Question

clue 3: start at $2\frac{5}{8}$. move $\frac{7}{8}$ to the right. complete the equation to show your new location as a mixed number. $2\frac{5}{8} + \frac{7}{8} = \boxed{?} \frac{\boxed{?}}{\boxed{?}}$

Explanation:

Step1: Add the fractions

First, we add the fractional parts of the mixed number and the fraction. The mixed number is \(2\frac{5}{8}\) and we are adding \(\frac{7}{8}\). So we add the numerators of the fractions: \(5 + 7 = 12\), so the sum of the fractions is \(\frac{12}{8}\).

Step2: Simplify the fraction and add to the whole number

Now, simplify \(\frac{12}{8}\). We can divide numerator and denominator by 4, but also note that \(\frac{12}{8}=1\frac{4}{8}\) (since \(12\div8 = 1\) with a remainder of 4). Now we add this to the whole number part of the original mixed number, which is 2. So \(2+1 = 3\), and the remaining fraction is \(\frac{4}{8}\), which can be simplified to \(\frac{1}{2}\), but wait, actually, let's do it step by step. Wait, originally, \(2\frac{5}{8}+\frac{7}{8}=2+\frac{5 + 7}{8}=2+\frac{12}{8}\). Now, \(\frac{12}{8}=1\frac{4}{8}\), so \(2 + 1\frac{4}{8}=3\frac{4}{8}\), and \(\frac{4}{8}\) simplifies to \(\frac{1}{2}\), but actually, maybe we can just keep it as \(\frac{4}{8}\) or simplify. Wait, no, let's check again. Wait, \(5 + 7 = 12\), so \(\frac{12}{8}\). Now, \(12\div8 = 1\) with a remainder of 4, so \(\frac{12}{8}=1\frac{4}{8}\). Then, adding to the whole number 2: \(2+1\frac{4}{8}=3\frac{4}{8}\). But \(\frac{4}{8}\) can be simplified to \(\frac{1}{2}\), but maybe the problem just wants the fraction as is or simplified. Wait, but let's do it correctly. So \(2\frac{5}{8}+\frac{7}{8}=\frac{2\times8 + 5}{8}+\frac{7}{8}=\frac{16 + 5}{8}+\frac{7}{8}=\frac{21}{8}+\frac{7}{8}=\frac{28}{8}\). Now, \(\frac{28}{8}\) as a mixed number: divide 28 by 8. 8*3 = 24, remainder 4, so \(\frac{28}{8}=3\frac{4}{8}\), which simplifies to \(3\frac{1}{2}\), but \(\frac{4}{8}\) is also correct. Wait, but let's check the steps again. Wait, the first step: add the numerators of the fractions when the denominators are the same. So \(2\frac{5}{8}+\frac{7}{8}=2+\frac{5 + 7}{8}=2+\frac{12}{8}\). Then, \(\frac{12}{8}=1\frac{4}{8}\), so \(2 + 1\frac{4}{8}=3\frac{4}{8}\). So the mixed number is \(3\frac{4}{8}\), which can be simplified to \(3\frac{1}{2}\), but maybe the problem accepts \(3\frac{4}{8}\) or simplified. Wait, but let's see, the original problem has the boxes: the first box is the whole number, the second is the numerator, the third is the denominator. So let's do it:

\(2\frac{5}{8}+\frac{7}{8}\):

First, add the fractional parts: \(\frac{5}{8}+\frac{7}{8}=\frac{12}{8}\).

Now, \(\frac{12}{8}=1\frac{4}{8}\) (since 12 divided by 8 is 1 with remainder 4).

Now, add the whole number part: 2 + 1 = 3, and the remaining fraction is \(\frac{4}{8}\).

So the mixed number is \(3\frac{4}{8}\), which can be simplified to \(3\frac{1}{2}\), but \(\frac{4}{8}\) is also correct. Wait, but let's check the arithmetic again. \(2\frac{5}{8}\) is equal to \(\frac{21}{8}\) (because 28 + 5 = 21). Then, \(\frac{21}{8}+\frac{7}{8}=\frac{28}{8}\). Now, \(\frac{28}{8}\) as a mixed number: 28 divided by 8 is 3 with a remainder of 4 (because 83 = 24, 28 - 24 = 4), so \(\frac{28}{8}=3\frac{4}{8}\). So the whole number is 3, the numerator is 4, the denominator is 8.

Answer:

\(2\frac{5}{8}+\frac{7}{8}=\boxed{3}\frac{\boxed{4}}{\boxed{8}}\) (or simplified, \(3\frac{1}{2}\), but since the problem has three boxes, the first for whole number, second numerator, third denominator, so 3, 4, 8)