denominators

A common denominator is a shared denominator between two or more fractions. It allows you to combine fractions more effectively. In our example, $-\frac{23}{u}$ and $-\frac{15}{u}$ already have $u$ as a common denominator. This means we can directly work with the numerators: -23 and -15. No additional steps are needed to equalize the denominators.

If fractions don鈥檛 have a common denominator, you鈥檇 need to find one. This usually involves finding the Least Common Denominator (LCD), which is the smallest number that both denominators can divide into evenly. Once the denominators match, you can combine the fractions as detailed above.

Simplifying Fractions

Simplifying fractions involves making the fraction as simple as possible. This typically means reducing it to its lowest terms. In our given example, after combining the fractions with a common denominator, we get $\frac{-38}{u}$. Simplification here involves careful subtraction.

When you simplify a fraction, check if the numerator and the denominator have any common factors other than 1. If they do, divide both by their Greatest Common Divisor (GCD). In our case, $u$ is already simplified as much as possible. Just make sure your final answer is in the simplest form for ease of understanding and clarity.

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91影视

Subtract. $$ -\frac{23}{u}-\frac{15}{u} $$

Short Answer

Step by step solution

Identify the denominators

Combine the fractions

Simplify the numerator

Key Concepts

Introduction to Subtracting Fractions

Understanding Common Denominators

Simplifying Fractions

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