Question

How do you simplify $1\dfrac{1}{4}. - \dfrac{5}{9}$ ?

Answer 1

Hint: Here we see a ‘dot’ between two fractional numbers $1\dfrac{1}{4}$ and$ - \dfrac{5}{9}$. This ‘dot’ denotes ordinary multiplication between two numbers, i.e. we have to multiply the given two fractions. First we have to change the first fraction having an integer part into a simple fraction.

Complete step-by-step solution:
We are given the expression $1\dfrac{1}{4}. - \dfrac{5}{9}$
Interpreting the ‘dot’ between the two fractional numbers as a sign of multiplication, we have to multiply the two given fractional numbers $1\dfrac{1}{4}$ and $ - \dfrac{5}{9}$.
The first fraction is $1\dfrac{1}{4}$. In fact, this is a mixed fraction. A mixed fraction is a combined form of a non-zero integer and a fraction, here $1$ and $\dfrac{1}{4}$. A mixed fraction can be changed into a simple fraction by the process: \[\dfrac{{(Denominator \times Integer) + Numerator}}{{Denominator}}\]
Thus, $1\dfrac{1}{4} = \dfrac{{(4 \times 1) + 1}}{4} = \dfrac{{4 + 1}}{4} = \dfrac{5}{4}$
Now we have to multiply $\dfrac{5}{4}$ and $ - \dfrac{5}{9}$,
i.e. $\dfrac{5}{4} \times ( - \dfrac{5}{9})$
To multiply two fractions, we multiply the numerators of both the fractions and keep the result in the numerator, and then we multiply the denominators of both the fractions and keep the result in the denominator of the resulting fraction.
For numerator: $5 \times 5 = 25$
For denominator: $4 \times 9 = 36$
When we multiply a positive number with a negative number, we get a negative number as a result. So, a negative sign will remain in the resulting fraction.
Thus, we get, $\dfrac{5}{4} \times ( - \dfrac{5}{9}) = - \dfrac{{25}}{{36}}$
Hence, the simplified form of the given expression is $ - \dfrac{{25}}{{36}}$

Note:In this question we have a negative sign after the ‘dot’ so one can mistake it for a question of subtraction if the ‘dot’ is missed in hurry. A mixed fraction has to be converted into simple fractional form to perform mathematical operations. This can be also be done simply by adding the integer part and the fraction part, i.e. for $1\dfrac{1}{4}$ we can also write it as $1 + \dfrac{1}{4} = \dfrac{5}{4}$.