Question

f87b
(5) $3\frac{5}{12} + \frac{1}{4} - \frac{5}{9}$
(7) $\frac{11}{12} \div \left(2\frac{7}{10} - \frac{2}{15}\
ight)$
$=$ $=$
(6) $1\frac{1}{2} + 1\frac{1}{3} \div \frac{1}{5}$
(8) $1\frac{1}{4} \times 1\frac{1}{15} \div \frac{1}{2}$
$=$ $=$

Explanation:

(5) Step1: Convert to improper fractions

$3\frac{5}{12}=\frac{41}{12}$, so $\frac{41}{12}+\frac{1}{4}-\frac{5}{9}$

(5) Step2: Find common denominator (36)

$\frac{123}{36}+\frac{9}{36}-\frac{20}{36}=\frac{112}{36}=\frac{28}{9}?$ Wait correction: $\frac{41}{12}+\frac{1}{4}=\frac{41+3}{12}=\frac{44}{12}=\frac{11}{3}$; $\frac{11}{3}-\frac{5}{9}=\frac{33-5}{9}=\frac{28}{9}≈3.111$? Wait original: $3\frac{5}{12}=3+5/12$, $5/12+1/4=5/12+3/12=8/12=2/3$, $3+2/3=11/3$, $11/3-5/9=33/9-5/9=28/9$. Correct.

(7) Step1: Simplify parentheses

$2\frac{7}{10}-\frac{2}{15}=\frac{27}{10}-\frac{2}{15}=\frac{81-4}{30}=\frac{77}{30}$

(7) Step2: Divide fractions

$\frac{11}{12}÷\frac{77}{30}=\frac{11}{12}×\frac{30}{77}=\frac{330}{924}=\frac{5}{14}$

(6) Step1: Do division first

$1\frac{1}{3}÷\frac{1}{5}=\frac{4}{3}×5=\frac{20}{3}$

(6) Step2: Add to $1\frac{1}{2}$

$\frac{3}{2}+\frac{20}{3}=\frac{9+40}{6}=\frac{49}{6}≈8.166$? Wait $1\frac{1}{2}=3/2$, yes: $3/2+20/3=49/6$.

(8) Step1: Convert to improper fractions

$1\frac{1}{4}=\frac{5}{4}$, $1\frac{1}{15}=\frac{16}{15}$

(8) Step2: Multiply then divide

$\frac{5}{4}×\frac{16}{15}=\frac{80}{60}=\frac{4}{3}$; $\frac{4}{3}÷\frac{1}{2}=\frac{8}{3}≈2.666$

Wait final answers:
(5) $\frac{28}{9}$
(7) $\frac{5}{14}$
(6) $\frac{49}{6}$
(8) $\frac{8}{3}$

Correct answer list: $\frac{28}{9}$, $\frac{5}{14}$, $\frac{49}{6}$, $\frac{8}{3}$

Answer:

$\frac{107}{18}$; $\frac{55}{156}$; $\frac{37}{6}$; $3$