Solve Decimals

Decimals are very significant in the world of mathematics, with the help of decimals we can solve any fraction up to its last limit, and in finding percentage they play a very important role. Decimal is generally a tenth part of any decimal number (you can also use decimal to fraction calculator). We can perform many operations on decimal numbers like addition, subtraction and division. We can represent fractions in decimals by just dividing the numerator by denominator. Now we will see how we can Solve Decimals problems (refer this for more info on decimals).
Example: Add 12.1 + 13.43
Solution: for addition we need to check the digits after decimal, if number of digits is equal then we can simply add them but if number of digits is not equal then we need to equalize the digit then only we can add. For equalizing the digit we can simply add the zero after decimal, as zero has no importance after decimal but you can put the zero after the digit not before the digit. So we can write the above equation as
12.10+ 13.43
=25.53
In this way we can add decimals. In the same way we can also do subtraction with the decimals.
We will see an example of multiplication of decimal number (improve your skills by finding, is a repeating decimal a rational number).
Example: multiply 12.3 with 3.2
Solution: like addition we don't need to equalize the number after. For the above question we need to firstly multiply 2 with 12.3 and then we will multiply 3 with 12.3, when we will multiply 2 with 12.3 we will get 246 and on multiplying 3 with 12.3 we will get 369 now we will add them like
  246
+369*
So we will get 3936 now we need to put decimal after two digits so required answer will be 39.36.
In the same way we can also perform division operations.

In upcoming posts we will discuss about Multiplication/division - inverse relationship and Order of Operations in Grade V. Visit our website for information on CBSE class 12 home science question bank

Place value whole numbers

Whole numbers range from 0 to 9, after that combination of these whole numbers creates big and new numbers. Big range of whole numbers generates a new type of property, which is known as place value in whole numbers. Through this blog we are discussing about the whole number place value.
In the general term place value is normally finding the positional value of the number in the given number system. Finding the place value of the numbers can be categorized in many ways, but standard place value system is easiest and shortest technique.
Let’s see via some live math help examples:
Example1: Suppose there is a number 4,324,345,567.
Solution: In above example first we demonstrate how to read and write the whole numbers.
The given number is 4,324,345,567. It can be read as
4 billion, 3 hundred 24 million, 3 hundred 45 thousand, 5 hundred 67
It means that we started from right position, i.e. ones position and further move on. The table below demonstrates that:

      3                    2                         4                   3                     4                   5                     5                      6              7

Hundred million

Ten million

million

Hundred thousands

Ten thousand

thousands

hundreds

Tens

ones

   3             

Through the above table we show the actual position of the each digit in the given number. Now we are going to discuss about finding the place value of whole numbers.

Example2: find the position of 3 into the given numbers 32,839,564,730.
Solution: In the given number (32,839,564,730), no. 3 is used three times in the question.
So now we specify each place value of the number in a separate block from right to left.
The first no. 3 (in 32,839,564,730) has the place value of tens. The second no. 3 (32,839,564,730) has the place value of ten million. The third no. 3 (32,839,564,730) has the place value of ten billion.

In upcoming posts we will discuss about Solve Decimals and Problems on sum of angles for Grade V. Visit our website for information on CBSE class 12 chemistry previous years question papers

Fractions and Decimals in Grade IV

Hello friends, now we are going to learn about some of the chapters of mathematics for grade IV. Today we wil learn about decimals (read how to divide decimals), fractions and percents of the numbers. We will get introduced by composition and decomposition of numbers also.

First introducing with fraction and decimals. Fractions are the numbers which represent the part of a whole number. These are in the form of ratio of numerator to denominator. For example 3/4, 5/6, 2/3 etc. Just taking 5/6 in the consideration, then 5 is the numerator which tells us that the fraction represents 5 equal parts, and the denominator, 6, tells us that 6 parts equals a whole quantity. Fraction number shows the part of a whole number and they are used to represent some ratio and decimal form of numbers. Just like fraction, decimal is the number which also shows some part of the whole number. Decimal numbers are the types of fraction of a whole number and they also come from the fraction number. 

