Fraction least to Greatest

Introduction to fraction least to greatest:

   A fraction number value is one part of the whole number value in decimals.  A Fraction number value consisting of a two division in the number. The one part is top place of a number value is called as a numerator value. Another part is bottom place of the number value is called as a denominator value. That is numerator value of the fraction number divided by a denominator value of the fraction number. In this article we shall discuss about fraction least to greatest.

Sample Problem for Fraction least to Greatest:

This problem shows proper fraction for least to greatest:

Problem 1:

Find the value of given fraction numbers `(2)/(5)` + `(3)/(5)`

Solution:

   In the proper fraction a denominator values are same. So we directly add or subtract the numerator value.

Step 1: In the denominator values are same.

Step 2: Add the numerator values and put over the same denominator values.

       `(2)/(5)` + `(3)/(5)` = `(2 + 3)/(5)`

                 = `(5)/(5)`

Step 3: Now we simplify the fraction values.

               = 1

Problem 2:

Find the value of given fraction numbers `(2)/(9)` + `(7)/(9)`

Solution:

   In the proper fraction a denominator values are same. So we directly add or subtract the numerator value.

Step 1 Here  denominator values are same.

Step 2: Add the numerator values and put over the same denominator values.

      `(2)/(9)` + `(7)/(9)`   = `(2 + 7)/(9)`

                   = `(9)/(9)`  

Step 3: Now we simplify the fraction values.

               = 1

Improper fraction problem for least to greatest:

Problem 1:

Find the value of given fraction numbers `(11)/(7)` + `(13)/(5)`

Solution:

   In the improper fraction a denominator values are not same. So we don’t directly add or subtract the numerator values. So, we take least common multiplier for the denominator values.

Step 1: In the denominator values are not same. So, we take LCM for denominator

Step 2: multiply the numerator and denominator values for common multiplier.

The LCM value of the given fraction denominator value is 33

       `(11)/(7)` * `(5)/(5)` = `(55)/(35)`

        `(13)/(5)` * `(7)/(7)`   = `(91)/(35)`

 Step 3: Now we add the numerator values.

     `(11)/(7)` + `(13)/(5)` = `(11 + 13)/(35)`

                    = `(24)/(35)`

Practice Problem for Fraction least to Greatest:

Problem 1:

Find the value of given fraction numbers `(5)/(8)` + `(7)/(8)`

               Answer: `(4)/(3)`

Problem 2:

Find the value of given fraction numbers `(5)/(6)` - `(11)/(6)`

             Answer: -1

Mixed Word Problems

Introduction:

                A mixed word problems contain different types of word problems. The types of word problems are age problem, percent problems, quadratic problems, etc, to find the solution for the word problems first step is to analyze the word problem. After analyzing the problem use the appropriate method to find the answer.

Example on Mixed Word Problems

Example 1- Mixed word problems:

Kevin is two times old as john. The sum of their age is 30. Find the age of Kevin and john.

Solution:

Given Kevin is two times old as john.

So K = 2J `=>` 1

The sum of their age is 30

So, K+J = 30 `=>` 2

Now substitute the equation 1 in equation 2

2J + J = 30.

3J = 30

Now divide by 3 on both sides

3J/3 = 30/3

J = 10.

Substitute the value of J in equation 1 to find the value of K.

K= 2 (10)

K = 20.

Kevin’s age is 20 and John’s age is 10.

Example 2 - Mixed word problems:

What is 8 percent of 100?

Solution:

Given, what is 8 percent of 100

Let us take unknown as x, is is same as =, of refers ()

So what is 8 percent of 100

x = 8 %( 100)

8% = 8 /100

So the above expression would be

x = 8/100(100)

x= 8.

So 8 is 8 percent of 100.

More Example on Mixed Word Problems:

Example 3 - Mixed word problems:

The area of the rectangle is 24 cm² and the perimeter of the rectangle is 20cm

Solution:

Given, Area of the rectangle = 24cm² and the perimeter of the rectangle is 20cm.

The formula to find the area of the rectangle is length * width

The formula to find the perimeter of the rectangle is 2*(length + width)

Let us take l as length and w as width.

l*w =24

Divide by w on both sides

l= 24/w`=>` 1

2(l+w) =20

Divide by 2 on both sides

l+w =10`=>`

24/w + w =10

24+w² =10w

w² -10w +24 =0

w² – 6w-4w +24 =0

Take w as common from first two terms

w(w-6)-4w+24=0

Take -4 as common from last two terms

w (w-6)-4(w-6)=0

(w-6)(w-4)=0

w=6 or w=4

Now substitute w=6 and w=4 in equation 1 to find the corresponding length

When w=6`=>` l=24/6 `=>` l=4

When w=4`=>` l=24/4`=>` l=6

The length of the rectangle =6 and the width of the rectangle =4.

Exponential Functions Calculator

Introduction exponential functions  calculator:
Exponential function has the form of f(x) = b^x for a permanent base b which can be any positive real number. These exponential functions are defined by the fact that their rate of growth is proportional to their value.  Let us start with a population of cells so that its growth rate at any moment is proportional to its size. The number of cells after p years will then be a^p, an exponential function for some a>0.

How to Calculate Exponential Function:

The exponential function calculator is used to calculate the functions involving the exponential expressions.

Rules and examples:

These are the rules that should be followed by the exponential functions calculator.

 Rule1:  a^xa^y = a^{x + y}

           a^x , here the x is called exponential function Example: 2³2⁵ = 2³⁺⁵ = 2⁸

 Rule 2:  (a^x)^y = a^xy

            Ex: (4²)⁵ = 4¹⁰

 Rule3:  (ab) ^x = a^xb^x

           Ex: (3*7)³ = 3³7³

 Rule 4:  (`(a)/(b)` ) ^x = `(a^x)/(b^x)`

           Ex: (`(3)/(5)` )³ = `(3^3)/(5^3)`

 Rule 5: `(a^x)/(a^y)` = a^{x - y}

           Ex: `(5^7)/(5^4)`  = 5³

Ex 1:Simplify: 3^x - 3^{x + 1}

Solution:Step 1: Use rules:

Here apply rule1: 3^{x + 1} we can wriiten as 3^x3¹ in the given expression

so , 3^x - 3^{x + 1} written as 3^x - 3^x3¹

Step2: Factor 3^x out (take common term)

            = 3^x (1 - 3)

It provides the easy method of calculating the exponential functions using the exponential functions calculator.

Calculating Exponential Functions Using Calculator:

Ex1: Use this button in calulator for find exponential function.. Following points are showing how to use exponential function in a calculator.

Step 1: find the exponential value for (1.03E2)

Step 2: (1.03E2) the number is  1.03 x 10² so 

Step 3: press the following buttons.

                      1.03 EXP 2    

Step 4 : therefore answers is 103.

Ex 2: Step 1: find the exponential value for (12.3E5)

Step 2: (12.3E5) the number is  12.3 x 10⁵ so

Step 3: press the following buttons.

                      12.3 EXP 5  

Step4 : Therefore the answer is 123000