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Chapter 1: Problem 90

Multiply. $$ -1 \cdot \frac{2}{5} $$

Short Answer

Expert verified
The result is \( \frac{-2}{5} \).

Step by step solution

01

Understand the Problem

The exercise requires you to multiply a negative integer by a fraction: \( -1 \times \frac{2}{5} \).
02

Multiply the Numerator

To multiply \( -1 \) by \( \frac{2}{5} \), first multiply \( -1 \) by the numerator of the fraction.\( -1 \times 2 = -2 \).
03

Retain the Denominator

The denominator of the fraction remains the same during multiplication. Thus, the denominator stays \( 5 \).
04

Form the Resulting Fraction

Combine the resulting numerator with the unchanged denominator to get the resulting fraction: \( \frac{-2}{5} \).

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Key Concepts

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

Negative Integers
Negative integers are numbers less than zero. They have a minus sign (-) in front of them. Examples include -1, -2, and -3. When multiplying negative integers by other numbers, it's essential to consider the rules of multiplication involving negatives.
For multiplication:
  • A positive number times a negative number results in a negative number. For example, \( 2 \times -3 = -6 \).
  • A negative number times a negative number results in a positive number. For example, \( -2 \times -3 = 6 \).
In our exercise, we are multiplying \( -1 \) (a negative integer) by a fraction.
Fractions
A fraction represents a part of a whole. It consists of a numerator and a denominator.
In our exercise, the fraction is \( \frac{2}{5} \). Fractions can be multiplied by whole numbers or other fractions. When multiplying fractions by a whole number, you only multiply the numerator (top number) of the fraction, and the denominator (bottom number) remains unchanged.
Multiplying entire fractions is similar: you multiply the numerators together and the denominators together. In this case, we only multiply by a whole number, so the denominator stays the same.
Numerator and Denominator
The numerator and the denominator are two parts that make up a fraction.
The numerator is the top number and indicates how many parts of the whole are being considered. For example, in \( \frac{2}{5} \), 2 is the numerator, showing we have 2 parts out of 5.
The denominator is the bottom number and indicates into how many equal parts the whole is divided. Using our previous example, 5 is the denominator, showing the whole is divided into 5 equal parts.
When you multiply fractions by a whole number, you multiply the whole number by the numerator and keep the denominator the same. This preserves the proportion represented by the fraction.

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Most popular questions from this chapter

Calculate using the rules for order of operations. Use the commutative, associative, and distributive laws to show that \(5(a+b c)\) is equivalent to \(c(b \cdot 5)+a \cdot 5 .\) Use only one law in each step of your work.

Translate to an algebraic expression. Three times the sum of the cubes of two numbers

Find an equivalent expression by factoring. $$ x y+x $$

Find an equivalent expression by factoring. $$ a b+b $$

Write an equivalent expression using the distributive law. $$ 6(s-t) $$
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