Calculating the Sum of Fractions
The question asks for the sum of three fractions: $\frac{1}{3}$, $\frac{4}{3}$, and $\frac{3}{4}$.
Step-by-Step Calculation
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First, add the fractions that share a common denominator:
$ \frac{1}{3} + \frac{4}{3} = \frac{1+4}{3} = \frac{5}{3} $
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Now, add the result ($\frac{5}{3}$) to the remaining fraction ($\frac{3}{4}$):
$ \frac{5}{3} + \frac{3}{4} $
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To add these fractions, find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
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Convert the fractions to equivalent fractions with the denominator 12:
- $ \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} $
- $ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $
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Add the numerators of the equivalent fractions:
$ \frac{20}{12} + \frac{9}{12} = \frac{20+9}{12} = \frac{29}{12} $
Therefore, the sum of $\frac{1}{3}$, $\frac{4}{3}$, and $\frac{3}{4}$ is $\frac{29}{12}$.
Similar Questions
- $1.236576576...$
can be written in the form of: - 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?
- 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?
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.
\(\frac{3}{5}\)
