Percent of a Number Calculator

The word per cent  means per hundred.  Its symbol is %.
90% means 90 parts out of 100 parts.  A fraction can be converted to a per cent.  For example 50/100 is a fraction.  It can be converted to percent as 50%. A decimal can be converted to per cent.  For example 0.33 is a decimal.  It can be written as
33%.
Percent of a number can be calculated by the following methods.
# Find 8% of the number 125
Solution 8% can be written as 8/100
so 8% of 125  is  8 x 125                1000
_______   =          _____     =    10

100                       100
Answer 8% of the number 125 is 10
#  What percent of the number 36 is 9?
Solution:  Let the number be x
Then x% of the number 36   =   9
We can write  x  times 36   =   9
100

36x   =  9
100
Transposing 36/100 to the other side, we get    x  =  9 times 100   =  900  =  25
36                  36
Hence the answer is 25% of a number 36 is  9
Fractions of Percent of a Number Calculator:
Fractions can be converted into percents.
# Convert the following fraction 9/20 into percent
To convert into percent we multiply the fraction by 100
We get  9  x   100   =    900  =   45     Solution  is  45
20                    20
# Find  6½% of 75 metres.

Solution  Step 1 convert  6½ into improper fraction.  We get 13/2
Step 2   (13/2) %  of  75  is   13 x  1    x  75   =   975  = 4.88 metres.
2    100                 200
Decimals can be converted to percent.
# Find 7.5% of 80 kgs.
Solution  : -  7.5% can be written as (75/10) times 100
7.5% of 80 kgs =  7.5  x  80  =   600  =  6 kgs.
100                 100

Word Problems on Percent of a Number Calculator:
Let us do some word problems on finding the percent of a number.
# A basket contains 350 eggs.  12% of the eggs are rotten.  Find the number of good eggs.
Solution. Total number of the eggs in the basket = 350
Percent of the rotten eggs = 12%
Number of rotten eggs =  12% of 350
=  12  x  350  = 4200  = 42
100                 100
Number of rotten eggs = 42
Number of good eggs  =    350 - 42  =  308
Answer 308 eggs are good.
#If 15% of the workers in a  factory are females, and the number of male workers  is 272, find the total number of workers
in the factory.
Solution:-  Let the total number of workers be x
Then percentage of females = 15%'
Percentage of male workers = 100 -15= 85%
Male workers are 272
Hence 85% of  x  = 272
That is 85x  = 272
100
Therefore   x  =  272 . 100  =  27200   =  320
85              85
Answer:  There are 320 workers in the factory.
Practice Problems:
1.Find the percent of 3/4 (answer 75%)
2.If x% of 75 is 9, find the value of x (Answer 12)
3.What % of 2/7 is 1/35 (Answer 10%
4.What % is $15 of $ 120(Answer 12.5%)
5. Find the number whose 13% is 65(Answer 500)

Algebraic Expressions Product

An expression is the important topic in algebra. Algebraic expression product  is the combination of variables and constants with basic arithmetic operators, they are add, subtract and then divide and multiplication.  For Example (p-9) is the algebraic expression.  Here p is the variable and 9 is the constant value and then ‘-‘is the subtraction operation.  In algebraic expressions product we can multiply the two algebraic expressions.
General Process of Algebraic Expressions Product

General process of algebraic expressions product: Now we have to assume the algebraic expressions (fx + gy) and (ax +by). This contains the below steps. They are,

Step 1: First we have to take multiplication of first term of the first expression with second expression. That is fx (ax+ by).

Step 2: Now we have to multiply the inner term values. That is fx(ax) +fx(by). It gives afx2 +bfxy

Step 3: Now we have to take multiplication of Second term of the first expression with second expression. That is gy (ax+ by) .

