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
- The numerator of a fraction is increased by $20\%$ and the denominator is decreased by $50\%$. If the resultant fraction is $\frac{5}{6}$, then what will be the original fraction?
- $1.236576576...$
can be written in the form of: - What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
- What is the positive difference between $\frac{5}{16}$ and its reciprocal?
- 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.
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- Solve the following:
$(0.\overline{5} + 0.\overline{6} + 0.\overline{7} + 0.\overline{8}) = ?$ - 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?
- 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.
Important Questions from Fractions
Which fraction among the following is the least ?
\(\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}\)
Find the value of the following expression:
\(\frac{{3 \div 1 \times 2 + 5 - 2}}{{3 \times 3 - 2}}\)
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
