/*! 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 3 (1) Without using a calculator e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 3

(1) Without using a calculator evaluate (a) \(1-2\) (b) \(-3-4\) (c) \(1-(-4)\) (d) \(-1-(-1)\) (e) \(-72-19\) (f) \(-53-(-48)\) (2) Confirm your answer to part (1) using a calculator.

Short Answer

Expert verified
(a) -1, (b) -7, (c) 5, (d) 0, (e) -91, (f) -5.

Step by step solution

01

Evaluate the Expression

(a) Evaluate the expression: Start with the expression: \(1 - 2\) Since 1 is positive and 2 is negative, subtract 2 from 1: \(1 - 2 = -1\)
02

Evaluate the Expression

(b) Evaluate the expression: Start with the expression: \(-3 - 4\) Both terms are negative, so add their absolute values and keep the negative sign: \(-3 - 4 = -7\)
03

Evaluate the Expression

(c) Evaluate the expression: Start with the expression: \(1 - (-4)\) Subtracting a negative number is the same as adding its positive equivalent: \(1 - (-4) = 1 + 4 = 5\)
04

Evaluate the Expression

(d) Evaluate the expression: Start with the expression: \(-1 - (-1)\) Subtracting a negative number is the same as adding its positive equivalent: \(-1 - (-1) = -1 + 1 = 0\)
05

Evaluate the Expression

(e) Evaluate the expression: Start with the expression: \(-72 - 19\) Both terms are negative, so add their absolute values and keep the negative sign: \(-72 - 19 = -91\)
06

Evaluate the Expression

(f) Evaluate the expression: Start with the expression: \(-53 - (-48)\) Subtracting a negative number is the same as adding its positive equivalent: \(-53 - (-48) = -53 + 48 = -5\)
07

Confirm with Calculator

Confirm each solution using a calculator by entering the original expressions and verifying that the results match the manual calculations.

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.

integer subtraction
Integer subtraction is a fundamental arithmetic operation that involves finding the difference between two whole numbers. When subtracting integers, it is important to recognize whether the numbers involved are positive or negative.

For example:
  • In the expression: \(1 - 2\), since 1 is positive and 2 is negative, you subtract 2 from 1 to get \(1 - 2 = -1\).

  • In the expression: \(-3 - 4\), where both terms are negative, you add their absolute values and keep the negative sign, giving \(-3 - 4 = -7\).
By understanding these basic rules, you can correctly solve integer subtraction problems without confusion.
negative numbers
Negative numbers are numbers less than zero. They are denoted by a minus sign (-) in front of the number. Understanding how to work with negative numbers is crucial, especially in subtraction.

When dealing with negative numbers in subtraction:
  • Subtracting a negative number is the same as adding its positive equivalent. For instance, in the expression: \(1 - (-4)\), it becomes \(1 + 4 = 5\).

  • Similarly, in the expression: \(-1 - (-1)\), it simplifies to \(-1 + 1 = 0\).
Grasping these principles makes it easier to handle arithmetic operations that include negative numbers, preventing errors and simplifying calculations.
confirming calculations
Confirming your calculations is a vital step to ensure accuracy. After solving a problem manually, it is always a good practice to verify your result using a calculator.

For example, after manually solving the expression \(-72 - 19\) to get \(-91\), you should input the original expression into a calculator to check if the result matches.
This step helps to:
  • Identify any arithmetic errors made during manual calculations.
  • Build confidence in your mathematical skills.
Consistently confirming your work guarantees reliability and precision.
manual calculation
Manual calculation means performing arithmetic without the aid of a calculator. This practice is essential for developing strong mathematical foundational skills.

Here are some points to consider when doing manual calculations:
  • Understand the operation rules: Knowing how to handle positive and negative numbers can simplify processes considerably.

  • Pay attention to signs: Small mistakes with positive and negative signs can lead to incorrect results.
  • Practice regularly: Consistent practice improves accuracy and speed.
Engaging in manual calculations ensures a deep understanding of arithmetic operations and enhances problem-solving capabilities.

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

Plot the following points on graph paper: $$ \mathrm{P}(4,0), \mathrm{Q}(-2,9), \mathrm{R}(5,8), \mathrm{S}(-1,-2) $$ Hence find the coordinates of the point of intersection of the line passing through \(\mathrm{P}\) and \(\mathrm{Q}\), and the line passing through \(\mathrm{R}\) and \(\mathrm{S}\).

Check that the points $$ (-1,2),(-4,4),(5,-2),(2,0) $$ all lie on the line $$ 2 x+3 y=4 $$ and hence sketch this line on graph paper. Does the point \((3,-1)\) lie on this line?

(a) Solve the equation $$ 1 / 2 Q+13=17 $$ State clearly exactly what operation you have performed to both sides at each stage of your solution. (b) By performing the same operations as part (a), rearrange the formula $$ 1 / 2 Q+13=P $$ into the form $$ Q=\text { an expression involving } P $$ (c) By substituting \(P=17\) into the formula derived in part (b), check that this agrees with your answer to part (a).

Without using a calculator work out (a) \((5-2)^{2}\) (b) \(5^{2}-2^{2}\) Is it true in general that \((a-b)^{2}=a^{2}-b^{2} ?\)

$$ \begin{aligned} &\text { If } 4 x+3 y=24 \text {, complete the following table and hence sketch this line }\\\ &\begin{array}{l|l} x & y \\ \hline 0 & \\ & 0 \\ 3 & \end{array} \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.