Elementary Math Practice

Introduction to elementary math practice:

In elementary math the children are mostly study about arithmetics. Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone. It involves the study of quantity, especially as the result of combining numbers. Professional mathematicians sometimes use the term arithmetic when referring to more advanced results related to number theory, but this should not be confused with elementary school arithmetic. Let us see elementary math practice. (Source: Wikipedia)

Example Problems for Elementary Math Practice:

Example 1: Find the prime number from the following: 14, 17 and 60

Solution:

Given 14, 17 and 60

14 is divisible by 1, 2, 7, 14.

17 is divisible by 1, 17.

60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

From the given 17 is a prime number.

Answer: 17 is a prime number and 14, 60 are composite numbers.

Example 2: Multiply the following: `12/5 * 3/4`

Solution:

Given `12/5 * 3/4`

Multiply the denominators and numerators individually ,

`12/5 * 3/4 = (12*3) / (5*4) `

=  ` (36/20)`

=  ` 9/5 `(divide by 4)

Answer: `12/5 * 3/4 = 9/5.`

Example 3: Solve for `x/2` = 10.

Solution:

Given `x/2` = 10

x = 10 * 2 (multiply by 2 on both sides)

x=20.

Answer: x=20.

Practice Problems for Elementary Math Practice:

Problem 1: Add the followings: 3458 + 0.24 + 457 + 0.97

Answer: 3916.21

Problem 2: Find the common multiples of 6, 10 and 15.

Answer: Common multiples of 6, 10 and 15 are 30, 60, 90 …..

Problem 3: Find the summation of fraction numbers `2/5` , `3/5` and `10/5` .

Answer: Summation of fraction numbers` 2/5` , `3/5` and `10/5` = `18/5` .

Problem 4: Solve for z: (2z + 9) – (z – 10) =2z.

Answer: z=19.

Problem 5: Solve for k: k+11 =25.

Answer: k = 14.

Problem 6: Solve for s: 2s + 4 =10.

Answer: s=3.

Problem 7: Divide 455 ÷ 5

Answer: 91.

Pure Math Explained

Introduction to pure math explained:

The pure mathematics is defined as combinations of algebra, geometry, topology and number theory and analysis. Pure mathematics looks at the boundary of math and pure reason. It has been explained as "that part of math activity that is done without explicit or immediate consideration of direct application," although what is "pure" in one era often becomes applied later. In this article we will solve geometry and algebra examples for pure math explained.

Examples – Pure Math Explained:

Let us we will solve the example problems for pure math explained.

Now we are going to solve the example problem in geometry using line and circle shape for pure math explained.

Example 1:

The slope of the geometric line which passes through (3.3, 17.2) and (9.8, 21.5), find the slope value of this line?

Solution:

We know that the slope of a line can be found as m =`(Y2-Y1)/(X2-X1)`

Here, x1 = 3.3 x2 = 9.8 y1=17.2 y2 =21.5

m = `(21.5 - 17.2)/(9.8-3.3)`

= `4.3/6.5`

m =0.66

So the slope of the line is found to be 0.66.

Example 2:

What is the area of the circle if r=1.8cm?

Solution:

Formula = `pi` r2

= 3.14*1.8*1.8

= 10.17cm2

Example for Pure Math Explained:
Let us we will solve the example problem in algebra for pure math explained.

Problem 3:

Solve the given polynomial equations.

7x2 + 5 + 6x + 3x2 + 2x + 4 + 8x

Solution:

Step 1:

First we have to mingle terms x2

7x2 + 3x2=10x2

Step 2:

Now combine the terms x

6x + 2x + 8x = 16x

Step 3:

Then join the constants terms

5 + 4 =9

Step 4:

Finally, combine all the terms

10x2 + 16x +9

So, the final answer is 10x2 + 16x +9

Example 4:

Enlarge the following using identities, (6m)2-(15n)2

Solution:

Step 1:

Given, (6m)2-(15n)2

Take, (6m)2 - (15n)2, for this we need to use the identity, a2 - b2 = (a+b) (a-b)

Here, a = 6m and b = 15n.

Step 2:

As a result, (6m)2 -(15n)2 = (6m+15n) (6m-15n)

These are example problems for pure math explained.

That’s all about pure math explained.

