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Chapter 1: Problem 89

Multiply. $$ \frac{3}{7}(-1) $$

Short Answer

Expert verified
\frac{-3}{7}

Step by step solution

01

Identify the numbers

The two numbers to be multiplied are \(\frac{3}{7}\) and \(-1\).
02

Multiply the numerators

Multiply the numerator of the fraction by the second number: \(3 \times -1\). This gives \-3\.
03

Determine the denominator

The denominator remains the same as in the original fraction, 7.
04

Combine the result

Combine the numerator and the denominator to get the product: \(\frac{-3}{7}\).

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Key Concepts

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

Rational Numbers
A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers. The denominator must not be zero. For example, \(\frac{3}{4}\) and \(\frac{-5}{2}\) are rational numbers.

Understanding rational numbers is essential because they allow us to accurately represent quantities that are not whole numbers. This includes most real-world measurements like distances, weights, and probabilities.

When multiplying rational numbers, like \(\frac{3}{7} \times -1\), you are essentially dealing with the multiplication of the numerators and denominators separately.
Negative Numbers
Negative numbers are numbers less than zero and are denoted with a minus sign (-). They are opposite in value to their positive counterparts. For example, -3 is the opposite of 3.

When multiplying a fraction by a negative number, like in the exercise \(\frac{3}{7}(-1)\), the product will also be a negative number. This means:
  • Multiplying a positive number by a negative number results in a negative number.
  • Multiplying two negative numbers results in a positive number.
  • Negative numbers follow the same arithmetic rules as positive numbers but with the opposite sign.

In our example, multiplying \(\frac{3}{7} \times -1\) gives \(\frac{-3}{7}\). Notice how the numerator changes sign while the denominator remains positive.
Numerator and Denominator
In a fraction, the numerator is the top number, which represents how many parts of a whole are taken. The denominator is the bottom number, which indicates the total number of equal parts that make up that whole.

For instance, in the fraction \(\frac{3}{7}\), 3 is the numerator, and 7 is the denominator. It signifies taking 3 parts out of a whole that is divided into 7 equal parts.

When performing operations like multiplication, each part of the fraction (the numerator and the denominator) can be treated separately:
  • The numerators multiply with the numerators.
  • The denominators multiply with the denominators.
In the given exercise, only the numerator \(3 \times -1 = -3\) changes, while the denominator (7) stays the same, resulting in the final fraction \(\frac{-3}{7}\).

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Most popular questions from this chapter

Calculate using the rules for order of operations. Find the greatest value of \(a\) for which \(|a| \geq 6.2\) and \(a<0\)

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \sqrt{10} \in \mathbb{R} $$

Find an equivalent expression by factoring. $$ 9 p-3 $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 4.3 \notin \mathbb{Z} $$

Use set-builder notation to write each set. \(\\{11,13,15,17,19\\}\)
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