Add \(1\dfrac{1}{4}\) and \(6\dfrac{1}{2}\).
\(7\dfrac{3}{4}\)
We will add the two mixed numbers step by step.
Convert each mixed number to an improper fraction.
\(1\dfrac{1}{4} = \dfrac{1\times 4 + 1}{4}\)
\(= \dfrac{4 + 1}{4}\)
\(= \dfrac{5}{4}\)
\(6\dfrac{1}{2} = \dfrac{6\times 2 + 1}{2}\)
\(= \dfrac{12 + 1}{2}\)
\(= \dfrac{13}{2}\)
Make the denominators the same. (LCM of 4 and 2 is 4)
Change \(\dfrac{13}{2}\) to a denominator of 4:
\(\dfrac{13}{2} = \dfrac{13\times 2}{2\times 2} = \dfrac{26}{4}\)
Add the fractions with the same denominator.
\(\dfrac{5}{4} + \dfrac{26}{4} = \dfrac{5 + 26}{4}\)
\(= \dfrac{31}{4}\)
Convert the improper fraction back to a mixed number.
Divide 31 by 4: \(31 \div 4 = 7\) remainder \(3\)
So, \(\dfrac{31}{4} = 7\dfrac{3}{4}\)
Final answer:
\(1\dfrac{1}{4} + 6\dfrac{1}{2} = 7\dfrac{3}{4}\)