The Sum of Twice a Number and Seven

The sum of twice a number and seven :

In general ,twice means a number multiplied by 2 .the sum of twice a number means a number multiplied by 2 +7.in other words,Sum of twice a number and seven means ,the product of  number by 2  plus seven.

For example : Let us consider the unknown number x,y,z, The expression should becomes 2x+7,2y+7,2z+7

Example Problems to Find Sum of Twice a Number and Seven :
Example 1:

The sum of twice a number and seven is 19.Find the number ?

Solution:

The sum of twice a number and 7 is 19.

Let us consider the unknown number is x,

Write this sentence into equation,we get,

2x+7 =19

Subtract 7 on both sides, 2x+7-7=19-7

2x=12

Divide both sides by 2,x=`12/2`

x=6

Therefore the unknown number x=6

Example 2:

The sum of twice a number and seven is 17.Find the number ?

Solution:

The sum of twice a number and 7 is 17.

Let us consider the unknown number is x,

Write this sentence into equation,we get,

2x+7 =17

Subtract 7 on both sides, 2x+7-7=17-7

2x=10

Divide both sides by 2,x=`10/2`

x=5

Therefore the unknown number x=5

Example 3:

The sum of twice a number and seven is 53.Find the number ?

Solution:

The sum of twice a number and 7 is 53Let us consider the unknown number is x,

Write this sentence into equation,we get,

2x+7 =53

Subtract 7 on both sides, 2x+7-7=53-7

2x=46

Divide both sides by 2,x=`46/2`

x=23

Therefore the unknown number x=23

Example 4:

The sum of twice a number and seven is 121.Find the number ?

Solution:

The sum of twice a number and 7 is 121

Let us consider the unknown number is x,

Write this sentence into equation,we get,

2x+7 =121

Subtract 7 on both sides, 2x+7-7=121-7

2x=114

Divide both sides by 2,x=`114/2`

x=57

Therefore the unknown number x=57

Please express your views of this topic What is a Composite Number? by commenting on blog.

Practice Problem to Find the Sum of Twice a Number and Seven:

1)The sum of twice a number and seven is 13.Find the number ?

Answer:3

2)The sum of twice a number and seven is 25.Find the number ?

Answer:9

Primary Solutions Math

Introduction to primary solutions math:

In this article, we are going to learn about,

"What is the definition of Mathematics"

"Primary math problems with solutions"

Definition of Mathematics:
Mathematics is a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

Primary Solutions Math:

Here are provided some examples of primary math along with the solutions.

Ex 1:

Cost of 3 pencils is 45 cents and that of 5 pencils is 75 cents. What is the proportion?

Sol:

Ratio of the two quantities = 3 : 5

Ratio of their costs = 45 : 75

Therefore, the proportion is 3 : 5 = 45 : 75

Ex 2:

Find the slope of given line 2x+3y=0

Sol:

Given line is: 2x+3y=0

Slope =-x/y

Y==3

X=2

M=slope=-2/3

Ex 3:

Solve 2x + 12 = 0

Sol:

2x + 12 = 0

Put all the variables aside and value on other side.

We get, 2x = -12

Now to get x value divide both sides with 2

2x/2 = -12/2

x = -6

Ex 4:

Is 6 a composite or a prime?

Sol:

1 x 6 = 6

2 x 3 = 6

6 can be divided with 1 and 6 and also with 2 and 3. So 6 is a composite number.

Ex 5:

Write 9 table.

Sol:

Given: 9 table

9 × 1 = 9 (9)

9 × 2 = 18 (9+9=18)

9 × 3 = 27 (9+9+9=27)

9 × 4 = 36 (9+9+9+9=36)

9 × 5 = 45 (9+9+9+9+9=45)

9× 6 = 54 (9+9+9+9+9+9=54)

9 × 7 = 63(9+9+9+9+9+9+9=63)

9 × 8 = 72 (9+9+9+9+9+9+9+9=72)

9 × 9 = 81(9+9+9+9+9+9+9+9+9=81)

9x10=90(9+9+9+9+9+9+9+9+9+9=90)

Ex 6:

A die is rolled on a desk; what is the probability to get number 2 face.

Sol:

Given data:

Total number of out comes = 6 (A die has 6 faces)

Favorable outcome = 1 (only one face is having number 2)

P (E) = Number of favorable outcomes/Total possible outcomes.

Probability to get 2 face is = 1/6.