Step 4: Now we have to multiply the inner term values. That is gy(ax) +gy(by). It gives agxy +bgy2

Step 5: No we have to add the step 2 and step 4 values. That is afx2 +bfxy + agxy +bgy2

Step 6: Take the common terms we can get, afx2 + xy(bf + ag) +bgy2

This is the general rule of algebraic expressions product.
Problems Using the Algebraic Expressions Product

Problems 1 : Take algebraic expressions product of (j + 5) and (k− 6)

Solution: multiply the two given algebraic expressions

(j + 5)(k− 6)

= j(k − 6) + 5(k − 6)

= jk – 6j + 5k − 30

Problems 2 : Take algebraic expressions product of (2u +8)(u2− 2u − 10)

Solution: multiply the two given algebraic expressions

(2u +8)(u2− 2u − 10)

= (2u) (u2− 2u − 10) + (8) (u2− 2u − 10)

= (2u3 – 4u2 – 20u) + (8u2 – 16u − 80)

= 2u3 + 4u2 – 36u − 80

Solving Factoring Rules

Factoring is the method of finding out the multiples of an expression. The expression may be algebraic equation or a real numbers. It is like making an expression into simpler one by splitting them with multiplication. There are many factoring rules and also there are many formulas for factoring rules. Here the rules are divided into four types which are Greatest Common Factor (GCF), four terms, three terms and two term Expressions.
Solving Factoring Rules i and Ii

Solving Factoring Rules I: Greatest Common Factor (GCF)

GCF is the basic factoring rule in both integers and algebraic expressions. When factoring, always start with finding the largest expression and dividing them into simple term.

Ex: Factor the expression 14 x2 y3 + 21x

Sol:

Factor of 14 is 1, 2, 7, 14

Factor of 21 is 1, 3, 7, 21

Therefore GCF of 14 and 21 is 7.

Also GCF of  x2 y3 and x is x.

Therefore GCF of  14 x2 y3 + 21x is 7x.

First we have to factor the GCF. So the factors are,

7x (2 x y3 + 3)

Solving Factoring Rules II: 4 – Terms (Factor by Grouping)

Sometimes there are four or terms in an expression and also they wont have common factors. In this case, group up together terms to  get common factors.

Ex: Factor 2x3 – x2 + 18x – 9

Sol:

The given expression 2x3 – x2 + 18x – 9 does not have common factors for all of the terms. Here we have to group the terms.

= 2x3 – x2 + 18x – 9
= x2 (2x – 1) + 9 (2x – 1)
= (2x – 1) (x2 + 9)
Solving Factoring Rules Iii and Iv

Solving Factoring Rules III: 3 – Terms (Trinomials)

In order to factor trinomials, we have to begin with multiplying two binomials.

Ex: Factor 2x2 + 2x – 60

Sol:

= 2x2 + 2x – 60
= 2x2 + 12x – 10x – 60
= 2x (x + 6) – 10 (x + 6)
= (2x – 10) (x + 6)

Solving Factoring Rules IV: 2 – Terms

Difference of Squares       a2 – b2 = (a + b) (a – b)

Difference of Cubes          a3 – b3 = (a – b) (a2 + ab + b2)

Sum of Cubes                  a3 + b3 = (a + b) (a2 – ab + b2)

Decimal Equivalent for Fractions

Decimals are a kind of fractional number. The decimal 0.6 signifies the fraction 6/10. The decimal 0.75 signifies the fraction 5/100. Decimal fractions forever have a denominator based on a exponent of 10.We know that 5/15 is equal to 1/3 since 1/5 times 5/5 is 5/15.In this article we shall discuss the table of decimal equivalent for fractions.
Table of Decimal Equivalents for Fractions:

Example problems- table of decimal equivalents for fractions:

Example problem1:

Convert the decimal value into fraction, 0.5

Solution:

Here to convert 0.5 into fraction, multiply and divide by 10,

=   0.5*10*`1/10`

=   5*`1/10`

= `5/10`

= `1/2`

Equivalent fraction is `1/2.`

Example problem2: table of decimal equivalents for fractions:

Convert the decimal value into fraction, 0.75

Solution:

Here to convert 0.5 into fraction, multiply and divide by 100,

=   0.75*100*`1/100`

=   75*`1/100`

= `75/100`

= `15/20` =` 3/4`

Equivalent fraction is `3/4` .



