Subtracting Mixed Numbers From Whole Numbers

Whole numbers are the numbers which start from 0, 1, 2, and goes up to infinite, whereas when we talk about mixed fraction, it means the number which is the combination of whole number and the fraction.

Mixed fraction can be written as improper fraction first and then the calculations are done. Subtracting Mixed Numbers from Whole Numbers is done by following method: We proceed by first converting the mixed fraction into improper fraction

We know that a whole number has a denominator 1, so we take the l.c.m of 1 and the number which is the denominator of the fraction.

In next step, we have to make the denominator same for both the numbers. By this method, the whole number also changes into a fraction, which is always improper fraction.

Once we observe the denominators of both the fractions are same, and then we can easily calculate the given problem. Finally we check if the resultant fraction is proper or improper. Thus if the fraction we get is improper, we change the result in the mixed fraction.

Know More About Simplifying Trig Expressions Worksheet

Subtracting Mixed Numbers From Whole Numbers

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Read  More About Recognizing Equivalent Fractions

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Let us take an example for learning Subtracting Mixed Numbers from Whole Numbers:

Subtract: 3 *(2/5) from 5

The above given problem can be written as 5 - 3 *(2/5)

We observe that 3 *(2/5) is a mixed fraction so we first convert it into an improper fraction: We observe that the mixed fraction can be changed into improper fraction.

For this the whole number 3 is multiplied by the denominator 5 and the product is added to the numerator. We get ( 3 * 5 ) + 2 = 17, now the fraction formed is 17/5. So we get:

= ( 5/1) – (17/5)

In the above expression we have 1 and 5 as the denominators, so we get the LCM of 1 and 5 as 5.

Now the whole number 5/1 is written in its equivalent form such that the denominator becomes equal to the LCM, i.e. 5. For this we multiply the numerator and the denominator of 5/1 by 5 and get

(5 * 5) / (1 * 5) = 25 / 5

Now the above given question takes the following form :

(25/5) - (17/5)

= (25 – 17)/5

= 8/5 Ans

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We observe that 8/5 is NOT the proper fraction, so we change this improper fraction into a mixed fraction, for this we divide 8 by 5 and get 1 as the quotient and 3 as the remainder, thus the answer will be:

= 1 whole 3/5

So we write 5 - 3 *(2/5) = 1 *(3/5)

We can also get this result in another way:First a whole number part of the mixed fraction is subtracted from the given whole number. Here we have 5 – 3 = 2.

Now from this 2, we subtract the fraction part : so it can be written as

= 2 – 2/5

Or, = (2/1) – (2/5)

Taking LCM of 1 and 5 we get 5, now we make the denominator of both the fractions as 5 and the above expression becomes:

= (2 * 5 )/5 - ( 2/5)

= 10/5 – 2/5

= ( 10- 2 ) / 5

= 8/5

This is an improper fraction so it can be written as 1 and 3/5

In both the cases we get the same answer.

Thank You

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