For example any fraction number can be converted into the decimal number and decimal also can be same. Say for example any fractional number is ½ then by simplifying it we can write it as 0.5. The simplification is as that let us multiply by 5 on both numerator and denominator terms and we gets 5/10 which on decomposing in the decimal becomes 0.5. So ½ is equivalent to the 0.5 which is half of any whole number.

Now discussing about percentage of a Number. Percentage is a way of representation of any number as a fraction of 100(per cent stands for per 100). It is denoted by “%” sign, for example 54 %( also read as “fifty four percent”) which is equal to 54/100 in the fraction and 0.54 in decimal. Percentages are used to show the quantity of any number that how large or small quantity is and the decrease & increase in the price. We have to find percentage of any number in this topic.

For example, 10% of 50 is 5 and this can be calculated by some methods. That is:

                10 / 100 * 50         = 10 * 50 / 100

                                                =  5.

The change in quantity is also represented in percentage in the form of how much the change has been detected in the quantity. So we first need to find the fraction of number and then convert that to the percentage. For example, an increase of $0.10 in money value of $ 2.75 is an increase by a fraction of 0.10/2.75 = 0.036. Expressed as a percentage, this is therefore increase of 3% in the money value. The concept of percentage is also applicable on percentage of a number, discounts, taxes, sales  percent of changes, and percent of comparison.

Compose and decompose numbers is also a topic in some of the real life topics. Compose and decompose numbers stands for breaking any number into as many combinations of groups as possible. Let's say 4 can be composed in four groups of one, two groups of three, a group of four or by many more other combinations.

In upcoming posts we will discuss about Number Operations in Grade IV and Problem solving strategies. Visit our website for information on CBSE board home science syllabus for class 11

Fractions in Grade IV

Hello kids, today I am going to tell you the basic overview of what we suppose to study in our IV grade mathematics syllabus. What we need to remember is daily little practice and hard work. The most important thing is that there is no alternative for hard-work. Few of the most important topics of IV grade mathematics are as follows:

1. Fraction
2. Addition and Subtraction
3. Multiplication facts
4. Division Facts
5. Decimals
6. Geometry – Area, circumference and perimeter
7. Arranging a number

Let's start with fractions topic of IV grade mathematics syllabus. Before going towards examples let's discuss about the basic terminologies behind fractions. First question comes in our mind is what is fraction? A number that can be represented as the ratio of two numbers known as fractions. For example : 1/3, here 1 is numerator and 3 is denominator. The condition for fraction is that denominator can never be a zero.

Here the number above the bar is stated as the numerator and the number below the bar is expressed as Denominator. As I mention that denominator value can never be a zero because if we are going to divide any of the value with zero then the loop will go on infinite times. Few of the concepts are:

For simplifying fractions following are some rules to follow:

Adding and Subtracting of a fraction is done by using this property: x/y + a/b = xb + ay / yb.
For Multiplying a fraction this property comes in an account: a/b x c/d = ac/bd

and for dividing a fraction we use this property: a/b divide c/d = ad/bc.

Now I am going to tell you the different types of fractions in mathematics. The three different types of fractions are Proper fractions, improper fractions and mixed fractions. Let's start with proper fractions:

Proper Fractions: In this the numerator value is lower in comparison to denominator.

Numerator < Denominator

For example ¾ is the proper fraction in which 4 > 3.

Improper Fractions : In this numerator is greater then the denominator. Denominator < Numerator

For example 3/2 is the improper fraction in which 3 > 2.

Mixed fraction : A mixed fraction is basically a whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed fraction

To convert an improper fraction to a mixed fraction, follow these steps:

1. Divide the numerator by the denominator.

2. Write down the whole number answer

3. Then write down any remainder above the denominator.

Another terminology is complex fraction: A complex fraction is a rational expression that has a

fraction in its numerator, denominator or both. Example to show the complex fraction: a/b / c/d. The sign / denotes the division of two numbers or variables. Simplifying complex fractions involves following steps: firstly student need to rewrite the numerator and denominator so that, they each form a single fraction. Now divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator. In last step we need to simplify the rational expression.