Ex 7:

Write the place value of  748   

Sol:

Place value of 8 = 8 x ones = 8
Place value of 4 = 4 x tens = 40
Place value of 7 = 7 x hundreds = 700

Ex 8:

Simplify x + y+2x-3y=0

Sol:

Given expression,

x + y+2x-3y=0

Add and subtract the like terms we get ,

X+2x+y-3y=0

3x-2y=0

Front End Estimation Math

Introduction to front end estimation math:

The front end estimation is typically produces the earlier estimation of the addition or the difference than the answer formed through adding or subtracting rounded numbers for the estimation in the mathematics. It may give the closer estimated values for the actual estimation for the given problem.

In the front end estimation of math, one takes the two maximum digits of a number, and then put zeros on the other position values. This is supposed to create the earlier estimation rather than rounding and then addition numbers. In this article we shall discuss the front end estimation in the math.

How to Calculate an Addition by front End Estimation Math:

Add the digits of the two maximum place values

Plug in zeros for the other place values

Ex 1:  5596 + 3845 is estimated to be 9300 through front end estimation math(i.e. 5500 + 3800).

Ex 2: 5596 + 855 is estimated to be 6300 through front end estimation math(i.e. 5500 + 800).

Examples for front End Estimation:

Ex 1: 77 + 53 = 80 + 50 = 130

Sol: Make a note of that we are only adding the left the majority numbers (8 and 5)



31 + 68 = 30 + 70 = 100



77 - 52 = 80 - 50 = 30



88 - 42 = 90 - 40 = 50.



But the numbers contains the three digits; round it to the nearby hundred places earlier than adding the left the majority digits or numbers

Ex 2:    264 + 590 = 300 + 600 = 900.



Sol: Make the note of that the front end estimation for the every other numbers apart from the left the majority digits (3 and 6) are equivalent to zero and we only added the left the majority digits as stated before.



335 + 555 = 300 + 600 = 900
666 - 354 = 700 - 400 = 300
832 - 678 = 800 - 700 = 100.


But the numbers contains the four digits, so round it to the nearby thousand place earlier than adding the left the majority digits or numbers



Ex 3:  3354 + 2677 = 3000 + 3000 = 6000.



Sol: Make a note of that the other numbers apart from the left the majority digits (3 and 3) are equivalent to zero and we only added the left the majority digits as stated before

6687 - 3765 = 7000 - 4000 = 3000

4245 + 2897 = 4000 + 3000 = 7000

8501 - 5508 = 9000 - 6000 = 3000.

But the numbers contains the five digits; round it to the nearby ten thousand places before adding the left the majority digits or numbers

Ex 4:  59974 - 36799 = 60000 - 40000 = 20000.

Sol: Make a note of that the other numbers apart from the left the majority digits (6 and 4) are equivalent to zero and we only subtracted the left the majority digits as stated before

93113 + 48893 = 90000 + 50000 = 140000

Determining Sample Space

Introduction to determining sample space:

The probability separation be capable of be described regarding the sample space. The probability may be describing more requisites as, experiment, outcome, sample space, events. The probability is a one of dimension from the set of events. The many algorithms can be used to determining the sample spaces. The simply to determining the probable outcomes is straightforward represented as sample spaces. The probability triple is a further name of the sample space. The probability process can be classified three types like sample space, events and function of event.

Determining Sample Space-definition:

Sample space is defined as; the amount of probable outcomes is known as determining sample space. The determining sample space is helped to calculate the whole space, so it is normally represented as measure space.  The sample space can be specified as ?, and it is one of the chances of non- empty set.

Some of the results can be followed through the experiment so it is simply called as deterministic experiments. From the experiments, set of possible outcome is called as random experiment. The put of probable outcomes of a random research is known as determining sample space

Determining Sample Space-examples:

Problem 1:

Determining the sample space, when three coins are tossed randomly.

Solution:

Basically the coins contain two sample outcomes like head or tail. Here, we have to toss three coins randomly. The possible outcomes are,

The required sample space = {HHH,HHT,HTH,THH,THT,TTH,HTT,TTT}

Checking:

The number of coins (n) = 3.

Normal formula for sample space = 2number of entity.

The sample space       = 23.

So, the sample space = {HHH,HHT,HTH,THH,THT,TTH,HTT,TTT}.

Understanding Least Common Multiple Finder is always challenging for me but thanks to all math help websites to help me out.

