Question

lesson 12 refine
2 michael rides his bike $2\frac{2}{3}$ miles on satur
$1\frac{5}{6}$ miles on sunday. how many miles

Explanation:

Step1: Identify the problem type

This is a problem of adding mixed numbers, which falls under the subfield of Arithmetic (a part of Mathematics). We need to add \(2\frac{2}{3}\) and \(1\frac{5}{6}\) (assuming the question is to find the total miles ridden over Saturday and Sunday, as the text seems cut off but the pattern suggests addition of the two distances).

Step2: Convert mixed numbers to improper fractions

For \(2\frac{2}{3}\): Multiply the whole number \(2\) by the denominator \(3\) and add the numerator \(2\). So, \(2\times3 + 2=6 + 2 = 8\). Thus, \(2\frac{2}{3}=\frac{8}{3}\).

For \(1\frac{5}{6}\): Multiply the whole number \(1\) by the denominator \(6\) and add the numerator \(5\). So, \(1\times6+5 = 6 + 5=11\). Thus, \(1\frac{5}{6}=\frac{11}{6}\).

Step3: Find a common denominator

The denominators are \(3\) and \(6\). The least common denominator is \(6\). Convert \(\frac{8}{3}\) to a fraction with denominator \(6\): Multiply numerator and denominator by \(2\), so \(\frac{8\times2}{3\times2}=\frac{16}{6}\).

Step4: Add the fractions

Now add \(\frac{16}{6}\) and \(\frac{11}{6}\). Since the denominators are the same, we add the numerators: \(\frac{16 + 11}{6}=\frac{27}{6}\).

Step5: Simplify the result

Simplify \(\frac{27}{6}\). Divide numerator and denominator by \(3\): \(\frac{27\div3}{6\div3}=\frac{9}{2}\). Convert back to a mixed number: \(\frac{9}{2}=4\frac{1}{2}\).

Answer:

\(4\frac{1}{2}\) miles (or \(\frac{9}{2}\) miles)