Question

i. add.
(1) $1\frac{4}{5} + 2\frac{8}{15} = 1\frac{12}{15} + 3\frac{8}{15} = 4\frac{1}{4}$
(2) $4\frac{7}{10} + 3\frac{7}{15} = 4\frac{21}{30} + 3\frac{14}{30} = 8\frac{1}{6}$
(3) $2\frac{2}{9} + 5\frac{8}{21} = 2\frac{14}{63} + 5\frac{24}{63} = 7\frac{38}{63}$
(4) $2\frac{3}{10} + 3\frac{11}{30} = 2\frac{9}{30} + 3\frac{11}{30} = 5\frac{2}{3}$
(5) $2\frac{11}{24} + 4\frac{5}{32} = $
(6) $1\frac{13}{18} + \frac{19}{36} = $

Explanation:

Step1: Simplify the fractional parts

For \(2\frac{11}{24} + 4\frac{5}{32}\), first find the least common denominator (LCD) of 24 and 32. Prime factorize 24 = \(2^3\times3\) and 32 = \(2^5\), so LCD is \(2^5\times3 = 96\).
Convert \(\frac{11}{24}\) to \(\frac{11\times4}{24\times4}=\frac{44}{96}\) and \(\frac{5}{32}\) to \(\frac{5\times3}{32\times3}=\frac{15}{96}\).

Step2: Add the whole numbers and fractional parts

Whole numbers: \(2 + 4 = 6\).
Fractional parts: \(\frac{44}{96}+\frac{15}{96}=\frac{59}{96}\).
Combine: \(6+\frac{59}{96}=6\frac{59}{96}\).

Step3: Simplify the second problem \(1\frac{13}{18}+\frac{19}{36}\)

Find LCD of 18 and 36, which is 36.
Convert \(\frac{13}{18}\) to \(\frac{13\times2}{18\times2}=\frac{26}{36}\).

Step4: Add the whole number and fractional parts

Whole number: 1.
Fractional parts: \(\frac{26}{36}+\frac{19}{36}=\frac{45}{36}=\frac{5}{4}=1\frac{1}{4}\).
Combine: \(1 + 1\frac{1}{4}=2\frac{1}{4}\).

Answer:

(5) \(6\frac{59}{96}\)
(6) \(2\frac{1}{4}\)