Math Help 5th Grade

Introduction to math help 5th grade:
The topics involved in 5th grade math help are number sense, patterns, addition, measurement, subtraction, multiplication, functions,  fractions & mixed numbers, division, algebra, decimals, adding and subtraction of decimals and probability & statistics. In this article we shall discuss about the problems involved in 5th grade math help.

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Math Help 5th Grade Problems:


Example 1:Find the area of a rectangle with base of length is 10 inches and height of 4 inches.

Solution:

Area of a rectangle = length * height

So, Area of a rectangle = 10 *  4

= 40 square inches

Example 2: Find the median of 8, 6, 9, 3, 2, 7

Solution:

Evaluate the total numbers from the given set of values.

From the given set of values, there are totally 6 numbers, Which is even,

Now arrange the total numbers in ascending order,

2, 3, 6, 7, 8, 9

As the given set of numbers is even , Sort out two middle numbers from the above given list of numbers,

Which is  6 & 7 are the two middle numbers,

In order to find the median, add both middle terms and divide by 2,

Adding both numbers `(6+7)/(2)` = 6.5

Therefore median=6.5.

Example 3: Find the value form the expanded form 2 × 10000 + 4× 1000 + 10 × 10 + 8

Solution:  2 × 10000 + 4 × 1000 + 10 × 10 + 8

= 20000 + 4000 + 100 + 8

=> 24108.

Example 4: Find the mode for given set of data. 60, 19, 15, 50, 15, 80, 30

Solution: Mode:The mode is the number that occurs most often in a set of data.

Form the given data set we can say that 15 is the number that has occurred twice.

For the given set of data, Mode = 15.

Example 5: Find the perimeter of a square with length 8.

Solution: The perimeter of a square = 4 * a ( a-> length)

Here length =5, So perimeter of square = 4 * 8 = 32.

Example 6: Find the circumference of a circle with diameter 14.

Solution:  The circumference of a circle = 3.14(pi) * diameter of the circle.

Here diameter = 10, So Circumference of a circle = 3.14 * 14

Therefore the Circumference of a circle =   43.96

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Math Help 5th Grade Practice Problems:


Problem 1:Find the area of a rectangle with base of length is 10 inches and height of 6 inches.

Answer: Area of rectangle =40 square inches.

Problem 2:Find the mode for given set of data. 6, 9, 5, 5, 1, 8, 3

Answer: Mode = 5

Problem 3: Find the value form the expanded form   8× 1000 + 12 × 10 + 10

Answer: 8130

Logic and Set Theory Learning

Introduction to Logic and Set Theory Learning:

Logic theory is a set of sentences in a formal language. The individual sentences of a theory are called as the theorems. A first-order theory is a set of first-order sentences. Many authors require that the theory be closed under logical consequence; a theory with this property can be called a deductive theory. Set theory is the studies of sets, which are collections of objects. Although any type of object can be collected into a set.

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Basic operations of logic and set theory learning


Union in Set theory Learning:
If A and B are different sets then union of A and B denoted as A U B.

For example {3, 4, 5} and {6, 7, 8} is the set {3, 4, 5, 6, 7, 8.

Intersection in Set theory Learning:
If A and B are different sets then intersection of A and B denoted as A n B.

For example {3, 4, 5} and {6, 4, 3} is the set {3, 4}.

Complement in Set theory Learning:
If A and B are different sets then A relative to set b, denoted Ac.

For example complement of {3, 4, 5} relative to {6, 4, 3} is {6}.

Symmetric difference in Set theory Learning:
If A and B are different sets then member of exactly one of A and B.

For example complement of {3, 4, 5} relative to {6, 4, 5} is {3, 6}.

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logic and set theory learning


Negation (NOT) ˜ p in logic learning:
If value of proposition is true then transform into false and vice versa.

Disjunction (OR) p v q in logic learning:
If two propositions are false then the result is false otherwise true.

Conjunction (AND) p ^ q in logic learning:
If two propositions are true then result is true otherwise false.

Conditional (IF…THEN…) p?q in logic learning :
Truth of the proposition p is sufficient to truth of proposition q.

Biconditional (IF AND ONLY IF) p?q in logic learning:
p is sufficient condition for q. q is necessary for p. Unless q not p. Not p unless q. Not p without q.

How to Explain Divide Math

Introduction for explain divide math:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) widely used in day to day life. In these articles we are going to see about how to explain divide math. Division can be considered as repeated subtraction or equal distribution.

Simple division teach to find the how frequently one whole number called the divisor, is contain in an additional whole number, called the dividend, or to divide a whole number into some proposed number of equivalent parts, and is a small method of performing frequent subtraction.

The number arise from the procedure is called the quotient; it shows how often the divisor is contain in the dividend, that is into how many equal parts the dividend is divided.

