Elementary Math Factorize

Introduction:

Factorization is one of the basic topics in mathematics. Factorization helps to find the factors for the given equation. Generally factorization is done in algebra equations. It is applicable only with constants and numbers. Factors generally defined as extracting numbers from the given terms. It is also defined as expressing the given numbers as a product of its factors.  Elementary math factorize involves basic factorization problems. Elementary math factorization problems are easy to solve. Elementary math factorize also involves some simple algebra problems. In this article, we are going to see about elementary math factorize.

Elementary math factorize:


Elementary math factorize example 1:

Find the factors for the given number, 24

Solution:

The factors for the given numbers are

24 = 2, 3, 4, 6, 8, 12, 24

These numbers are multiples of 24 hence these are the factors of 24.



Elementary math factorize example 2:

Find the factors for the given number, 32

Solution:

The factors for the given numbers are

32 = 2, 4, 8, 16, 32

These numbers are multiples of 32 hence these are the factors of 32.



Elementary math factorize example 3:

Find the factors for the given number, 52

Solution:

The factors for the given numbers are

52 = 2, 13, 26, 52

These numbers are multiples of 52 hence these are the factors of 52.



Elementary math factorize example 4:

Find the factors for the given number, 45

Solution:

The factors for the given numbers are

45 = 3, 5, 9, 15, 45

These numbers are multiples of 45 hence these are the factors of 45.

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Algebra math factorize:


Algebra math factorize example:

Factorize, x^2 + 5x + 6 = 0

Solution:

We need to factorize the given equation,

x^2 + 5x + 6 = 0

x^2 + 3x + 2x + 6 = 0

(x^2 + 3x) + (2x + 6) = 0

x(x + 3) + 2(x + 3) = 0

(x + 2) (x + 3) = 0

x + 2 = 0

Subtract 2 on both sides,

x + 2 – 2 = 0 – 2

x = -2.

x + 3 = 0

Subtract 3 on both sides,

x + 3 – 3 = 0 – 3

x = - 3

The factors are -2,-3.

Math Financial Equations

Introduction:

Most of the mathematical financial equations have been derived from the fundamental finance formulas which have been related to the time value of money. Some of the specific formulas that are in correspondence with the financial equations are derived using the derivatives of the fundamental formulas. Some of the mathematical finance equations include statistics, randomness and probability.

The mathematical finance equations are used to calculate and derive the answers for more complicated finance problems.


Symbols used in math finance equations:


There are various symbols that are used in the math finance equations which are listed below,
PMT represents the periodic payment
T indicates the terminal period or the last period
CF represents the flow of cash
FV indicates the future value
PV indicates the present value
rN indicates the nominal interest rate
rE represents the Effective interest rate where r = interest rate
m indicates the compounding frequency
B is used to indicate the balance
N represents the number of periods
G is to represent the rate of growth

Some basic math finance equations:


There are some of the fundamental formulas which are used to calculate the math financial equations.

The math financial equation used to calculate the number of payments is given by

N = - log (1-rFV / PMT)
log (1+r)

The equation to convert the interest rate compounding bases are given by

r2 = [(1+ (r1 / n2))n1/n2-1]n2

Here r1 indicates the original rate of interest with the compounding frequency n1, and r2 represents the stated interest rate with the compounding frequency n2.

The math financial equation which is used to calculate the future value of a single sum is given by

FV = PV (1+r) n

To calculate the future value with compounding the finance math equation is given by

FV = PV(1+(r/m))n-m

The equation used to calculate the future value of a cash flow series is given by

FV =`sum_(j-1)^n` CFj(1+r)j

The expanded net present value formula using the math financial equation is given by

NPV = `sum_(T=0)^T` CFT/ (1+r)T = CF0 + CF1/ (1+r)1 + CF2 / (1+r)2 + ... + CFT / (1+r)T

The present value of a single sum is calculated using the equation

PV = FV / (1+r) n

Thus the math financial equation which is used to calculate the present value with compounding is given by

PV = FV / (1+(r/m)) n-m

Math Measurement CM

Introduction of math measurement cm:

In mathematics, measurement is a main part. Similar to inches, centimeters, kilometers, meters, feet, yards and millimeter. This is also the basic concepts in math .Here we are going to see some example problems of measurement cm. Some times the number is also represent some standard measurement, such as meter, kilogram in math.

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Example problems of measurement cm in math:


Measurement of inches to centimeters:

1 inches = 2.54 centimeters

Example 1:

Convert 13 inches to centimeters.

Solution:

Step 1: We know that 1 inches = 2.54 centimeters.

Step 2: We need find 12 inches to centimeters.

Step 3: Multiply 12 with 2.54 = 30.48

Step 4: Therefore, 12 inches = 33.02 centimeters.



Measurement of millimeter to centimeter:

1 millimeter = 0.1 centimeters

Example 2:

Convert 45 millimeters to centimeter.

Solution:

Step 1: We know that 1 millimeter = 0.1 centimeter.

