/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Without using a calculator evalu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 10

Without using a calculator evaluate (a) \(10 \times(-2)\) (b) \((-1) \times(-3)\) (c) \((-8) \div 2\) (d) \((-5) \div(-5)\) (e) \(5-6\) (f) \(-1-2\) (g) \(7-(-4)\) (h) \(-9-(-9)\) (i) \(\frac{(-3) \times(-6) \times(-1)}{2-3}\).

Short Answer

Expert verified
(a) -20, (b) 3, (c) -4, (d) 1, (e) -1, (f) -3, (g) 11, (h) 0, (i) 18.

Step by step solution

01

Evaluate 10 \times (-2)

Multiplying a positive number and a negative number produces a negative result. So, \(10 \times (-2) = -20\).
02

Evaluate (-1) \times (-3)

Multiplying two negative numbers results in a positive number. Therefore, \((-1) \times (-3) = 3\).
03

Evaluate (-8) \backslash 2

Dividing a negative number by a positive number results in a negative number. Thus, \((-8) \backslash 2 = -4\).
04

Evaluate (-5) \backslash (-5)

Dividing a negative number by another negative number results in a positive number. Hence, \((-5) \backslash (-5) = 1\).
05

Evaluate 5 - 6

Subtracting a larger positive number from a smaller positive number results in a negative number. So, \(5 - 6 = -1\).
06

Evaluate -1 - 2

Subtracting a positive number from a negative number makes the result more negative. Therefore, \(-1 - 2 = -3\).
07

Evaluate 7 - (-4)

Subtracting a negative number is the same as adding its positive counterpart. Thus, \(7 - (-4) = 7 + 4 = 11\).
08

Evaluate -9 - (-9)

Subtracting a negative number is the same as adding its positive counterpart. So, \(-9 - (-9) = -9 + 9 = 0\).
09

Evaluate \frac{(-3) \times (-6) \times (-1)}{2 - 3}

First, multiply the numbers in the numerator: \((-3) \times (-6) \times (-1) = 18 \times (-1) = -18\). Next, calculate the denominator: \(2 - 3 = -1\). Now, divide the numerator by the denominator: \(\frac{-18}{-1} = 18\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Multiplication of negative numbers
Multiplication is a fundamental arithmetic operation. When it comes to negative numbers, there are a few key points to remember:
  • Multiplying a positive number by a negative number results in a negative product. For example, \(10 \times (-2) = -20\).
  • Multiplying two negative numbers results in a positive product. For instance, \((-1) \times (-3) = 3\).
Understanding these rules is essential when dealing with problems involving negative numbers, ensuring you get the correct sign for your answer.
Division of negative and positive numbers
Division is another basic arithmetic operation that frequently involves various sign combinations of numbers. Here are the important takeaways:
  • Dividing a negative number by a positive number yields a negative quotient, like in the case of \((-8) \backslash 2 = -4\).
  • Dividing one negative number by another negative number gives a positive quotient. An example is \((-5) \backslash (-5) = 1\).
Remembering these simple rules will help you avoid mistakes with signs in division problems.
Subtraction involving negative numbers
Subtraction with negative numbers can be a bit tricky but follows clear rules:
  • Subtracting a larger positive number from a smaller positive number results in a negative number, such as \(5 - 6 = -1\).
  • Subtracting a positive number from a negative number makes the result more negative, for example, \(-1 - 2 = -3\).
  • Subtracting a negative number is the same as adding its positive counterpart. This rule simplifies expressions such as \(7 - (-4) = 7 + 4 = 11\).
These rules help simplify what might otherwise seem like complex problems.
Order of operations
Evaluating arithmetic expressions correctly requires following the order of operations, often remembered by the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (i.e., powers and roots, etc.)
  • MD: Multiplication and Division (left-to-right)
  • AS: Addition and Subtraction (left-to-right)
For example, to simplify \(\frac{(-3) \times (-6) \times (-1)}{2 - 3}\), start by addressing the multiplication in the numerator and subtraction in the denominator before performing the division:
  • Multiplication of the negative numbers: \((-3) \times (-6) = 18\)
  • Resulting multiplication \(18 \times (-1) = -18\)
  • Subtracting the denominator: \(2 - 3 = -1\)
  • Finally performing the division: \(\frac{-18}{-1} = 18\)
Integer arithmetic
Integer arithmetic covers operations involving whole numbers including zero. The important operations include:
  • Multiplication: Pay attention to signs. A positive times a positive or a negative times a negative yields a positive. A positive times a negative yields a negative.
  • Division: Ensure the correct sign. A negative divided by a positive or vice versa is negative, while a negative divided by a negative is positive.
  • Subtraction: Subtracting a larger number from a smaller one results in a negative.
Mastering these basic rules will make dealing with integers much easier and less prone to errors, helping you in exercises and beyond.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The demand, \(Q\), for a certain good depends on its own price, \(P\), and the price of an alternative good, \(P_{\mathrm{A}}\), according to $$ Q=30-3 P+P_{\Lambda} $$ (a) Find \(Q\) if \(P=4\) and \(P_{\mathrm{A}}=5\). (b) Is the alternative good substitutable or complementary? Give a reason for your answer. (c) Determine the value of \(P\) if \(Q=23\) and \(P_{A}=11\).

(1) Without using a calculator evaluate (a) \(5 \times(-6)\) (b) \((-1) \times(-2)\) (c) \((-50) \div 10\) (d) \((-5) \div(-1)\) (e) \(2 \times(-1) \times(-3) \times 6\) (f) \(\frac{2 \times(-1) \times(-3) \times 6}{(-2) \times 3 \times 6}\) (2) Confirm your answer to part (1) using a calculator.

The demand function of a good is $$ Q=100-P+2 Y+1 / 2 A $$ where \(Q, P, Y\) and A denote quantity demanded, price, income and advertising expenditure respectively. (a) Calculate the demand when \(P=10, Y=40\) and \(A=6\). Assuming that price and income are fixed, calculate the additional advertising expenditure needed to raise demand to 179 units. (b) Is this good inferior or superior?

Find the coordinates of the points where the line $$ x-2 y=2 $$ intersects the axes. Hence sketch its graph.

Simplify the following expressions by collecting together like terms: (a) \(2 x+3 y+4 x-y\) (b) \(2 x^{2}-5 x+9 x^{2}+2 x-3\) (c) \(5 x y+2 x+9 y x\) (d) \(7 x y z+3 y x-2 z y x+y z x-x y\) (e) \(2(5 a+b)-4 b\) (f) \(5(x-4 y)+6(2 x+7 y)\) (g) \(5-3(p-2)\) (h) \(\frac{2 x+3}{4}+\frac{x-1}{2}\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.