Question

1)2 2/3* 9/32*5 1/32)4 2/5*1 1/35*2 1/33)18/25*10/27*7 1/2​

Answer 1

Ответ:

1) 2 2/3 * 9/32 * 5 1/3 = 8/3 * 9/32 * 5 * 1/3 = 3/4 * 5 * 1/3 = 1/4 * 5 = 5/4

2) 4 2/5 * 1 1/35 * 2 1/3 = 22/5 * 11/35 * 7/3 = 22/5 * 11/5 * 1/3 = 242/75

3) 18/25 * 10/27 * 7 1/2​ = 18/5 * 2/27 * 15/2 = 9/5 * 2/9 * 5 = 2

Answer 2

Let's simplify each of the expressions:

1. $2 \frac{2}{3} \times \frac{9}{32} \times 5 \frac{1}{32}$

To multiply mixed numbers, first convert them to improper fractions:

$2 \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}$ $5 \frac{1}{32} = \frac{160}{32} + \frac{1}{32} = \frac{161}{32}$

Now, multiply the fractions:

$\frac{8}{3} \times \frac{9}{32} \times \frac{161}{32} = \frac{8 \times 9 \times 161}{3 \times 32 \times 32} = \frac{11664}{3072}$

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 384):

$\frac{11664}{3072} = \frac{11664 \div 384}{3072 \div 384} = \frac{30}{8}$

Now, simplify further:

$\frac{30}{8} = \frac{15}{4}$

So, $2 \frac{2}{3} \times \frac{9}{32} \times 5 \frac{1}{32} = \frac{15}{4}$

2. $4 \frac{2}{5} \times 1 \frac{1}{35} \times 2 \frac{1}{33}$

Convert the mixed numbers to improper fractions:

$4 \frac{2}{5} = \frac{22}{5}$ $1 \frac{1}{35} = \frac{35}{35} + \frac{1}{35} = \frac{36}{35}$ $2 \frac{1}{33} = \frac{66}{33} + \frac{1}{33} = \frac{67}{33}$

Now, multiply the fractions:

$\frac{22}{5} \times \frac{36}{35} \times \frac{67}{33} = \frac{22 \times 36 \times 67}{5 \times 35 \times 33}$

To simplify this fraction, you can first find the greatest common divisor (GCD) of the numerator and denominator and divide both by it:

The GCD of 22, 36, and 67 is 1.

$\frac{22 \times 36 \times 67}{5 \times 35 \times 33} = \frac{22 \times 36 \times 67}{5 \times 7 \times 11 \times 33}$

Now, simplify further:

$\frac{22 \times 36 \times 67}{5 \times 7 \times 11 \times 33} = \frac{22 \times 36 \times 67}{5 \times 7 \times 11 \times 33} = \frac{107136}{1155}$

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