NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - True or False Questions

Question 49

Why the statement is TRUE

What is a fraction? A fraction is any number of the form (dfrac{a}{b}), where (a) and (b) are integers and (b eq 0).

Take two fractions:

(dfrac{a}{b})

(dfrac{c}{d})

To subtract them, first make the denominators the same.

(dfrac{a}{b} = dfrac{ad}{bd})

(dfrac{c}{d} = dfrac{bc}{bd})

Now subtract:

(dfrac{ad}{bd} - dfrac{bc}{bd} = dfrac{ad - bc}{bd})

Here, (ad - bc) is an integer and (bd) is a non-zero integer. So the result is of the form “integer ÷ non-zero integer,” which is a fraction.

Notes:

• Even if the result is a whole number, we can write it as (dfrac{k}{1}), so it’s still a fraction.
• If the result is negative, we can write it as (-dfrac{p}{q}), which is also a fraction.

Example:

(dfrac{5}{6} - dfrac{1}{3} = dfrac{5}{6} - dfrac{2}{6} = dfrac{3}{6} = dfrac{1}{2})