If any thing be over following the division is performing it is called the remainder. The mark for division is ÷ it is name by and shows that the number status previous to the sign is to be divided by the number.


Explain divide math - Definition and steps:


Explain divide math - Definition:

Division is defined as an arithmetic function, which is the opposed process of multiplication. From the process of division, the proportion or ratio of two numbers be capable of be calculated.

Otherwise, the process of decision how many periods of one number is included in a further one. Symbol of division is ‘/’ or ‘÷’. If we divide a number by another number, then

Dividend = (Divisor * Quotient) + Remainder

Explain divide math - Steps:

Step1. Division of two integers by the related signs resolve be positive sign

a) Positive ÷ positive = positive

b) Negative ÷ negative = positive

Step2. Division of two integers by the unlike signs will be negative

a) Positive ÷ negative = negative

b) Negative ÷ positive = negative.


Explain divide math – Example problems:


Problem 1:

The school's Internet connection transferred 646 megabytes of data in 6 seconds. How many megabytes can it transfer in just one second?

Solution:

The school's Internet connection transferred 646 megabytes Data in 6 seconds.

So, therefore total megabytes can it transfer in just one second

= 646 ÷ 6

Step 1: Determine whether the divisor 6 will divide the first digit of the dividend 646. It will since it is not greater than this digit. The result of division is 1, which is placed under the 6.

Step 2: Determine whether the divisor 6 will divide the second digit of the dividend. Since 6 will not divide 4, a zero is placed under the 4.

Step 3: The 4 is now taken with the third digit 6 to become 46. The divisor 6 divides 46 and the quotient 7 is placed under the 7 and remainder 4. The answer is 107.66

= 107.66 megabytes

Problem 2:

There are 48 soft drink machines in the university. They hold 768 cases of soda altogether. How many cases does each machine hold?

Solution:

There are 48 soft drink machines in the university.

They hold 768 cases of soda altogether.

= 768 ÷ 48

= 16

16 cases do each machine hold.

Sixth Grade Math Fractions

Introduction

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. Source wikipedia

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Sixth grade math fractions problems:

Sixth grade math problem 1

Add the two fractions `2/3` and `5/3`

Solution:

The given two fractions `2/3` and `5/3`

=`2/3` +`5/3`

Add above the fraction `2/3` and `5/3`

= `(2+5)/3`

We get

=`7/3`

This can be simplified has

=2.33

Answer of the two fraction = `7/3` or 2.33

Sixth grade math problem 2

Add the two fractions `12/3` and `15/3`

Solution:

The given two fractions `12/3` and `15/3`

=`12/3` +`15/3`

Add above the fraction `2/3` and `5/3`

= `(12+15)/3`

We get

=`27/3`

This can be simplified has

=9

Answer of the two fraction = `17/3 ` or 9

Sixth grade math problem 3

Add the two fractions `22/8` and `25/8`

Solution:

The given two fractions `22/8` and `25/8`

=`22/8` +`25/8`

Add above the fraction `22/8` and `25/8`

= `(22+25)/8`

We get

=`47/8`

This can be simplified has

=5.875

Answer of the two fraction = `47/8` or 5.875

Sixth grade math problem 4

Subtract the two fractions `9/3` and `5/3`

Solution:

The given two fractions `9/3` and` 5/3`

=`9/3` -`5/3`

Subtract above the fraction `2/3` and `5/3`

= `(9-5)/3`

We get

=`4/3`

This can be simplified has

=1.33

Answer of the two fraction = `4/3` or 1.33

Sixth grade math problem 5

Multiply the two fractions `2/3` and`5/3`

Solution:

The given two fractions `2/3` and `5/3`

=`2/3` +`5/3`

Multiply above the fraction `2/3` and `5/3`

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

We get

=`10/9`

This can be simplified has

=1.11

Answer of the two fraction = `10/9` or 1.11

Sixth grade math problem 6

Multiply the two fractions `5/3` and `5/6`

Solution:

The given two fractions `5/3` and `5/6`

= `5/3* 5/6`

Multiply above the fraction `5/3` and `5/6`

= `(5*5)/ (3*6)`

We get

=`25/18`

This can be simplified has

=1.38

Answer of the two fraction = `25/18` or 1.38

Learning Sure Event

Introduction to learning sure event:

The word sure event is coming in probability theory.

Probability is the likelihood of occurring of an event. P (A) denotes the probability of an event.

Probabilities of events are always between 0 and 1.

0<=P(A)<=1

We say that an event is a sure event if it is having a probability of occurrence 1.

As we know that the probability varies from 0 to 1.

So if an event has the maximum probability, that is 1;then that event is a sure event.

For example we can consider the case of tossing a coin

In that case the probability of getting a head or tail one.

As one of these event will surely happen. So it is a sure event.

As we talk about sure event we cant avoid the case of impossible events.

Which is the opposite case to the sure event. That is never going to happen.