Step 2: We need find 45 millimeter to centimeter.

Step 3: Multiply 0.1 with 45 = 4.5

Step 4: Therefore, 45 millimeters = 4.5 centimeter.

Measurement of feet to centimeter:

1 feet = 30.48 centimeters.

Example 3:

Convert 12 feet into centimeters.

Solution:

Step 1: We know that 1 feet = 30.48 centimeters.

Step 2: We need find 12 feet in to centimeters.

Step 3: Multiply 12 with 30.48 = 365.76

Step 4: Therefore, 12 feet = 365.76 centimeters.


More about cm measurement in math


Measurement of yards to centimeters:

1 yards = 91.44 centimeters.

Example 4:

Convert 5 yards into centimeters.

Solution:

Step 1: We know that 1yard = 91.44 centimeters.

Step 2: We need find 5 yards into centimeters.

Step 3: Multiply 91.44 with 5 = 457.2

Step 4: Therefore,  5 yards = 457.2 centimeters.



Measurement of miles to centimeters:

1 miles = 1,60,934.4 centimeter

Example 5:

Convert 2 miles into centimeter.

Solution:

Step 1: We know that 1 miles = 1,60,934.4 centimeter.

Step 2: We need find 2 miles into centimeters.

Step 3: Multiply 2 with 1,60,934.4  = 321868.8

Step 4: Therefore, 2 miles = 321868.8 centimeters.



Measurement of meter to centimeters:

1 meter = 100 centimeters.

Example 5:

Convert 27 meter to centimeters

Solution:

Step 1: We know that 1 meter =100 centimeters.

Step 2: We need find 27 meter in to centimeters.

Step 3: Multiply 100 with 27 = 2700

Step 4: Therefore, 27 meter = 2700 centimeters.

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Measurement of kilometer to centimeters:

1 kilometer = 1,00,000 centimeters.

Example 6:

Convert 2 kilometer to centimeters

Solution:

Step 1: We know that 1 kilometer =1,00,000 centimeters.

Step 2: We need find 2 kilometer in to centimeters.

Step 3: Multiply 1,00,000 with 2 = 2,00,000

Step 4: Therefore, 2 kilometer = 2,00,000 centimeters.

These are the examples of measurement cm in math .

Math Percents Problems

Introduction to percentage:

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in French). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to `45 / 100` , or 0.45. In this article you will get help on how to find percentages with some example problems.

- Source from Wikipedia

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Help on finding percents:


To convert a fraction and a decimal to a percentage we have, multiply it by 100.

Similarly to convert a percentage to a fraction and decimal, divide it by 100.

We can express a fraction and a decimal as a percentage.

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Help on percentage problems:


Problem 1:

What is the decimal value of percentage 84%?

Solution:

84% =  ` 84 /100` = 0.84

84% is 0.84

Problem 2:

What is the decimal value of percentage 72.3%?

Solution:

72.3% = `(72.3) / 100 ` = 0.723

72.3% is 0.723

Problem 3:

How to add 89% to 23?

Solution:

89% + 23 = 0.89 + 23 = 23.89

Problem 4:

What is the 76% of 24?

Solution:

Let us take 76% as `76 /100`

76% of 24 =` 76 / 100` * 24

=  3.16

Problem 5:

In a box there are 72 peanut packets. If a girl took 60% of peanut packets, how many peanut packets did she left in the box?

Solution:

The girl took the peanut packets from the box is 60% of 72 or else `60/100` × 72

`60 / 100` × 72 = 43.2%

So the box contains 72 peanut packets and the girl took 43 peanut packets. The number of peanut packets girl left in the box is 72 – 43 = 29.
Therefore the girl left 29 peanut packets in the box.

Help on Practice problem for finding percentage:

Problem 1:

What is decimal value of the percentage  22%?

Solution:

= 0.22.

Problem 2:

What is the decimal value of percentage 61%?

Solution:

= 0. 61

Problem 3:

What is 84% of 22?

Solution:

= 18.48 is 84% of 22.

Subtraction Answer

Introduction to subtraction answer:

Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Subtraction is denoted by a minus sign in infix notation.

c − b = a

where minuend (c) − subtrahend (b) = difference (a). Now we see about subtraction answer.

(Source: Wikipedia)

About subtraction answer:


In the subtraction, the given parts are named as the minuend and the subtrahend and the resultant answer will be named as the difference. The Minuend which is the first number and the subtrahend is the second number. Thus, we have to subtract the number in this format only.

The Subtraction answer is nothing but the resultant of the numbers which have been subtracted. Let us see one example for the subtraction answer method.

Example:

Subtract the number 1 from 4 and give the subtraction answer.

Solution:

It can be given as (4 - 1). The Following is for the subtraction answer as follows,

4       ->Minuend

-1      ->Subtrahend

-----------------------------------

3      ->Difference

--------------------------------------

Thus, the subtraction answer or the difference can be given as 3.

