# IMO Class 5 Chapter 2:Fractions and Decimals

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## IMO Class 5 Chapter 2:Fractions and Decimals detailed notes

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects can be the whole. When we cut a piece of cake in real life from the entire cake, the portion represents the fraction of the cake. The word “fraction” is derived from Latin. “Fractus” means “broken” in Latin. The fraction was expressed verbally in earlier times. It was later presented in numerical form.

A portion or section of any quantity is another name for the fraction. It is indicated by the symbol “/,” such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the upper part the numerator. The definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and numerous examples with fully explicated solutions are all covered in this article.

### What are Fractions?

Definition 1: A fraction is a unit of measurement that identifies the components of a whole.

Definition 2: A fraction is a number that symbolizes a portion of a whole.

In general, the whole can be any particular thing or value, and the fraction can be a portion of any quantity out of it.

The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number represents the total number of parts, while the top number represents the number of chosen or shaded portions of the whole.

Fractions are essential to our daily lives. You will encounter fractions frequently in everyday life. Whether we want to or not, we have to share that delicious pizza with our loved ones. Four slices for three people. It will be more enjoyable and exciting if you can easily learn and visualize fractions. For instance, if you divide an apple into two pieces, each piece will represent a fraction (equal to 1/2).

### Parts of Fractions

• There are two components to fractions: a numerator and a denominator.
• The numerator, or upper portion of the fraction, denotes the various parts of the fraction.
• The lower or bottom portion, known as the denominator, represents all of the components into which the fraction is divided.
• For instance, if 3/4 is a fraction, the numerator is 3 and the denominator is 4.

### Properties of fractions

A fractional number has some of the same significant properties as real numbers and whole numbers. As follows:

• Fractional addition and multiplication are consistent with commutative and associative properties.
• Fractional addition’s identity element is 0 and fractional multiplication’s identity element is 1.
• B/a is the multiplicative inverse of a/b, where a and b are elements that should not be zero.
• The distributive property of multiplication over addition is observed in fractional numbers.

### What are Decimals?

One of the number types in algebra that has a whole number and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction.

An example of a decimal number is 34.5.

In this case, the whole number part is 34, and the fractional part is 5.

The decimal point is “.”.

Let’s talk about a few more instances.

The decimal representation of the number “thirty-four and seven-tenths” is given below:

Among Ones and Tenths is where the decimal point is located.

3 tens, 4 ones, and 7 tenths make up the number 34.7.

### Properties of Decimals

• Following are some crucial characteristics of decimal numbers when performing division and multiplication operations:
• No matter what order any two decimal numbers are multiplied, the result is always the same.
• Any order of adding a whole number and a decimal number produces the same result.
• A decimal fraction’s product when multiplied by one is that same decimal fraction.
• A decimal fraction multiplied by 0 produces a result of zero (0).
• The result of dividing a decimal number by one is the decimal number itself.
• When a decimal number is divided by itself, the result is 1, or 1.
• Any division of 0 by decimal results in a quotient of 0.
• Since there is no reciprocal of 0, it is impossible to divide a decimal number by 0.

### Importance of IMO

The Math Olympiad also referred to as the International Maths Olympiad (IMO), is a very helpful test for students who want to get better at math. It guarantees accurate calculations in the shortest amount of time. It presents challenging and difficult questions to the class. They gain the self-assurance needed to get over their fear of numbers. They become flawless in a variety of concepts, including trigonometry, algebra, measurements, theorems, and data handling, among others. One of the competitions that benefit students the most by uniting them on one platform is this one. It cultivates in young minds the skills of analytical thinking and problem-solving. Children’s strengths and weaknesses are revealed by practicing a variety of problems from the Math Olympiads. It gives more insight into the areas that need more practice.

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