Basic Concepts of Fractions

Basics of Fractions

Basic Concepts of Fractions

Last Updated on Nov 18, 2019

A fraction simply tells us how many parts of a whole we have. You can recognize a fraction by the slash that is written between the two numbers. We have a top number, the numerator, and a bottom number, the denominator.

For example, 3/6 is a fraction. You can write it with a slanted slash like we have or you can write the 1 on top of the 2 with the slash between the two numbers. The 3 is the numerator, and the 6 is the denominator.

What does this fraction mean?

Well, if we picture a pizza, the bottom number tells us how many slices to slice the pizza, and the top number tells us how many of those slices we can have. So 3/6 tells us that we have sliced our pizza into six slices, and we can take three of those slices. Isn't that half of the pizza? So 3/6 of a pizza is half a pizza!

Fraction

The most proper way to write a fraction is in the vertical format, equation image indicator. The slanted format, a/b, is for writing fractions in a typed sentence. Many students who learn to write fractions only in the slanted form have problems interpreting mixed numbers and working with rational expressions in algebra.

Decimal numbers
A decimal number, in general, has two parts:

The integer part on the left of the decimal point, and the fractional part on the right of the decimal point.

For example, in 72.3241, the integer part is 72 and the fractional part is, 0.3241.

The special characteristic of the fractional part is, its value is always greater than zero and less than 1. In other words,

0 < Fractional part < 1.

It cannot be equal to 0 or 1. In case that happens, the fractional part doesn't remain any more a fractional part.

Place values of the fractional part of a decimal number
We know the place values of an integer follow the pattern,

100, 101, 102, 103,...., the power of 10 increasing by 1 from right to left all the way up indefinitely.

For the fractional part, a similar and complementary system makes the place value system whole.

The power of 10 in place values for the fractional part decreases by 1 starting from −1 all the way down indefinitely as a mirror image of the positive powers of 10 in the place values for integers, but in this case of the fractional part, from left to right.

Thus the first digit on the left of the decimal point, the unit's digit with the power of 10 as 0, is the center point.

All place values on its left have monotonously increasing (each increment step +1) positive powers of 10. Conversely, all place values on its right have monotonously decreasing (each decrement step −1) negative powers of 10.

The fractional part place values are,

10−1, 10−2, 10−3, 10−4, 10−5, 10−6.... decreasing all the way down the negative part of the number line.

Thus the integer part has place values with powers of 10 as positive Whole numbers, [0, 1, 2, 3, 4, 5, ....] and the fractional part has place values with powers as negative of the natural numbers, [-1, -2, -3, -4, ......]. These two parts then perfectly join together to form place value powers of 10 as the complete number line with non-fraction values.

For Example,

43.82=4×101+3×100+8×10−1+2×10−2.

This video lays out the basics of fractions. Understanding this topic well is necessary to solve questions that are asked in various competitive exams in the Logical Reasoning and Quantitative Aptitude section - applicable to CAT, XAT, MAT, SNAP, IIFT, CLAT, AILET, DU LLB, any other entrance exam as well.
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