Question

А) 24 4/5 - 19,5 : 7 2/9 б ) 2,4+ 5,6*(13 3/4 - 12 13/14)

Answer 1

А) 24 4/5 - 19,5 : 7 2/9 = 22,1
1) 19,5 : 7 2/9 = 19,5 : 65/9 = 195/10 * 9/65 = (3*9)/(10*1) = 27/10 = 2,7
2) 24 4/5 - 2,7 = 24,8 - 2,7 = 22,1 

б) 2,4 + 5,6 * (13 3/4 - 12 13/14) = 7
1) 13 3/4 - 12 13/14 = 13 21/28 - 12 26/28 = 12 49/28 - 12 26/28 = 23/28
2) 5,6 * 23/28 = 56/10 * 23/28 = (2*23)/10*1) = 46/10 = 4,6
3) 2,4 + 4,6 = 7

Answer 2

а)

We can simplify the expression step by step, following the order of operations (PEMDAS):

24 4/5 - 19,5 : 7 2/9

First, let's simplify the division:

19,5 : 7 2/9 = 19,5 ÷ (7 + 2/9) = 19,5 ÷ 7 + 19,5 ÷ 9 = 2,78571428571 + 2,16666666667

Next, let's add the two fractions:

2,78571428571 + 2,16666666667 = 4,95238095238

Now we can substitute that result back into the original expression:

24 4/5 - 4,95238095238

To subtract mixed numbers, we need to convert them into improper fractions first:

24 4/5 = (24 × 5 + 4) / 5 = 124/5

So the expression becomes:

124/5 - 4,95238095238

To subtract decimals, we need to make sure they have the same number of decimal places. In this case, we can multiply 4,95238095238 by 10/10 to get rid of the decimal places:

124/5 - 49,5238095238/10

Now we can find a common denominator:

124/5 - 49,5238095238/10 = 248/10 - 49,5238095238/10

And subtract:

248/10 - 49,5238095238/10 = 198,4761904762/10 = 19,84761904762

Therefore, the final result is 19,84761904762.

б)

2,4+ 5,6*(13 3/4 - 12 13/14)

First, let's simplify the expression inside the parentheses:

13 3/4 - 12 13/14

Again, we need to convert the mixed numbers into improper fractions:

13 3/4 = (13 × 4 + 3) / 4 = 55/4

12 13/14 = (12 × 14 + 13) / 14 = 173/14

So the expression becomes:

55/4 - 173/14

To subtract fractions, we need to find a common denominator:

55/4 - 173/14 = 385/28 - 173/14

We can simplify 385/28 by dividing both the numerator and the denominator by 7:

385/28 = (385 ÷ 7) / (28 ÷ 7) = 55/4

So the expression becomes:

55/4 - 173/14 = 55/4 - 173/14

Now we can find a common denominator:

55/4 - 173/14 = 385/28 - 1109/28

And subtract:

385/28 - 1109/28 = -724/28 = -26

So the expression inside the parentheses simplifies to -26.

Now we can substitute that result back into the original expression:

2,4+ 5,6*(-26)

Multiplying by a negative number changes the sign of the result:

2,4 - 145,6

And subtracting decimals is straightforward:

-143,2

Therefore, the final result is -143,2.