Question

at the beach, dave built a sandcastle that was $2\\ 2/5$ feet high. if he added a flag that was $2\\ 1/2$ feet high, what is the total height of his creation? ______

Explanation:

Step1: Convert mixed numbers to improper fractions

The height of the sandcastle is \( 2\frac{2}{5} \) feet. To convert this to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 2\frac{2}{5}=\frac{2\times5 + 2}{5}=\frac{10 + 2}{5}=\frac{12}{5} \) feet.

The height of the flag is \( 2\frac{1}{2} \) feet. Converting this, we get \( 2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{4 + 1}{2}=\frac{5}{2} \) feet.

Step2: Find a common denominator and add the fractions

The denominators are 5 and 2, so the least common denominator (LCD) is \( 5\times2 = 10 \).

Convert \( \frac{12}{5} \) to tenths: \( \frac{12}{5}=\frac{12\times2}{5\times2}=\frac{24}{10} \).

Convert \( \frac{5}{2} \) to tenths: \( \frac{5}{2}=\frac{5\times5}{2\times5}=\frac{25}{10} \).

Now, add the two fractions: \( \frac{24}{10}+\frac{25}{10}=\frac{24 + 25}{10}=\frac{49}{10} \).

Step3: Convert the improper fraction back to a mixed number

\( \frac{49}{10}=4\frac{9}{10} \) (since \( 49\div10 = 4 \) with a remainder of 9).

Answer:

The total height of his creation is \( 4\frac{9}{10} \) feet (or \( 4.9 \) feet).