   Chapter 2.4, Problem 42E

Chapter
Section
Textbook Problem

Perform the indicated operations and simplify: ( − 3 4 ) + ( 2 − 3 ) − ( − 1 − 2 ) − ( − 5 6 )

To determine

To calculate: The simplified form of the expression (34)+(23)(12)(56) by performing the indicated operation.

Explanation

Given Information:

The provided expression is:

(34)+(23)(12)(56).

Formula used:

Equivalent signed fractions:

ab=ab=ab

The equivalent signed fraction shows that a negative fraction can be written in three different but equivalent forms.

Where,

ab Is the customary form.

In case of ab=ab, use dividing signed numbers rules.

Adding and subtracting combinations of signed numbers includes:

1. The sign of each number being subtracted must be changed.

2. And then the resulting signed numbers must be added.

Adding two numbers with unlike signs includes:

1. In order to add a negative number with a positive number, first thing is to obtain the difference of their absolute values.

2. And then sign of the number having the larger absolute value must be placed before the result.

And,

Dividing two signed numbers includes:

1. In order to divide two numbers having same sign, their absolute values must be divided. With this a positive quotient will be obtained.

2. And in order to divide two numbers with different signs, their absolute values must be divided and before the quotient a negative sign must be placed.

Calculation:

Consider the expression:

(34)+(23)(12)(56)

First, change the given expression to customary form. That is,

(34)+(23)(12)(56)=(34)+(23)(12)(56)

The absolute values of the signed numbers will be divided. The quotient will be positive because the two numbers have the same sign.

(34)+(23)(12)(56)=(34)+(23)(+12)(56)

In case of combinations of additions and subtractions of signed numbers, only the sign of each number being subtracted must be changed

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