Question

How do you combine like terms to simplify the expression \[\dfrac{7}{8} + \dfrac{9}{{10}} - 2m - \dfrac{3}{5}\] ?

Answer 1

Hint: In the given question, we have been asked to simplify a quadratic expression which has a single variable. Fractions can only be added or subtracted if they are of the same denominators. If the denominators are not the same, you need to find the least common multiple (LCM) of the two denominators. Then, make all the denominators the same, by multiplying the numerator and denominator by the same number. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both the integers. It can be calculated using two methods which are- Prime factorization method and grid method.

Complete step by step solution:
We are given,
\[\dfrac{7}{8} + \dfrac{9}{{10}} - 2m - \dfrac{3}{5}\]
Now we’ll bring all the like terms together to simplify it,
\[ \Rightarrow \dfrac{7}{8} + \dfrac{9}{{10}} - \dfrac{3}{5} - 2m\]
To solve the following fraction, we need to make the denominator of each fraction the same. To make a common denominator we need to find LCM. LCM of $ 8,10\;and\;5 $ is $ 40 $ .
To make the denominator $ 40 $ , we’ll multiply the numerator and denominator by the same number.
\[ \Rightarrow \dfrac{{35}}{{40}} + \dfrac{{36}}{{40}} - \dfrac{{24}}{{40}} - 2m\]
\[ \Rightarrow \dfrac{{35 + 36 - 24}}{{40}} - 2m\]
\[ \Rightarrow \dfrac{{47}}{{40}} - 2m\]
This is the required expression.
So, the correct answer is “\[ \dfrac{{47}}{{40}} - 2m\]”.

Note: If numerator and denominator are multiplied or divided by the same number, then the value of fraction does not change. Terms can only be operated if they are alike, a fraction and a variable cannot be operated together. While writing the answer in fraction form, always check whether it is in simplest form or not, if it is not in its simplest form then convert it into its simplest form.