What Does It Mean to Simplify Fractions?

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Simplify Fractions

Simplifying a fraction means expressing a fraction in a simple form so that its numerator and denominator have only one common factor and that is 1. Simplification of a fraction is an important step in solving problems related to fractions. We can make a large value fraction to its simplest form by following the process of simplifying fractions. It is important to note that as we simplify a fraction, the value of the fraction remains unchanged. In other words, the simplest form of fraction and the actual fraction are equivalent fractions. 

For example, the fraction 2/5 is in the simplest form of fraction because 2 and 5 have no common factor except 1. 

The process of simplifying a fraction involves the method using the highest common factor. The steps for simplifying the fraction are given below. 

Find the factors of both numerator and denominator and write down the factors of both separately.

  • Find out the highest common factor (HCF) of numerator and denominator.
  • Divide both the numerator and denominator by their highest common factor found in the above step.
  • The result thus obtained gives the simplest form of the original fraction.

For example, we must simplify the fraction 16/28. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 28 are 1, 2, 4, 7, 14, and 28. So the highest common factor of 16 and 28 is 4. Dividing the numerator 16 and the denominator 28 by 4, we get the fraction 4/7 which is the simplest form of the fraction 16/28. 

In order to simplify a mixed fraction, we need to simplify only the fraction part of the mixed fraction using the above method and use it along with the integer part to get the simplified form. The steps for simplifying mixed fractions are explained below.

  • Find the highest common factor (HCF) of the numerator and denominator of the fraction part.
  • Divide both the numerator and the denominator by HCF to get the simplified fraction.
  • Write the mixed fraction using the whole and the simplified fraction which gives the simplest form of the mixed fraction.

DECIMAL NUMBERS

In mathematics, decimal numbers are another way of representing fractions. A decimal number consists of a whole part and a decimal part. These parts are separated by a point/decimal. The number of digits in the decimal part of a decimal number denotes the decimal places.

For example, 12.345 is a decimal number in which 12 is the whole number and 345 is the decimal part. It has three decimal places. Again, 0.89 is also a decimal number in which the whole part is zero and the decimal part is 89. This number has two decimal places.

In the above examples, 12.345 can be considered as a decimal number representing a mixed fraction which is a combination of a whole part denoted by 12 and a proper fraction denoted by 0.345. The decimal number 0.67 represents a proper fraction with no whole part in it.

In decimals, as we look from left to right after the decimal point is located, the place value of digits will get divided by 10, so the decimal place value measures tenth, hundredth, etc. Thus, the decimal form 0.7 means 7/10, and the decimal from 0.13 refers to 13/100. 

Types of Decimal Numbers

Decimal Numbers can be of different kinds. These are as follows:  

Recurring Decimal Numbers (Repeating decimal digits)

Example: 3.241241 

Non-Recurring Decimal Numbers (Non-Repeating decimal digits)

Example: 2.1438

Like Decimal Numbers (Decimals having the same decimal places)

Example: 5.02. 7.81, 13.75 are like decimals as all of them have two decimal places.

Unlike Decimal Numbers (Decimals having different decimal places)

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Example: 1.5, 6.08, 25.137 are unlike decimals having different decimal places.

Decimal is a confusing concept and can be learned easily through practice and the right guidance. You can log on to cuemath.com to understand this in a fun way.

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