$71 \frac{2}{5} + 1 \frac{1}{2}$
To add the mixed numbers \(71 \frac{2}{5}\) and \(1 \frac{1}{2}\), we can break them down into their integer and fractional parts. The expression is written as:
\[71 \frac{2}{5} + 1 \frac{1}{2} = \left(71 + \frac{2}{5}\right) + \left(1 + \frac{1}{2}\right)\]
By regrouping, we get:
\[(71 + 1) + \left(\frac{2}{5} + \frac{1}{2}\right) = 72 + \left(\frac{2}{5} + \frac{1}{2}\right)\]
To add the fractions \(\frac{2}{5}\) and \(\frac{1}{2}\), we must find a common denominator. The least common multiple of 5 and 2 is 10.
Converting the fractions to have a denominator of 10:
\[\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}\]
\[\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}\]
Now, sum these fractions:
\[\frac{4}{10} + \frac{5}{10} = \frac{9}{10}\]
Finally, combine the sum of the integer parts and the sum of the fractional parts:
\[72 + \frac{9}{10} = 72 \frac{9}{10}\]
This can also be expressed as a decimal:
\[72 + 0.9 = 72.9\]
Therefore, the result of the addition is \(\boxed{72 \frac{9}{10}}\).
Imagine you are baking cookies and need to combine ingredients. If one recipe calls for \(71 \frac{2}{5}\) grams of sugar and another calls for \(1 \frac{1}{2}\) grams, you need to add these two amounts to find the total quantity of sugar required. Adding mixed numbers accurately is a fundamental skill in cooking, construction, and any situation where you are measuring quantities of items or materials to be combined. By ensuring your measurements are precise, you guarantee your recipes turn out just right every time!