Problem 2:

Determining the sample space, where the two dice throw same time. Find the equal pair of dice.

Solution:

The each dice has been providing the six possible outcomes.

So, the two dice has been providing 36 possible outcomes.

The possible outcomes of two dice = { (1,1), (1,2),(1,3), (1,4),(1,5),(1,6),

(2,1),(2,2),(2,3) ,(2,4), (2,5),(2,6),

(3,1),(3,2),(3,3),(3,4), (3,5),(3,6),

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),

(5,1), (5,2),(5,3),(5,4),(5,5),(5,6),

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

These are the possible outcomes by throwing two dice.

From the given problem, we have to find the pair of outcomes.

The pair of sample space = { (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}.

This is the sample spaces for throwing two dice at the same time.

Solve Calculus Help Integrals

Introduction for solve calculus help integrals:

Calculus is divisions in mathematics. It contains limits, functions, derivatives, integrals, and infinite series. Calculus is divided into two major parts, differential and integral calculus, which are associated by the basic theorem of calculus. Calculus is the learning of vary, in the equal way that geometry is the learning of shape and algebra is the learning of procedure and their application to solving equations.A math tutorial is one technique of shifting knowledge and may be used as a piece of learning. More interactive and detailed than a book; a tutorial look for to tutor by example and provide the information to complete a certain task.I like to share this Triple Integrals with you all through my article.

3 important topics involved in Calculus are,

Limits

Derivatives

Integrals

Solve Calculus Help Integrals - Examples

Solve calculus help integrals - Example 1:

Integrate the given equation with respect to x, we get

`int ` x7 dx = `(x^7 +1)/(7 + 1) ` + c

= `(x^8)/8 ` + c

Answer:

The final answer is  ` (x^8)/8` + C

Solve calculus help integrals - Example 2:

I am planning to write more post on Integration by Part, Fundamental Theorem of Calculus Examples. Keep checking my blog.

Evaluate:

`int` e(5x+3) dx

Solution:

Put (5x+3) =t so that 5 dx = dt or dx =`1/5` dt.

= `int` e(5x+3) dx =`1/5` et + C

= `1/5` e (5x+3) + C

Solve calculus help integrals - Example 3:

Integrate the given function int 2 sin 4x dx

Solution:

Integrate the given function with respect to x, we get

`int` 2 sin 4x dx = 2 `int` sin 4x dx

= 2 `xx`  - cos `(4x)/4`

= - cos `(4x)/4`

Answer:

The final answer is - cos` (4x)/4`

Solve Calculus Help Integrals - more Examples:

Solve calculus help integrals - Example 1:

Integrate int arcsin 2x dx

Solution:

U = arcsin 2x and du = dx = 1 dx

du =` 1/sqrt (1-(2x)^2) 2 dx = 2/sqrt(1-4x^2) dx ` and  v=x..

Therefore,

int arcsin 2xdx = x arcsin 2x – `int x 2/(sqrt(1-4x^2))` dx  = x arcsin 2x – 2` int x/(sqrt(1-4x^2))` dx.

Now apply u-substitution.

Let     U = 1-4x2

du = -6x dx,

`(-1/6)` du = x dx.

`int `  arcsin 2x dx = x arcsin 2x – 2` int` `x/sqrt(1-4x^2)` dx

= x arcsin 2x-2 `int 1/(sqrt(1-4x^2))` x dx

= x arcsin 2x-2 `int 1/sqrt(u) (-1/6)` du

= x arcsin 2x + `(1/3) int 1/sqrt(u)` du

= x arcsin 2x +` (1/3) int ` u-1/2 du

= x arcsin 2x+ `(1/3) (u^(1/2))/(1/2)` + C

= x arcsin 2x + `1/3(1-4x2)^(1/2)` + C

= x arcsin 2x +` (1/3) sqrt(1-4x^2)` + C.

Solve calculus help integrals - Example 2:

Evaluate:

1) `int` cos 2x dx

2) `int` e(4x+3) dx

Solutions:

1)    Put 2x =t so that 2 dx    = dt or dx =`1/2` dt.

= `int` cos 2x dx =`1/2` sin t + C

= `1/2` sin 2x + C

2)    Put (4x+3) =t so that 5 dx = dt or dx =`1/4` dt.

= `int` e(4x+3) dx =`1/4` et + C

= `1/4` e (4x+3) + C