For example, let us take the example of tossing a die. Here probability of getting an eight is zero

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learning sure event-Examples


1) While drawing a dice,probability of getting one event less than 7

here the sample space is (1,2,3,4,5,6)

Probability of the event is P(E) =1

Here E is a sure event.

2)Suppose a bag contains 4 balls of red color.

Here the probability of getting a red ball is P(getting a red ball)=1

Which is also a sure event.

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learning sure event-Practice problems


1.      Find the probability of getting a green ball, from the bag, which contains 5 green balls

2.      Find the probability of getting a white pearl from the bag of 500 white pearls and one cream pearl.

3.      Find the probability of getting a black ball from the pack of white balls.

Answers:

1.      Here the sample space contains only events that contain the occurring of green balls. There is no chance of getting any other ball.

Here the number of events favorable is 5

And total number of events is also 5

So here the probability of getting a green ball is

P (Getting a green ball)=5/5

So it is 1..

2. This is the chance of almost sure event.

Probability of getting the other color pearl is almost 0 here.

3. This is the case of Impossible events.

Here the probability of occurring the event is 0

As it a not possible to get a black ball from the white ball pack

Array Definition Math

Introduction to array definition math:
Array has a list of data. In math array is a rectangular arrangement of elements. The elements are shown in rows and columns. In math array elements are put in the parenthesis or square brackets. In math the arrays are represented by capital letters for example A, B, C……An array is a symbolic way to represent math facts. Using symbols like circle, square or rectangle is one way of writing math facts in array.

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Definition of Array:

Definition of array:

The symbol m `xx` n is used to represent the array in math. The number of columns is represented by first element in the symbol and number of rows is represented by second element in the symbol. For example 2 `xx` 3 mean that array has 2 rows and 3 columns. The structure of array is rectangle. Array is used to be a symbol of the number of data.

Here

First row elements = a1, a2, a3

Second row elements = b1, b2, b3

Third row elements = c1, c2, c3

First column elements = a1, b1, c1

Second column elements = a2, b2, c2

Third column elements = a3, b3, c3

Symbol representation of above array is 3 `xx` 3

Total rows =3

Total column = 3

Types of Array or Matrix:

Types of array or matrix:

Column matrix
Row matrix
Square matrix
Diagonal matrix
Triangular matrix
Scalar matrix
Identity matrix
Zero matrix
Equality of matrix

Definition of column matrix:

Only one column is present in the column matrix.

Definition of row matrix:

Only one row is present in the row matrix.

Definition of square matrix:

If one matrix has equal number of row and column means called as square matrix.

Definition of diagonal matrix:

Other than diagonal elements in the array is zero means called as diagonal matrix.

Definition of triangle matrix:

Triangle matrix must be a square matrix. All the elements in above the diagonal are zero means called as lower triangle matrix. All the elements in below the diagonal are zero means called as upper triangle matrix.

Definition of unit matrix:

Unit matrix must be a square and diagonal matrix. The diagonal elements are one and the remaining elements in the array is zero means call as unit matrix.

Growth Factor in Math

Introduction to growth factor in math:

Growth factor in math article deals with the definition of growth factor in math and the model problems related to growth factor.

Definition of growth factor in math:

Growth factor is defined, as the constant rate that is multiplied by it self over a certain period.the growth factor is always a positive number. Growth factor cannot be represented in percentage.

Formula to growth factor in math:

When the growth rate is given

Increase in value = P* G*T

P is the principle or original value.

G is the growth rate.

T is the period.
Growth factor is calculating by dividing the increased value by original value

Growth factor = `(("increased value")/("original value"))`

it is always positive value not the negative one.

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Model problems to growth factor in math:

Problem: 1

Find the growth factor of the original value $500 over a period of 7 years with the growth rate of 6%.

Solution:

The original value is $500

Period of time = 7 years

Growth rate is 6%

The increase value is `(500*7*(6/100))`

=(5*7*6)

= 210

The increased value is $710

Now we have to calculate the growth factor:

Growth factor = `(("increased value")/("original value"))`

= `(710/500)`

= 1.42

The growth factor is 1.42

Problem: 2

Find the growth factor of the original value $300 over a period of 9 years with the growth rate of 8%.

Solution:

The original value is $300

Period of time = 9 years

Growth rate is 8%

The increase value is `(300*9*(7/100))`

(3*9*7)

= 147

The increased value is $447

Now we have to calculate the growth factor:

Growth factor = `(("increased value")/("original value"))`

= `(447/300)`

= 1.49

The growth factor is 1.49

Problem: 3 find the growth factor of the numbers behind the numbers 12.5,50, 100, 200, 400.

Solution:

To find the growth, we have to divide the previous value by present value

(50/12.5) = 2
(100/50) =2
(200/ 100)= 2
(400/200)=2

Here the growth factors between the numbers are 2

the growth factor of the numbers is 2