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Chapter 4: Problem 119

Multiply, and write the answer in simplified form. \(-8\left(\frac{17}{4}\right)\)

Short Answer

Expert verified
-34

Step by step solution

01

Understand the Expression

The problem requires the multiplication of a whole number, -8, with a fraction, \(\frac{17}{4}\).
02

Multiply the Numerator

Multiply the whole number -8 by the numerator of the fraction (17). This results in: \(-8 \times 17 = -136\).
03

Division by the Denominator

Since the whole number -8 was multiplied with the numerator, the result \(-136\) should be divided by the denominator of the fraction (4). Thus: \(\frac{-136}{4}\).
04

Perform the Division

Divide -136 by 4 to simplify the expression: \(\frac{-136}{4} = -34\).

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Key Concepts

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

Multiplying Whole Numbers by Fractions
Multiplying a whole number by a fraction might seem tricky at first, but it's actually quite straightforward.
The key step is to break it down into a simple multiplication and division process.

First, you multiply the whole number by the numerator (the top number) of the fraction.
In our example, we multiply -8 by 17:
\(-8 \times 17 = -136\). After getting this result, the next step is to handle the denominator (the bottom number) of the fraction, which we'll cover in the next sections.
Simplification of Fractions
Once you have multiplied the whole number by the numerator, you need to simplify the result by dividing it by the denominator.
This step transforms your result into its final, simplified form.

Continuing with our example, we have \(-136\). Now, we need to divide it by the denominator of the fraction, which is 4: \(\frac{-136}{4}\)
Performing this division gives: \(-34\).
Simplifying fractions often means making sure the numerator and denominator are as reduced as possible. In this case, our solution -34 is already in its simplest form because there are no common factors left.
Division in Fractions
Understanding division within the context of fractions is crucial.
Here, division is used to simplify the fraction we obtained after multiplying the whole number by the numerator.

Let's break it down: After multiplying -8 by 17 to get -136, we divide by the denominator 4: \(\frac{-136}{4}\).
This division process involves either direct computation or simplifying in steps if the numbers are large.
For instance, dividing -136 by 4 directly gives us -34, which is straightforward in this example.
It's essential to keep the division process clear and simple to avoid mistakes.

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Most popular questions from this chapter

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs \(\frac{3}{16}\) yard of print fabric and \(\frac{3}{8}\) yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

In the following exercises, add. $$\frac{15}{32}+\frac{9}{32}$$

In the following exercises, perform the indicated operations and simplify. $$\frac{11}{12}-\frac{2}{3}$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\left(-\frac{11}{12}\right)\) when (a) \(x=\frac{11}{12} \quad\) (b) \(x=\frac{3}{4}\)

In the following exercises, subtract. $$-\frac{31}{30}-\frac{7}{30}$$
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