Question

How do you simplify $\dfrac{9}{10}-\dfrac{1}{5}$ ? \[\]

Answer 1

Hint: We recall that we can add and subtract when the denominator of the given fractions are the same. We find the least common multiple of the given denominators to find the lowest common denominator. We convert the denominators of both the fractions to lowest common denominator and subtract the numerators. \[\]

Complete step-by-step solution:
We are asked to simplify the following numerical expression
\[\dfrac{9}{10}-\dfrac{1}{5}\]
We see that we are asked to subtract the fraction $\dfrac{1}{5}$ from fraction $\dfrac{9}{10}$. The denominators of the fraction are $10,5$. We know that we can subtract fractions only when they are like a fraction which means they must have the same denominator. We find the same denominator called the lowest common denominator as the least common multiple of denominators. Here the least common multiple of denominators $10=5\times 2,5$ is 10. So the lowest common denominator is 10.\[\]
Now we need to convert both the denominators to 10. We see that in $\dfrac{9}{10}$ the denominator is already 10. We convert the denominator of $\dfrac{1}{5}$ to 10 by multiplying 2 in the numerator and denominator as $\dfrac{1}{5}=\dfrac{1\times 2}{5\times 2}=\dfrac{2}{10}$. Now the expression simplifies to
\[\dfrac{9}{10}-\dfrac{1}{5}=\dfrac{9}{10}-\dfrac{2}{10}\]
Now we subtract the respective numerators while keeping the denominator same and have the simplification as
 \[\dfrac{9}{10}-\dfrac{1}{5}=\dfrac{9}{10}-\dfrac{2}{10}=\dfrac{9-2}{10}=\dfrac{7}{10}\]

Note: We note that if $\dfrac{a}{b}$ is a fraction then we can find its equivalent fraction as $\dfrac{a\times k}{b\times k}$ where $k$ is any non-zero integer. If $d$ is any common factor of $a,b$ we can also find the equivalent fraction of $\dfrac{a}{b}$ as $\dfrac{a\div d}{b\div d}$. The general-like fractions are given as $\dfrac{a}{b},\dfrac{c}{b}$. We add $\left( \dfrac{a}{b}+\dfrac{c}{b}=\dfrac{a+c}{b} \right)$and subtract $\left( \dfrac{a}{b}-\dfrac{c}{b}=\dfrac{a-c}{b} \right)$only when the fractions are like fraction. We should remember that if the least common multiple of two numbers where one is a multiple of other then greater number is the least common multiple.