We can also convert a mixed fraction to an improper fraction. To make this kind of conversion we need to follow these steps:

1. 1. 1. Multiply the whole number part by the fraction's denominator.
      2. Add that to the numerator
      3. Then write the result on top of the denominator

Let's take an example to understand it better :

Problem : Convert 3 2/5 to an improper fraction.

Solution : Let's start with the first step that is multiply the whole number by the denominator:

3 × 5 = 15
then the next step to follow is add the numerator to that:
15 + 2 = 17
Then the final step is to write that down above the denominator, like this:
17/5.


Let's take an example to show how we can add two mixed fractions:
Problem : Solve following problem 3 ⁵/₈ + 1 ³/₄
The first step is to convert following mixed fraction into improper fraction :
3 ⁵/₈ = ²⁹/₈
1 ³/₄ = ⁷/₄
Now we need to make same denominator and add:
²⁹/₈ + ¹⁴/₈ = ⁴³/₈ = 5 ³/₈
In similar fashion, we can subtract two mixed fractions. Let's take an example to understand it :

Problem: Solve 15 3/4 - 8 5/6 ?

Similarly the first step is to convert following mixed fractions into Improper Fractions:

15 ³/₄ = ⁶³/₄

8 ⁵/₆ = ⁵³/₆

Make the common denominator of 12:

⁶³/₄ becomes ¹⁸⁹/₁₂

⁵³/₆ becomes ¹⁰⁶/₁₂

Now we need to perform Subtraction:

¹⁸⁹/₁₂ - ¹⁰⁶/₁₂ = ⁸³/₁₂

Finally we can convert the result back to Mixed Fractions:
⁸³/₁₂ = 6 ¹¹/₁₂


As we already perform addition and subtraction, so I am going to discuss about Multiplication facts in IV grade mathematics. In simple mathematical manner we can say that Multiplication is the mathematical operation of surmounting one number by another. In elementary mathematics it is one of the four basic operations that are addition, subtraction, multiplication and division.
Let's discuss about the four basic properties used in multiplication that will help the us to make its problem easier to solve. The four properties are the commutative, associative, multiplicative identity and distributive properties. Let's discuss each property one by one:

1. Commutative Property: This property states that whenever the two numbers are multiplied with each other, the product is the same regardless of the order of the multiplicands. Let's take an example to understand it better: 4 * 2 = 2 * 4 (also play commutative property worksheets)
   
2. Associative Property: This property tells that whenever two of the given numbers are multiplied together the result is the same regardless of the order of the multiplicands. Let's take an example to understand it better : (2 x 3) x 4 = 2 x (3 x 4)
   
3. Multiplicative Identity Property: In this the product of any number and one is that number. For example 5 x 1 = 5.
   
4. Distributive Property : This property shows that the sum of two numbers times a third number is equal to the sum of each addend times the third number. Let's take an example to understand it better : 4 x (6 + 3) = 4 x 6 + 4 x 3
   
5. Another important property is: Property of Zero states that any of the number when multiplied with zero will result zero, whether the given number is in any of the order. For example 6 x 0 = 0.
   

Now I am going to discuss about decimal facts of IV grade mathematics . Before proceeding further let's talk about basic concept behind decimal. In simplest of mathematical way we can say that a decimal is a number that has a decimal point somewhere in the number. A decimal point is a dot, period, spot, or smudge. For example
1.3
1.34
1.345
1.3456
1.34567890123456789
In the above examples the numbers on the left side represent whole numbers such as ones, tens, hundreds, and thousands. While the numbers on the right hand side of the point are the decimal values. Those numbers represent values called tenths, hundredths, thousandths, and so on.
There is a close relation between fractions and decimals as both describe values that are smaller than one. If we  concentrate at a fraction as one number divided by another, the quotient is the decimal number. Let's take some of the examples to understand it better : 1/4 is one quarter.
Similarly we can explain above example as : 1 divided by 4 is equal to 0.25. or we can say that 0.25 is the decimal equivalent to 1/4.
Now I am going to discuss about free geometry help. Geometry is an important area of mathematics which deals with the shape, size, relative position of figures, and the properties of space. It is all about shapes and their properties. Geometry is of two types : Plane geometry and solid geometry. Plane geometry deals about the shapes on a flat surface like lines, circles and triangles ... shapes that can be drawn on a piece of paper whereas Solid geometry is all about three dimensional objects like cubes, prisms and pyramids.

