Question

follow the three clues to find a hidden treasure. use the number line show eighths to help. 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. $2\frac{5}{8}+\frac{7}{8}=\square\frac{\square}{\square}$

Explanation:

Step1: Add the fractional parts

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: \(5 + 7 = 12\), and the denominator remains \(8\). So we have \(\frac{5}{8}+\frac{7}{8}=\frac{12}{8}\).

Step2: Simplify the fraction and adjust the whole number

Now, we simplify \(\frac{12}{8}\). We can divide both the numerator and the denominator by \(4\), but also, we know that \(\frac{12}{8}=1\frac{4}{8}\) (because \(12\div8 = 1\) 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 also be simplified further, but for the mixed number form here, we can use \(\frac{4}{8}\) or simplify to \(\frac{1}{2}\), but let's follow the steps with the given denominator). Wait, actually, let's do it step by step. The original mixed number's whole part is \(2\), and we have \(\frac{12}{8}\) from the fraction addition. \(\frac{12}{8}=1\frac{4}{8}\), so adding to the whole number: \(2 + 1\frac{4}{8}=3\frac{4}{8}\). Alternatively, we can think of \(2\frac{5}{8}+\frac{7}{8}=2+\frac{5 + 7}{8}=2+\frac{12}{8}=2 + 1\frac{4}{8}=3\frac{4}{8}\). We can also simplify \(\frac{4}{8}\) to \(\frac{1}{2}\), but since the number line is in eighths, maybe we keep it as eighths for now. So the sum is \(3\frac{4}{8}\) (and \(\frac{4}{8}\) can be simplified to \(\frac{1}{2}\), but let's check the calculation again. Wait, \(5 + 7 = 12\), so \(\frac{12}{8}\). Then \(12\div8 = 1\) with remainder \(4\), so \(\frac{12}{8}=1\frac{4}{8}\). Then \(2 + 1\frac{4}{8}=3\frac{4}{8}\). So the mixed number is \(3\frac{4}{8}\).

Answer:

\(2\frac{5}{8}+\frac{7}{8}=\boldsymbol{3}\frac{\boldsymbol{4}}{\boldsymbol{8}}\) (and \(\frac{4}{8}\) can be simplified to \(\frac{1}{2}\), so also \(3\frac{1}{2}\), but based on the calculation with eighths, it's \(3\frac{4}{8}\))