Question

Write ${\displaystyle \frac{-14}{42}}$ in the form so that the numerator is equal to – 70.

Answer 1

Hint: Now to convert the given fraction into a fraction with numerator – 70 we will have to multiply the numerator and denominator by some appropriate number. to find the appropriate number we will divide – 70 by – 14. Hence we can convert the fraction into the required fraction.

Complete step by step answer:
First let us understand the meaning of fractions.
Fractions are nothing but a part of a whole.
For example consider the fraction ${\displaystyle \frac{3}{4}}$ here the fractions means 3 parts out of 4. Now here in this fraction 3 is called the numerator of the fraction and 4 is called the denominator of the fraction.
Now when we multiply any number to the numerator and denominator the value of fraction does not change.
Hence let us say we multiply 2 then ${\displaystyle \frac{3\times 2}{4\times 2}}={\displaystyle \frac{6}{8}}$ is same fraction as ${\displaystyle \frac{3}{4}}$ .
Hence by multiplying or dividing the numerator and denominator by common number the value of fraction does not change.
Now consider the given fraction ${\displaystyle \frac{-14}{42}}$ . Here the numerator of the fraction is – 14 and the denominator of the fraction is 42.
Now we want the numerator of this fraction to be – 70.
Hence to do so we will multiply the numerator with a number such that the multiplication becomes – 70.
Let the required number be n.
Hence we want $-14\times n=-70$ .
Dividing the equation by – 14 we get n = 5.
Now that we have the required number we will multiply the numerator and denominator by 5.
Hence we get ${\displaystyle \frac{-14\times 5}{42\times 5}}={\displaystyle \frac{-70}{210}}$ .
Hence the required fraction is ${\displaystyle \frac{-70}{210}}$ .

Note: Note that when we add and subtract the fractions their denominator must be the same. For fractions with the same denominator we have ${\displaystyle \frac{a}{b}}\pm {\displaystyle \frac{c}{b}}={\displaystyle \frac{a\pm c}{b}}$ . If we have fractions with different denominators we will multiply the numerator and denominator by LCM of denominators so that we get common denominators.