Question

How do you subtract a negative fraction from a positive fraction?

Answer 1

Hint: A fraction is of the form $ \dfrac{p}{q} $ , the two numbers in a fraction are divided by a horizontal line, the number on the upper side of the horizontal line “p” is called the numerator and the number on the lower side “q” is called the denominator. For adding or subtracting two fractions, we first take the least common factor of the denominators of the two fractions that is the smallest number divisible by both the numbers. After finding the common denominator for the two fractions, we multiply the numerators with the quotient obtained on dividing the LCM by its denominator and then perform the given arithmetic operation like addition, subtraction, multiplication and division in the numerator.

Complete step-by-step answer:
Let the negative fraction be $ - \dfrac{a}{x} $ and positive fraction be $ \dfrac{b}{y} $ then we can subtract this negative fraction from the positive fraction as follows –
 $ \dfrac{b}{y} - ( - \dfrac{a}{x}) = \dfrac{b}{y} + \dfrac{a}{x} $
Now, x and y are unknown numbers so the LCM of x and y is xy, after taking the LCM, we multiply b with x and a with y –
 $ \dfrac{{bx + ay}}{{xy}} $
Hence, this way we subtract a negative fraction from a positive fraction.

Note: Numbers are of two types – real numbers and imaginary numbers, the numbers that can be shown on a number line are called real numbers. Fractions are real numbers as they are shown on the number line. The numbers on the left side of the zero are negative and the numbers on the right side are positive. When we multiply two numbers, we multiply their sign too. The signs are multiplied as (+)(+)=(+), (+)(-)=(-), (-)(+)=(-) and (-)(-)=(-) that’s why $ a - ( - b) = a + b $ .