Question

add the mixed numbers. enter your answers.
$2\frac{8}{7} + 2\frac{1}{2} = 2\frac{?}{14}+2\frac{?}{14}$
$= 4\frac{?}{14}$

Explanation:

Step1: Find equivalent fractions for \(\frac{5}{7}\) and \(\frac{1}{2}\) with denominator 14.

To convert \(\frac{5}{7}\) to a fraction with denominator 14, multiply numerator and denominator by 2: \(\frac{5\times2}{7\times2}=\frac{10}{14}\).
To convert \(\frac{1}{2}\) to a fraction with denominator 14, multiply numerator and denominator by 7: \(\frac{1\times7}{2\times7}=\frac{7}{14}\).
So \(2\frac{5}{7}+2\frac{1}{2}=2\frac{10}{14}+2\frac{7}{14}\).

Step2: Add the fractions.

Add the fractional parts: \(\frac{10}{14}+\frac{7}{14}=\frac{10 + 7}{14}=\frac{17}{14}\).
Now add the whole number parts: \(2 + 2 = 4\).
Then combine the whole number and the fraction: \(4+\frac{17}{14}=4\frac{17}{14}\) (but we can also note that \(\frac{17}{14}=1\frac{3}{14}\), but in the given form we just need the numerator for the fraction with denominator 14, which is 17).

Answer:

First box: 10, Second box: 7, Third box: 17