Question

(2 2/5 + 3 1/2)* 2- (1 3/4 + 5/6) * 3= 1/13* (22 2/6- 21 5/8) +1 31/ 44 *( 6 3/10-2 11/15)=

Answer 1

Ответ:

вот

Пошаговое объяснение:

1)2 2/5+3 1/2=11 4/5

2)1 3/4+5/6=2 7/12

3)11 4/5*2=23 3/5

4)2 7/12*3=7 3/4

5)23 3/5+7 3/4=31 7/20

Answer 2

To simplify the expression step by step, let's start with the first part:

(2 2/5 + 3 1/2) * 2 - (1 3/4 + 5/6) * 3

First, we'll add the mixed numbers within each set of parentheses:

(12/5 + 7/2) * 2 - (7/4 + 5/6) * 3

Now, find a common denominator for each addition:

(24/10 + 35/10) * 2 - (42/10 + 25/10) * 3

Combine the fractions:

(59/10) * 2 - (67/10) * 3

Now, multiply each term by its respective number:

(2 * 59/10) - (3 * 67/10)

(118/10) - (201/10)

Now, subtract the two fractions:

(118/10) - (201/10) = (118 - 201)/10 = (-83/10)

Now, let's move on to the second part of the expression:

1/13 * (22 2/6 - 21 5/8) + 1 31/44 * (6 3/10 - 2 11/15)

First, simplify the mixed numbers:

1/13 * (22 1/3 - 21 5/8) + 1 31/44 * (6 9/10 - 2 11/15)

Now, subtract the mixed numbers:

1/13 * (22 1/3 - 21 5/8) + 1 31/44 * (6 9/10 - 2 11/15) = 1/13 * (1/3 - 5/8) + 1 31/44 * (59/10 - 71/15)

Find a common denominator for the fractions within each set of parentheses:

1/13 * (8/24 - 15/24) + 1 31/44 * (177/30 - 284/30)

Now, subtract the fractions:

1/13 * (-7/24) + 1 31/44 * (-107/30)

Now, multiply each term by its respective number:

(-7/312) + (31/44 * -107/30)

Now, calculate each part:

-7/312 - 3337/1320

To subtract fractions, we need a common denominator. The common denominator for 312 and 1320 is 1320. So, we'll convert -7/312 to have a denominator of 1320:

(-7/312) * (5/5) = (-35/1560)

Now, we can subtract the fractions:

(-35/1560) - (3337/1320)

Now, find a common denominator:

(-35/1560) - (3337/1320) = (-35/1560) - (3337/1320) * (13/13)

Now, subtract:

(-35/1560) - (43481/17160)

To subtract these fractions, we need a common denominator:

(-35/1560) * (57/57) - (43481/17160)

Now, subtract:

(-1995/87420) - (43481/17160)

Now, find a common denominator:

(-1995/87420) * (5/5) - (43481/17160)

Now, subtract:

(-9975/437100) - (43481/17160)

Now, find a common denominator:

(-9975/437100) - (43481/17160) = (-9975/437100) - (252789/437100)

Now, subtract:

(-9975 - 252789)/437100 = -262764/437100

Now, simplify the fraction:

-262764/437100 = -131382/218550

So, the final result is:

-131382/218550

You can further simplify this fraction by finding the greatest common divisor (GCD) and dividing both the numerator and denominator by it if needed.