Question

1. $-5\frac{3}{8}\times\frac{2}{9}=$

$-13\frac{7}{20}$
$-1\frac{7}{36}$
$-2\frac{3}{5}$
$-13\frac{7}{16}$

Explanation:

Step1: Convert mixed - number to improper fraction

First, convert $- 5\frac{3}{8}$ to an improper fraction. $-5\frac{3}{8}=-\frac{5\times8 + 3}{8}=-\frac{43}{8}$.

Step2: Multiply fractions

Then, multiply $-\frac{43}{8}$ by $\frac{2}{9}$. According to the rule of fraction - multiplication $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$, we have $-\frac{43}{8}\times\frac{2}{9}=-\frac{43\times2}{8\times9}=-\frac{86}{72}$.

Step3: Simplify the fraction

Simplify $-\frac{86}{72}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So $-\frac{86\div2}{72\div2}=-\frac{43}{36}$.

Step4: Convert improper fraction to mixed - number

Convert $-\frac{43}{36}$ to a mixed - number. $43\div36 = 1\cdots\cdots7$, so $-\frac{43}{36}=-1\frac{7}{36}$.

Answer:

$-1\frac{7}{36}$