Algebra Tutorials!
   
 
 
Wednesday 6th of November
 
   
Home
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Percents
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Algebra
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
fractions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Quadratics
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Decimals
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
   

Calculations with Negative Numbers

Question: What is the value that satisfies -4 + ? = -10 ?

Misconception

There are several possible misconceptions including

? = 6

and

? = 14

or even

? = - 14

Correct

The correct answer is - 6 as this satisfies the sum -4 + (-6) = -10. It can be shown on a number line as given below.

Starting at negative 4 and adding negative 6 you get the answer negative 10.

Hence -4 + (-6) = -10.

Further Explanation

It is important to realise that there is no guessing, no doubts but straightforward logic. Here we can associate the meaning owning when the quantity is positive and owing if it negative. Also, as before, we associate the minus sign with opposite.

In this example,

I start by owing 4 ( i.e. the '- 4 ' )

What is this '+?' that must have happened if I ended up 'owing 10' ? ( i.e. the ' - 10 ')

Another debt of 6 must have been added to my plight

We write 'adding a debt of 6' as ' + ( -6) '

So in - 4 + ? = - 10 the ? must be - 6

This is equivalent to the use of a number line as shown above; it does not matter which way you argue as long as you get the logic correct!

Do you need a solution to the neverending question of "How can I do my math flawlessly?" Just contact domyhomework123.com best experts in the field.
Tired of sleepless nights because you can't figure out "Who can do my math problem for me"? Mypaperdone.com will guarantee your success.
Copyrights © 2005-2024