Question

1) 18*(5/9+1/3-7/6)2) 6,72:(3 2/14-12/35)3) 41+1 1/6*1,2​

Answer 1

18 · (5/9 + 1/3 - 7/6) = -5

1) 5/9 + 1/3 = 5/9 + 3/9 = 8/9

2) 8/9 - 7/6 = 16/18 - 21/18 = -5/18

3) 18 · (-5/18) = -5

Ответ: (-5).

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6,72 : (3 2/14 - 12/35) = 2,4

1) 3 2/14 - 12/35 = 3 10/70 - 24/70 = 2 80/70 - 24/70 = 2 56/70 = 2 4/5 = 2,8

2) 6,72 : 2,8 = 2,4

Ответ: 2,4.

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41 + 1 1/6 · 1,2 = 42,4

1) 1 1/6 · 1,2 = 7/6 · 12/10 = (7·2)/(1·10) = 14/10 = 1,4

2) 41 + 1,4 = 42,4

Ответ: 42,4.

Answer 2

1) 18 * ( 5/9 + 1/3 - 7/6 ) = 18 * ( -5/18 ) = -5
2) 6,72 / ( 3 2/14 - 12/35) = 168/25 / 68/35 = 294/85

3) 41 + 1 1/6 * 1,2 = 41 + 7/6 * 6/5 = 41 + 7 * 1/5 = 41 + 7/5 = 212/5

Answer 3

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

1. $18 \cdot \left(\frac{5}{9} + \frac{1}{3} - \frac{7}{6}\right)$

First, simplify the fractions inside the parentheses:

$\frac{5}{9} + \frac{1}{3} - \frac{7}{6} = \frac{10}{18} + \frac{6}{18} - \frac{21}{18}$

Now, find a common denominator and add/subtract the fractions:

$\frac{10}{18} + \frac{6}{18} - \frac{21}{18} = \frac{10 + 6 - 21}{18} = \frac{-5}{18}$

Now, multiply by 18:

$18 \cdot \frac{-5}{18} = -5$

So, the result of the first expression is -5.

2. $6.72 : \left(3 \frac{2}{14} - \frac{12}{35}\right)$

First, convert the mixed number to an improper fraction:

$3 \frac{2}{14} = 3 \frac{1}{7} = \frac{3 \cdot 7 + 1}{7} = \frac{22}{7}$

Now, simplify the expression:

$\frac{6.72}{\frac{22}{7} - \frac{12}{35}}$

To subtract fractions, find a common denominator:

$\frac{6.72}{\frac{22}{7} - \frac{12}{35}} = \frac{6.72}{\frac{35 \cdot 22}{7} - \frac{12}{35} \cdot \frac{35 \cdot 7}{7}}$

$\frac{6.72}{\frac{770}{7} - \frac{420}{35}}$

$\frac{6.72}{\frac{770}{7} - \frac{420}{35}} = \frac{6.72}{\frac{770}{7} - \frac{420}{7}}$

Now, subtract the fractions:

$\frac{6.72}{\frac{350}{7}}$

Divide by a fraction is the same as multiplying by its reciprocal:

$\frac{6.72}{\frac{350}{7}} = 6.72 \cdot \frac{7}{350}$

Now, simplify:

$6.72 \cdot \frac{7}{350} = \frac{6.72 \cdot 7}{350} = \frac{47.04}{350} = 0.1344$

So, the result of the second expression is approximately 0.1344.

3. $41 + 1 \frac{1}{6} \cdot 1.2$