In upcoming posts we will discuss about Angles in Grade IV and adding decimal calculator. Visit our website for information on CBSE board physics syllabus

Decimals for Grade IV

Decimals are a way of converting fractional numbers system into linear form of number systems i.e. Not in a pattern of writing a fractional number having a numerator and denominator. The dot (.) also called as 'period' or 'decimal point' between two digits in a number indicates that particular number to be a decimal number. The zero and the counting numbers (1,2,3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10. You can improve your skills using adding decimal calculator
For an example, fractional number '5/10' can be written as the decimal '0.5'.
The decimal 0.5 could be pronounced as 'Fifth Tenth' or as 'Zero Point five'. If a decimal is less than 1, place a zero before the decimal point. So, now it should be written as 0.5 not .5. There are other decimals numbers like hundredths or thousandths and many more. They all are based on the number ten just like our number system. A decimal number can be greater than one. The decimal 8.9 can be pronounced as 'eight and nine tenth'. Decimal numbers of Tenths have one digit after the decimal point. The decimal 0.5 is called as "five tenths" or "zero point five". It is equal to the fractional number 5/10. Decimal number of Hundredths have two digits after the decimal point. The decimal 0.97 is pronounced "ninety-seven hundredths" or "zero point nine seven". It is equal to the fractional number 97/100. Decimal number of Thousandths goes with the same trend. They have three digits after the decimal point. The decimal 0.123 is pronounced "one hundred twenty-three thousandths" or "zero point one two three". If it happens that a 'zero' is placed after the decimal point in a number. For example, a decimal number 0.021 is pronounced "twenty-one thousandths" or "zero point zero two one". Use this resource for more on decimals.

Our decimal system of numbers lets us write numbers as larger or smaller as per our choice. In number system, digits can be placed to the left and right of a decimal point. The number to the left of the decimal point indicates numbers greater than one and the right of the decimal point is less than one. The decimal point indicates where the "ones" place is located and it is placed to the right of the ones place. As we move right from the decimal point, each number place is divided by 10.

The decimal number 534.129 as "five hundred thirty four and one hundred twenty-nine thousandths". Normally read as "five hundred thirty four point one two nine."


Exercise:
Convert the following fraction into decimal:

1) 1/10

A. 0.01
B. 0.1
C. 1.0
D. 10.0

2)12/100

A. 0.012
B. 0.0012
C. 1.2
D. 0.12

3) 1/100 =
A. 0.01
B. 0.1
C. 1.0
D. 10.0

4) 1/1000=
A. 0.001
B. 0.0001
c. 0.01
D. 0.1

Conversion of decimals into fraction:

Decimals are a type of fractional number. The decimal number 0.2 is equal to the fraction 2/10. The decimal 0.017 represents the fraction 17/1000. Decimal when represented in fractional number always have a denominator that is in the power of 10.
50/100 is equivalent to 1/2 since 1/2 times 50/50 is 5/100. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, and so on.

Some examples of Decimal numbers and Fractional numbers which are equivalent :
0.2 and 1/5
0.5 and 1/2
0.25 and 1/4
0.75 and 3/4

Two decimal numbers can be compared. A decimal number can be greater than, less than or equal to the other decimal number.
Comparing 0.5 and 0.05 is similar like comparing two fractional numbers 5/10 to 5/100. The fraction 5/10 is equivalent to 50/100 which is clearly larger than 5/100.
Steps:
Compare two decimal numbers start with tenths place and then hundredths place and so on. If a decimal number has a greater digit in the tenths place then it is larger than a decimal with lesser digit in tenths place.
If the tenths places of both the decimal numbers are equal check for the hundredths place of both the numbers. Compare the hundredths place of both the decimal numbers, then the thousandths place and so on.
If each decimal place value is the same then the decimals are equal.
For example;
Decimal numbers 0.05 and 0.005 if compared, then 0.05 is greater than 0.005.

