Question

1)1 1/7 × 15/23 : 1 19/362)1 1/7 × (15/23 : 1 19/36)3)3 4/7 : 1 1/7 × 2/3​

Answer 1

1) 5940/19159

2) 5940/19159

3) 68/33

Answer 2

Let's solve each of these expressions step by step:

1. $1 \frac{1}{7} \times \frac{15}{23} : 1 \frac{19}{36}$

First, simplify the mixed numbers to improper fractions:

$1 \frac{1}{7} = \frac{7}{7} + \frac{1}{7} = \frac{8}{7}$

$1 \frac{19}{36} = \frac{36}{36} + \frac{19}{36} = \frac{55}{36}$

Now, the expression becomes:

$\frac{8}{7} \times \frac{15}{23} : \frac{55}{36}$

Now, multiply the fractions and then divide:

$\frac{8}{7} \times \frac{15}{23} \div \frac{55}{36} = \frac{8 \cdot 15}{7 \cdot 23} \div \frac{55}{36} = \frac{120}{161} \div \frac{55}{36}$

To divide fractions, invert the second fraction and multiply:

$\frac{120}{161} \cdot \frac{36}{55} = \frac{4320}{8855}$

Now, simplify the fraction by finding the greatest common divisor (GCD) of 4320 and 8855:

GCD(4320, 8855) = 5

So, divide both the numerator and denominator by 5:

$\frac{4320}{8855} = \frac{4320 \div 5}{8855 \div 5} = \frac{864}{1771}$

The result of the expression is $\frac{864}{1771}$.

2. $1 \frac{1}{7} \times \left(\frac{15}{23} : 1 \frac{19}{36}\right)$

First, simplify the mixed number:

$1 \frac{1}{7} = \frac{8}{7}$

Now, the expression becomes:

$\frac{8}{7} \times \left(\frac{15}{23} : \frac{55}{36}\right)$

Now, divide the fractions inside the parentheses:

$\frac{15}{23} \div \frac{55}{36} = \frac{15}{23} \times \frac{36}{55}$

Multiply the fractions:

$\frac{15 \cdot 36}{23 \cdot 55}$

Now, find the GCD of 15 and 55, which is 5:

$\frac{15 \cdot 36}{23 \cdot 55} = \frac{5 \cdot 3 \cdot 36}{23 \cdot 5 \cdot 11}$

Cancel out common factors:

$\frac{3 \cdot 36}{23 \cdot 11} = \frac{108}{253}$

Now, multiply this result by $\frac{8}{7}$:

$\frac{8}{7} \cdot \frac{108}{253} = \frac{864}{253}$