Ordering Fractions Ascendingly
To arrange the fractions $\frac{2}{3}, \frac{1}{2},$ and $\frac{1}{6}$ in ascending order, we need to compare their values. This is easiest done by converting them to equivalent fractions with a common denominator.
Finding Common Denominator
The denominators are 3, 2, and 6. The least common multiple (LCM) of these numbers is 6. We will convert each fraction so it has a denominator of 6.
- For $\frac{2}{3}$: Multiply the numerator and denominator by 2. $ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} $
- For $\frac{1}{2}$: Multiply the numerator and denominator by 3. $ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} $
- For $\frac{1}{6}$: This fraction already has the denominator 6. $ \frac{1}{6} $
Comparing Numerators
Now we compare the fractions based on their numerators:
- $\frac{4}{6}$ (from $\frac{2}{3}$)
- $\frac{3}{6}$ (from $\frac{1}{2}$)
- $\frac{1}{6}$ (from $\frac{1}{6}$)
Comparing the numerators 4, 3, and 1, the ascending order is 1, 3, 4.
Final Ascending Order
Arranging the fractions according to their ordered numerators gives us the ascending order:
$ \frac{1}{6}, \frac{3}{6}, \frac{4}{6} $Replacing the equivalent fractions with the original ones, the ascending order is:
$ \frac{1}{6}, \frac{1}{2}, \frac{2}{3} $Similar Questions
- $1.236576576...$
can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
- A beautician's income includes her salary and the tips she gets for her services. During a particular week, if her tips were $\frac{5}{4}$ of her salary, then what fraction of her income came from the tips?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
