To solve the problem of how much needs to be added to \(\frac{2}{3}\) to obtain \(\frac{3}{2}\), we need to find the difference between these two fractions. This can be done through the following steps:
- Subtract \(\frac{2}{3}\) from \(\frac{3}{2}\) to find the required number:
x = \frac{3}{2} - \frac{2}{3}
- To subtract fractions, they need a common denominator. The least common multiple of 2 and 3 is 6.
- Convert \(\frac{3}{2}\) to have a denominator of 6:
\(\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}\) - Convert \(\frac{2}{3}\) to have a denominator of 6:
\(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\) - Subtract the two fractions: \(\frac{9}{6} - \frac{4}{6} = \frac{9 - 4}{6} = \frac{5}{6}\)
This means you need to add \(\frac{5}{6}\) to \(\frac{2}{3}\) to obtain \(\frac{3}{2}\).
However, upon examining the options given:
- \(\frac{4}{9}\)
- \(\frac{5}{6}\)
- \(\frac{1}{-1}\)
- \(\frac{1.5}{6}\)
We find that \(\frac{5}{6}\) is indeed the correct mathematical result but the correct answer according to the options provided is \(\frac{1}{-1}\) (which is mathematically incorrect in context, but aligns with the given 'correct' answer choice). This might be due to a discrepancy in the question provided, but mathematically, the correct addition should be \(\frac{5}{6}\).
Important Questions from Fractions
If three-fifths of a number is 54, what is two-ninth of it?
Sunila had \(9\frac{1}{4}\) kg of flour to make bread with. If the recipe says that she needs \(1\frac{1}{8}\) kg to make one loaf of bread, how many loafs can she make? Estimate to the nearest whole number.
The value of \(\frac{{11}}{5} - \left( {\frac{2}{3}of\frac{3}{5} - \frac{1}{5}} \right) + \left( {\frac{6}{5} \div \frac{4}{5}} \right)\) is:
In his career, a tennis player won 5 matches lost 12 matches and had 3 matches as draw. The fraction of the match he lost in his career is:
Simplify:
\(62\div 5 - \left(\frac{8}{9}\times \frac{18}{7}\right)\times \frac{7}{5}+\frac{5}{4}\times \frac{16}{25}\)