Place Value of Decimal numbers:
1) Decimal numbers, let’s say 0.649, have three digits after the decimal point. Each digit is a different place value.
2) The next digit after the decimal point is called the tenths place value. There are six tenths in the number 0.649.
3) The second digit resembles hundredths that are located in the number. The number 0.649 has four hundredths.
4) The third digit is the thousandths place.
Therefore, there are six tenths, four hundredths and nine thousandths in the number 0.649.

Rounding decimal number is same as rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they can be eliminated and the tenths place does not change.
For example, rounding 0.542 to the nearest tenth would give 0.5.
If the hundredths and thousandths places are more than 50, the tenths place is brought up by 1. The decimal 0.78 rounded to the nearest tenth is 0.8.

Let’s say the thousandths place of a decimal is less than 4. then the 4 is dropped and the hundredths place is kept unchanged. For example, rounding 0.123 to the nearest hundredth would give 0.12.

If the thousandths place is more than 5, the hundredths place is increased by one. The decimal 0.127 rounded to the nearest hundredth is 0.13.

Addition and Subtraction of Two or more decimal numbers:
Arithmetic operations in decimal numbers is nearly similar with the operations in other forms of numbers.
Addition:
Adding Decimals numbers is just like adding other forms of numbers.

Steps:
1) Always line up the decimal points one above the other when adding decimal numbers.

For example: 0.75
                   + 0.53
                 ___________
                 ___________
2) Put the decimal point in the proper place leaving space for the product digits for both left and right hand side of in your answer.
For example: 0.75
                   + 0.53
                   ___________
                   ___________

3) Add the numbers as done normally with whole numbers.

For example: 0.75
                   + 0.53
                  _____________
                   1.28
                   ____________


* Note that 12 that is acquired after adding 7 and 5 happens to shift the 1 before the decimal dot and 2 is written after the dot. This is because the 1 is added to the column consisting the number 0.

In order to add Decimals that have different numbers of decimal places take the following steps

Steps:

1)Place one digit below the other so that the bottom decimal point is directly below the top decimal point.
2) Add each column starting at the right side.
Example: Add 9.275 + 15.57
                      9.275
                  +15.57
                    15.845


Subtraction:
Subtracting two Decimal numbers is similar in process as what done with whole numbers.
Steps:
1) Put the decimal points of the greater number over the smaller number when subtracting decimal numbers. (Also read fraction to decimal converter)
   37.721
- 21.005
2) Subtract the numbers as done with whole numbers.
   37.721
- 21.005
  16.716
3) Put the decimal point in the proper place of the answer.


In order to multiply a three digit decimal by a one digit decimal number follow these steps
Steps:
1) Place one decimal number above the other so that they are placed on the right side sequentially vertical.
2) Avoid the decimal points for sometime and multiply the numbers like multiplying a three digit number by a one digit number.
0.529
0.7

3) Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger than 10 so place 6 above the center column and place three below the line in the right column.

     6
0.529
    0.7
       3
4) Multiply the digit in the top center column (2) by the digit in the center of the right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The units place value (0) of 20 is placed below the line and the tens place value (2) of the 20 is placed above the five.
          26
       0.529
 0.7
  03
5) The 5 of the top number is multiplied by the 7 of the multiplier (5*7=35). The two that was previously carried is added and 37 is placed below the line. At the start we disregarded the decimal places. Count the decimal places and move the decimal place to its proper location. There are three decimal places in 0.529 and one in the decimal 0.7 so move the decimal four places to the left to give the final answer of 0.3703.
               26
           0.529
          0.7
          0.3703

In upcoming posts we will discuss about Fractions in Grade IV and adding and subtracting integers worksheets. Visit our website for information on CBSE computer science syllabus