Example problem 3: table of decimal equivalents for fractions:

Convert the decimal value into fraction, 0.25

Solution:

Here to convert 0.25 into fraction, multiply and divide by 100,

=   0.25*100*`1/100`

=   25*`1/100`

= `25/100`

= `1/4`

Equivalent fraction is `1/4` .

Example problem 4: table of decimal equivalents for fractions:

Convert the decimal value into fraction, 0.35

Solution:

Here to convert 0.35 into fraction, multiply and divide by 100,

=   0.35*100*`1/100`

=   35*`1/100`

= `35/100`

= `7/20`

Equivalent fraction is `7/20` .

Example problem 5: table of decimal equivalents for fractions:

Convert the decimal value into fraction, 0.45

Solution:

Here to convert 0.45 into fraction, multiply and divide by 100,

=   0.45*100*`1/100`

=   45*`1/100`

= `45/100`

= `9/20`

Equivalent fraction is `9/20` .

Is this topic physics problems hard for you? Watch out for my coming posts.

Example problem 6:

Convert the decimal value into fraction, 0.55

Solution:

Here to convert 0.55 into fraction, multiply and divide by 100,

=   0.55*100*`1/100`

=   55*`1/100`

= `55/100`

= `11/20`

Equivalent fraction is `11/20` .

Example problem 7:

Convert the decimal value into fraction, 0.3

Solution:

Here to convert 0.3 into fraction, multiply and divide by 10,

=   0.3*10*`1/10`

=   3*`1/10`

= `3/10`

Equivalent fraction is `3/10` .

The following table will explain you the decimal equivalent for the given fraction

Practice Problems - Table of Decimal Equivalents for Fractions:

Practice problem 1:

Convert the decimal value into fraction, 0.2

Result: `1/5` .

Practice problem 2:

Convert the decimal value into fraction, 0.8

Result: `4/5` .

Practice problem 3:

Convert the decimal value into fraction, 0.9

Result: `9/10` .

Congruence And Similarity

Robert finds two marbles that look exactly the same.
John has got a new baby. People visited him to congratulate John and say that the baby looks like him.
Note the two words exactly  and  looks like.
In mathematics these two words are defined as congruence and similarity.
Definition on Congruence and Similarity
Between congruence and similarity, let us see what is meant by similarity.
Two shapes are said to be similar if the shapes are same. The sizes may be different. The following is the example.

In the above diagram you find the two triangles look alike but the sizes are different. If the difference in size  is in a right proportion then the triangles are said to be similar.
That is, for the above triangles  to be similar, the ratio of the corresponding sides of the triangles must be same. Besides the measures of the angles must be equal.
Thus, the complete definition of similarity of two figures is both the figures must be of the same shape and the corresponding sides must be in the same ratio. Also the corresponding angles must be congruent.
The concept of similarity has many practical applications. You see a building. It is impossible to show the building to the same size on a drawing. What is normally done is to draw a smaller but the same shape of the building to a certain ratio. This ratio is called as the scale factor.
Definition on Congruence and Similarity
in congruence and similarity, we have seen what is meant by similarity of two figures.
If two figures are to be congruent, they must be of same shape and also of be same size.

In the above diagram you find the two triangles are of same shape and he measures of the corresponding sides and the measures of the corresponding angles are equal. Hence the two triangles can be said as congruent.
Thus, the complete definition of congrency of two figures is both the figures must be of the same shape and of the same size. Also the corresponding angles must be congruent.
Please note that the transformation of figures does not affect congruency.
The congruency of two shapes can be established if they fulfill certain geometric conditions. The concept of congruency helps in many geometric solutions.