Question

(5) $2\frac{11}{24} + 4\frac{5}{32} =$
(6) $1\frac{13}{18} + \frac{19}{36} =$

Explanation:

(5) Solution:

Step1: Add the whole numbers

The whole numbers are 2 and 4. So, \( 2 + 4 = 6 \).

Step2: Find a common denominator for the fractions

The denominators are 24 and 32. The least common multiple of 24 and 32 is 96.

Step3: Convert the fractions to have denominator 96

For \( \frac{11}{24} \), multiply numerator and denominator by 4: \( \frac{11\times4}{24\times4} = \frac{44}{96} \).
For \( \frac{5}{32} \), multiply numerator and denominator by 3: \( \frac{5\times3}{32\times3} = \frac{15}{96} \).

Step4: Add the fractions

\( \frac{44}{96} + \frac{15}{96} = \frac{44 + 15}{96} = \frac{59}{96} \).

Step5: Combine the whole number and the fraction

\( 6 + \frac{59}{96} = 6\frac{59}{96} \).

Step1: Separate the whole number and the fraction

The mixed number is \( 1\frac{13}{18} \), so the whole number is 1 and the fraction is \( \frac{13}{18} \).

Step2: Find a common denominator for the fractions

The denominators are 18 and 36. The least common multiple of 18 and 36 is 36.

Step3: Convert the fraction to have denominator 36

For \( \frac{13}{18} \), multiply numerator and denominator by 2: \( \frac{13\times2}{18\times2} = \frac{26}{36} \).

Step4: Add the fractions

\( \frac{26}{36} + \frac{19}{36} = \frac{26 + 19}{36} = \frac{45}{36} \). Simplify \( \frac{45}{36} \) to \( \frac{5}{4} = 1\frac{1}{4} \).

Step5: Combine the whole numbers and the fraction

\( 1 + 1\frac{1}{4} = 2\frac{1}{4} \).

Answer:

\( 6\frac{59}{96} \)

(6) Solution: