Chapter 5.CR, Problem 1CR

To determine

a)

To Perform:

$-4+5(-3)$

Answer to Problem 1CR

Solution:

$-19$

Explanation of Solution

Addition of integers:

To add integers first we have to look the signs of integers. Let us assume that $x$, $y$ and $z$ are integers.

Step1:

Check if it has at least one of the integers is 0; if so, then

$x+0=0+x=x$

Step2:

Check whether the two terms have the same sign. If so, then

Add both the numbers and give the same sign.

(i.e.)$x+y=z$

$(-x)+(-y)=-z$

Where z is the total value we get from adding the two terms.

Step3:

Check whether the two terms have the different sign. If so, then

Subtract the smaller one from the larger value and put the sign of larger value.

(i.e.)$x+(-y)=-z$ if $-y$ is the larger absolute value

Or $x+(-y)=z$ if $x$ is the larger absolute value.

Multiplication of Integers:

Let us assume that $x$, $y$ and $z$ are integers.

Step1:

First we have to check it has at least one of the integers is 0; if so, then

$x\cdot 0=0\cdot x=0$

Step2:

The product of two positive integers or two negative integers is positive.

The product of positive integer and a negative integer is negative.

Given:

$-4+5(-3)$

To remove the bracket, we can multiply the last two terms by using the multiplication of integers.

Step1:

We have to check whether it has at least one zero. There is no zero in the equation so we can move on.

Step2:

$5\times (-3)$

The product of positive integer and a negative integer is negative. After multiplying the above integers, we get

$-15$

Step3:

Now we can add the both numbers.

By using the addition of integers, we get

$(-4)+(-15)=-19$

Hence we got the answer.

To determine

b)

To Perform:

$\frac{4}{7}+\frac{5}{9}$

Answer to Problem 1CR

Solution:

$\frac{71}{63}$

Explanation of Solution

Rational number:

The set of rational numbers is denoted by $\mathbb{Q}$

The rational numbers is the set of all numbers in the fractional form $\frac{a}{b}$ where $a$ and $b$ are integers, and $b\ne 0$.

$\frac{a}{b}$ means $a÷b$ where $a$ is the numerator and $b$ is the denominator

Addition with Rational Numbers:

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{bc}{bd}=\frac{ad+bc}{bd}$

Given:

$\frac{4}{7}+\frac{5}{9}$

By using the addition with rational numbers, we can add the above rational numbers

$\frac{4\times 9}{7\times 9}+\frac{5\times 7}{9\times 7}=\frac{36}{63}+\frac{35}{63}$

Then $\frac{36+35}{63}=\frac{71}{63}$

Hence the answer is $\frac{71}{63}$.