Which one among the following is the largest?
11/14
Finding the Largest Fraction: Step-by-Step Comparison
To find the largest fraction among the given options, we can compare them. One common method for comparing fractions is to convert each fraction into its decimal equivalent. This allows for a direct comparison of their values.
Let's convert each of the given fractions into decimal form:
Decimal Conversion of Fractions
- For \( \frac{7}{9} \): Divide 7 by 9. \( \frac{7}{9} \approx 0.777... \) (It's a repeating decimal)
- For \( \frac{11}{14} \): Divide 11 by 14. \( \frac{11}{14} \approx 0.7857... \)
- For \( \frac{3}{4} \): Divide 3 by 4. \( \frac{3}{4} = 0.75 \)
- For \( \frac{10}{13} \): Divide 10 by 13. \( \frac{10}{13} \approx 0.7692... \)
Comparing the Decimal Values
Now we have the approximate decimal values for each fraction:
- \( \frac{7}{9} \approx 0.777 \)
- \( \frac{11}{14} \approx 0.7857 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{10}{13} \approx 0.7692 \)
Let's list these decimal values in ascending order to clearly see which one is the largest:
\( 0.75 < 0.7692 < 0.777... < 0.7857... \)
| Fraction | Decimal Value (Approx.) |
|---|---|
| \( \frac{3}{4} \) | 0.75 |
| \( \frac{10}{13} \) | 0.7692 |
| \( \frac{7}{9} \) | 0.777... |
| \( \frac{11}{14} \) | 0.7857... |
From the comparison, the largest decimal value is approximately 0.7857, which corresponds to the fraction \( \frac{11}{14} \).
Therefore, the largest fraction among the given options is \( \frac{11}{14} \).
Revision Table: Comparing Fractions for Size
| Fraction | Calculation | Decimal (Approx.) | Rank (Largest = 1) |
|---|---|---|---|
| \( \frac{7}{9} \) | \( 7 \div 9 \) | 0.777... | 3 |
| \( \frac{11}{14} \) | \( 11 \div 14 \) | 0.7857... | 1 |
| \( \frac{3}{4} \) | \( 3 \div 4 \) | 0.75 | 4 |
| \( \frac{10}{13} \) | \( 10 \div 13 \) | 0.7692... | 2 |
Additional Information: Other Ways to Compare Fractions
While converting to decimals is straightforward, here are other methods to compare fractions:
- Finding a Common Denominator: Convert all fractions to equivalent fractions with the same denominator (the least common multiple of all denominators). Then, compare the numerators. The fraction with the largest numerator is the largest. For example, to compare \( \frac{3}{4} \) and \( \frac{2}{3} \), the common denominator is 12. \( \frac{3}{4} = \frac{9}{12} \) and \( \frac{2}{3} = \frac{8}{12} \). Since 9 > 8, \( \frac{3}{4} > \frac{2}{3} \).
- Cross-Multiplication: To compare two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), compare \( a \times d \) and \( b \times c \).
- If \( a \times d > b \times c \), then \( \frac{a}{b} > \frac{c}{d} \).
- If \( a \times d < b \times c \), then \( \frac{a}{b} < \frac{c}{d} \).
- If \( a \times d = b \times c \), then \( \frac{a}{b} = \frac{c}{d} \).
- Comparing with a Benchmark: Compare fractions to a known value like \( \frac{1}{2} \) or 1. For instance, \( \frac{3}{4} \) is larger than \( \frac{1}{2} \) because \( 3 \times 2 > 4 \times 1 \).
Choosing the best method depends on the fractions you are comparing. Converting to decimals is often easiest when comparing multiple fractions directly, as done in this problem finding the largest fraction.
Similar Questions
What is the value of \(\sqrt[3]{{4\frac{{12}}{{125}}}}\) ?
If \(\frac{{\rm{a}}}{{\rm{b}}} = \frac{1}{3},\frac{{\rm{b}}}{{\rm{c}}} = 2,\frac{{\rm{c}}}{{\rm{d}}} = \frac{1}{2},\frac{{\rm{d}}}{{\rm{e}}} = 3\) and \(\frac{{\rm{e}}}{{\rm{f}}} = \frac{1}{4}\) , then what is the value of \(\frac{{{\rm{abc}}}}{{{\rm{def}}}}?\)
If \(\frac{{36}}{{11}} = 3\; + \;\frac{1}{{x\; + \;\frac{1}{{y\; + \;\frac{1}{z}}}}}\) , where x, y and z are natural numbers then what is (x + y + z) equal to?
What is \(\frac{{{6^2} + \;{7^2} + \;{8^2} + \;{9^2} + \;{{10}^2}}}{{\sqrt {7\; + \;4\sqrt 3 \;} - \;\sqrt {4\; + \;2\sqrt 3 } }}\) equal to?
In an examination, a student was asked to divide a certain number by 8. By mistake he multiplied it by 8 and got the answer 2016 more than the correct answer. What was the number?
What is \(\sqrt {1 + \frac{1}{{{1^{2}}}} + \frac{1}{{{2^{2}}}}} + \sqrt {1 + \frac{1}{{{2^{2}}}} + \frac{1}{{{3^{2}}}}} + \ldots \ldots .. + \sqrt {1 + \frac{1}{{{{2007}^{2}}}} + \frac{1}{{{{2008}^{2}}}}}\) equal to?
If \(x\, = \,7\, + \,4\sqrt 3 \) , then what is the value of \(\sqrt x \, + \,\frac{1}{{\sqrt x }}\) ?
What is \(\rm \frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)}\) equal to ?
If \(x + \frac{1}{{1 + \;\frac{1}{{2 + \;\frac{1}{3}}}}} = 2,\) then what is x equal to?
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.
\(\frac{3}{5}\)
