16 (3)/(7)+(square )/(14)=(15)/(14) (4)/(16)-(1)/(8)=(5)/(16)

Let's solve the first equation step by step:<br /><br />Given:<br />\[<br />\frac{3}{7} + \frac{\square}{14} = \frac{15}{14}<br />\]<br /><br />First, we need to find a common denominator for the fractions on the left side. The common denominator for 7 and 14 is 14.<br /><br />Rewrite \(\frac{3}{7}\) with a denominator of 14:<br />\[<br />\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}<br />\]<br /><br />Now the equation becomes:<br />\[<br />\frac{6}{14} + \frac{\square}{14} = \frac{15}{14}<br />\]<br /><br />Combine the fractions on the left side:<br />\[<br />\frac{6 + \square}{14} = \frac{15}{14}<br />\]<br /><br />Since the denominators are the same, the numerators must be equal:<br />\[<br />6 + \square = 15<br />\]<br /><br />Solve for \(\square\):<br />\[<br />\square = 15 - 6 = 9<br />\]<br /><br />So, the value of \(\square\) is 9.<br /><br />Now let's solve the second equation:<br /><br />Given:<br />\[<br />\frac{4}{16} - \frac{1}{8} = \frac{5}{16}<br />\]<br /><br />First, rewrite \(\frac{1}{8}\) with a denominator of 16:<br />\[<br />\frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \frac{2}{16}<br />\]<br /><br />Now the equation becomes:<br />\[<br />\frac{4}{16} - \frac{2}{16} = \frac{5}{16}<br />\]<br /><br />Combine the fractions on the left side:<br />\[<br />\frac{4 - 2}{16} = \frac{2}{16}<br />\]<br /><br />Simplify the fraction:<br />\[<br />\frac{2}{16} = \frac{1}{8}<br />\]<br /><br />So, the equation \(\frac{4}{16} - \frac{1}{8} = \frac{5}{16}\) is incorrect. The correct result should be \(\frac{1}{8}\), not \(\frac{5}{16}\).