Understanding 1.2 As A Fraction: Converting Decimals To Fractions

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Discover how to convert 1.2 to a fraction and gain a comprehensive understanding of fractions, including their definition, reading methods, proper vs. improper fractions, mixed numbers, and techniques for simplifying fractions.

Understanding 1.2 as a Fraction

Definition of a Fraction

Fractions are a fundamental concept in mathematics that represent a part of a whole. They consist of two numbers separated by a line, with the number above the line called the numerator and the number below the line called the denominator. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

How to Read Fractions

Reading fractions may seem daunting at first, but it’s actually quite simple. To read a fraction, you simply say the numerator as a cardinal number and the denominator as an ordinal number. For example, 3/4 is read as “three-fourths” or “three over four”.

Proper Fractions vs. Improper Fractions

When discussing fractions, it’s important to understand the distinction between and improper fractions.

  • Proper fractions are fractions where the numerator is smaller than the denominator. For example, 3/4 is a proper fraction because 3 is smaller than 4. Proper fractions represent a part of a whole and are always less than 1.
  • Improper fractions are fractions where the numerator is equal to or greater than the denominator. For example, 5/4 is an improper fraction because 5 is greater than 4. Improper fractions represent a whole or more than a whole.

Mixed Numbers and Fractions

Mixed numbers are a combination of a whole number and a fraction. They are useful when dealing with quantities that are larger than one whole. For example, 2 1/4 is a mixed number, where 2 is the whole number and 1/4 is the fraction part.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction, then add the numerator. The result becomes the numerator of the improper fraction, with the denominator remaining the same. For example, to convert 2 1/4 to an improper fraction, you would multiply 2 by 4 (8), then add 1 to get 9. The improper fraction is 9/4.

Converting Decimals to Fractions

Decimals can also be expressed as fractions. To convert a decimal to a fraction, you need to determine the place value of the decimal and express it as a fraction with the appropriate denominator.

For example, to convert 0.5 to a fraction, the decimal is in the tenths place. Since there is only one decimal place, the denominator will be 10. Therefore, 0.5 can be expressed as 5/10.

Converting 1.2 to a Fraction

To convert a decimal like 1.2 to a fraction, we need to consider the place value of the decimal. In this case, the decimal is in the tenths place and the hundredths place.

To convert 1.2 to a fraction, we express it as the sum of its place values. The tenths place is 1/10 and the hundredths place is 2/100. Simplifying these fractions, we get 1/10 + 2/100 = 10/100 + 2/100 = 12/100.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD).

For example, to simplify the fraction 12/100, we find the GCD of 12 and 100, which is 4. Dividing both the numerator and the denominator by 4, we get 3/25. The simplified form of 12/100 is 3/25.

By understanding the definition of fractions, reading fractions correctly, distinguishing between proper and improper fractions, converting decimals to fractions, and simplifying fractions, you’ll have a solid foundation for working with fractions. Whether you’re solving math problems or using fractions in real-life situations, these concepts will help you navigate the world of fractions with confidence.

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