Question

choose yes or no to tell if the fraction \\(\frac{1}{2}\\) will make each equation true.
\\(\underline{quad} + \frac{9}{9} = \frac{3}{2}\\) \quad \\(\frac{1}{5} + \underline{quad} = \frac{1}{7}\\)
\\(\frac{1}{42} + \frac{10}{21} = \underline{quad}\\) \quad \\(\frac{1}{26} + \frac{6}{13} = \underline{quad}\\)
\\(\circ\\) no
does the fraction \\(\frac{1}{2}\\) make the equation \\(\frac{1}{5} + \underline{quad} = \frac{1}{7}\\) true?
\\(\circ\\) yes
\\(\circ\\) no
click to select your answer and then click check answer.
1 part remaining

Explanation:

Step1: Calculate left - hand side with $\frac{1}{2}$

Substitute the blank with $\frac{1}{2}$ in the equation $\frac{1}{5}+\underline{\quad}=\frac{1}{7}$. Then the left - hand side is $\frac{1}{5}+\frac{1}{2}$.
To add these two fractions, we find a common denominator, which is $5\times2 = 10$.
$\frac{1}{5}+\frac{1}{2}=\frac{1\times2}{5\times2}+\frac{1\times5}{2\times5}=\frac{2}{10}+\frac{5}{10}=\frac{2 + 5}{10}=\frac{7}{10}$.

Step2: Compare with right - hand side

The right - hand side of the equation is $\frac{1}{7}$.
We know that $\frac{7}{10}
eq\frac{1}{7}$ (because cross - multiplying, $7\times7 = 49$ and $10\times1=10$, and $49
eq10$).

Answer:

No