CLASS-6
MIXED FRACTION TO IMPROPER FRACTION

MIXED FRACTION TO IMPROPER FRACTION -

The concept of mixed fractions and improper fractions is related to representing the same quantity in different ways. Both types of fractions involve a whole number and a fractional part.

1. Mixed Fraction:- A mixed fraction is a combination of a whole number and a proper fraction (a fraction where the numerator is less than the denominator). It is expressed in the form: whole number + (numerator/denominator). For example, 2 3/4 is a mixed fraction, where 2 is the whole number, 3 is the numerator, and 4 is the denominator.
2. Improper Fraction:- An improper fraction is a fraction where the numerator is equal to or greater than the denominator. It represents a value greater than 1. For example, 7/4 is an improper fraction, where 7 is the numerator and 4 is the denominator.

Converting Mixed Fractions to Improper Fractions:-

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

Step 1:- Multiply the whole number by the denominator.

Step 2:- Add the result from Step-1 to the numerator.

Step 3:- Place the sum from Step-2 over the original denominator to get the improper fraction.

                                        1

Let's take an example: Convert 3 ------ to an improper fraction.

                                        2

Step 1:- Multiply the whole number (3) by the denominator (2) => 3*2 = 6

Step 2:- Add the result from Step 1 (6) to the numerator (1) => 6+1 = 7

Step 3:- Place the sum from Step 2 (7) over the original denominator (2) => 7/2

          1

So, 3 ------ is equal to 7/2 as an improper fraction.

          2

The concept of converting mixed fractions to improper fractions is an essential skill in mathematics, particularly in arithmetic and algebra. A mixed fraction consists of a whole number and a proper fraction (a fraction with a numerator smaller than its denominator). An improper fraction, on the other hand, has a numerator that is equal to or greater than its denominator.

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

Step 1:- Identify the mixed fraction. A mixed fraction is typically written

                      b

in the form of "a -----," where "a" is the whole number part, "b" is the

                      c

numerator of the proper fraction, and "c" is the denominator of the proper fraction.

Step 2:- Convert the mixed fraction to an improper fraction. To do this, multiply the whole number part by the denominator of the proper fraction and then add the numerator. The result will be the new numerator of the improper fraction, with the original denominator retained.

                                                             1

For example, let's say we have the mixed fraction 3 ------.

                                                             4

                                                1

Step 1:- Identify the mixed fraction: 3 -------

                                                4

Step 2:- Convert to an improper fraction: 3 * 4 + 1 = 12 + 1 = 13 The improper fraction is 13/4.

          1

So, 3 ------ as an improper fraction is 13/4.

          4

                                                               2

Here's another example with a larger whole number: 5 ------

                                                               7

                                             2

Step 1:- Identify the mixed fraction: 5 ------

                                                7

Step 2:- Convert to an improper fraction: 5 * 7 + 2 = 35 + 2 = 37 The improper fraction is 37/7.

          2

So, 5 ------  as an improper fraction is 37/7.

          7

Converting mixed fractions to improper fractions can be useful for various mathematical operations, especially when dealing with fractions in equations, comparisons, or simplifications.