Way of checking the subtraction answers:

The subtraction answers can be checked or verified by using the technique given below.

The Difference number and the subtrahend number should be added together to give the minuend number.

The above example can be checked as follows,

1       ->subtrahend

+ 3    ->difference

------------------------------

4       ->minuend

--------------------------------

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Problems for subtraction answer:


Example 1:

Subtract the numbers :(-5 – 6)

Subtraction answer:

Now we are going to subtract the numbers as follows,

(-5 – 6) = -5 + (-6) = -11.

Subtracting 6 is the same as adding a -6.

Thus, we get the subtraction answer as -11.

Example 2:

Subtract the given expressions and find the value of x in the expression:

5x = 6

3x = 2

Subtraction answer:

Now we subtract the two expressions.

5x = 6

- 3x = 2

-------------

2x = 4

---------------

Now divide the equation on both the sides we get,

x = 2.

Thus, the subtraction answer for the given expression is 2x = 4 and the value of x is 2.

Math Practice 4

Introduction:

The math practice 4 is the basic concepts involved in mathematics. Here the topic discussed are  about the usual terms in algebra like addition, subtraction, multiplication and division. Then it also solves some word problems for easy understandings so that learning math becomes simple and easy for the learners.

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Basic concepts:


The math practice 4 involves some basic concepts in mathematics. In this we are going to see about algebra in math practice 4 .They are:

Variables
Expressions
Terms
Polynomials
Equations

Example problems:


Example 1: Solve for x?

79 + 33  = x

Solution:

To find x value

79 + 33 = x

x =112

The answer x is 112

Example 2:

The number decreased by 70 is 12 times its opposite. Find the number.

Solution: First we convert the algebra word problem to a numerical form to get the solution.
The number is decreased by 70 is 12 times its opposite.
Write an equation.

x - 70 = -12x                       (Equation)

x - 70 + 70 = -12x + 70       (add 70 on both sides we get)

x + 12x = -12x +12x + 70     (add 12x on both sides we get)

11x = 70

x = 6.36

Example 3 : Solve for M?

77 + 3 = M

Solution:

77 + 3 = M

M = 80

The answer M is 80

Example 4: Solve for q?

q + 7 = 49

Solution:

To solve the p value

q = 49 – 7

q = 42


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Example 5: Solve the following system of the linear equations using the method of substitution.

x - y = -6 ,4x+8y = -48

Solution:

Step 1: Rearrange the first equation,

x - y = -6

y = x + 6

Step 2: Substitute this value for y into the second equation;

4x + 8(x + 6) = -48

Step 3: Expand and simplify the equation:

4x + 8x + 48 = -48

12x = -96

x = -8

Step 4: Substitute x back into the one of that original equations;

-8 - y = -6

y = -2

4th Grade Math Expression

Introduction of 4th grade math expression:-

In mathematics, an expression is a finite combination of symbols that are well-formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities. The use of expressions can range from simple arithmetic operations like 3+ 5 x ((-2)^7 – 3/2) . (Source: Wikipedia)

Topics involves in 4th grade math expression:-


In 4th grade math expression to study the algebra expression in following types are used in algebra expression.

Variable expression
Variable expression using word
Expression using order of operation and parentheses.

Variable expression

In 4th grade math variable expression means to form a number and word in expression like as add, plus, greater, less than, increase, decrease etc.

For Example,

287 increased by x?

287 + x

Variable expression using word

In 4th grade math variable expression using word means the expression numbers and word are shows the sentence formation like as add, plus , greater ,less than ,decrease etc

For Example,

Haley earned 92 bonus points. Marisol earned b more bonus points than Haley. Choose the expression that shows how many bonus points Marisol earned.

92+b

Expression using order of operation and parentheses

In 4th grade math expression using order of operation and parentheses means to perform the arithmetic operations as addition, subtraction, multiplication and division.

For Example,

1 + 7 × 3 – 7 = 15.

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Example problems for 4th grade math expression


Problem 1:-

Solve expression using order of operation and parentheses 2 + 4 × 5 – 10?

Solution:-

Given 2+4x5-10

= 2+4x5-10

= 2+20-10

= 22-10

= 12

Problem 2:-

Solve expression using order of operation and parentheses (468 + 638) + (134 × 761) – 875 – 632?

Solution:-

Given (468 + 638) + (134 × 761) – 875 – 632

= (468 + 638) + (134 × 761) – 875 – 632

= 1106+101974-875-632

= 103080 – 243

=  102837


Practice problems for 4th grade math expression:-

Problem 1:-

Solve variable expression for 370 added to v.

Answer:-

V+370

Problem 2:-

Solve variable expression for 28 minus w.

Answer:-

28 –w

Problem 3:-

Solve variable expression for 703 increased by z.

Answer:-

703+z

Problem 4:-

Talia earned 64 bonus points. Jones earned d more bonus points than Talia. Choose the expression that shows how many bonus points Jones earned.

Answer:-

64+d