To express the fraction \(-\frac{40}{56}\) as a rational number with a numerator of \(-5\), follow these steps:
Start with the given fraction:
\(-\frac{40}{56}\)
Simplify the fraction by finding the greatest common divisor (GCD) of 40 and 56. The GCD of 40 and 56 is 8.
Divide both the numerator and the denominator by their GCD:
\(\frac{-40 \div 8}{56 \div 8} = \frac{-5}{7}\)
The simplified form of the fraction is \(-\frac{5}{7}\), which matches the requirement of having the numerator as \(-5\).
Thus, the answer is \(-\frac{5}{7}\), confirming that \(-\frac{5}{7}\) is equivalent to the given fraction \(-\frac{40}{56}\) when simplified.
By analyzing all the options, we can conclude that the correct option is \(-\frac{5}{7}\).
Similar Questions
- $(\sqrt{5} + \sqrt{7})^2$ is a:
- An irrational number between 3 and 5 is:
- Which of the following rational number lies between $\frac{1}{4}$ and $\frac{1}{2}$.
- Which of the following rational number lies between 9.2 and 10.5?
- The arrangement of rational numbers $-\frac{7}{10}, \frac{5}{-8}, \frac{2}{-3}$ in ascending order is:
Important Questions from Rational or Irrational Numbers
If \(\sqrt{1+\frac{\sqrt{3}}{2}}- \sqrt{1-\frac{\sqrt{3}}{2}}= c\) , then the value of c is:
If \(\frac{\sqrt{38-5\sqrt{3} } }{\sqrt{26+7\sqrt{3} } }= \frac{a+b\sqrt{3} }{23} \) , b > 0, then the value of (b – a) is:
If \( \frac{5}{4{\sqrt 2 }} + \frac{{3 + 2\sqrt 2 }}{{3 - 2\sqrt 2 }} - \frac{{3 - 2\sqrt 2 }}{{3 + 2\sqrt 2 }} = a + b\sqrt 2 \) , then what is the value of (3a + 4b)?
If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\) then the value of a + b is equal to:
If \(\frac{\sqrt{26-7\sqrt{3} } }{\sqrt{14+5\sqrt{3} } } = \frac{b+a\sqrt{3} }{11}\) , b > 0, then what is the value of \(\sqrt{(b-a)} \) ?
