Question

Напишите решение примера: а)1 2/7:3/56 б)1 3/4:7/10+1/4 в)(27 9/10-17 4/5)*3 г)23/81*3 6/7 д)7/8:1 5/16*3 1/2 е)(9 1/5-3 17/25)*2 1/2

Answer 1

А)9/7:56/3=9/7*3/56=3/1*8/1=3*8=24

Answer 2

а) 1 2/7 : 3/56

To solve this expression, we need to divide the mixed number 1 2/7 by the fraction 3/56.

To divide a mixed number by a fraction, we first convert the mixed number to an improper fraction. The improper fraction equivalent of 1 2/7 is (7 * 1 + 2) / 7 = 9/7.

Next, we multiply the numerator of the first fraction (9/7) by the reciprocal of the second fraction (3/56). The reciprocal of a fraction is obtained by swapping the numerator and denominator.

So, the expression becomes:

(9/7) * (56/3)

To multiply fractions, we multiply the numerators together and the denominators together.

9/7 * 56/3 = (9 * 56) / (7 * 3) = 504/21

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7.

504/21 = (7 * 72) / (7 * 3) = 72/3 = 24

Therefore, the solution to the expression 1 2/7 : 3/56 is 24.

б) 1 3/4 : 7/10 + 1/4

To solve this expression, we need to divide the mixed number 1 3/4 by the fraction 7/10 and then add 1/4 to the result.

First, let's convert the mixed number 1 3/4 to an improper fraction. The improper fraction equivalent of 1 3/4 is (4 * 1 + 3) / 4 = 7/4.

Next, we divide 7/4 by 7/10. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

So, the expression becomes:

(7/4) * (10/7)

To multiply fractions, we multiply the numerators together and the denominators together.

7/4 * 10/7 = (7 * 10) / (4 * 7) = 70/28

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 14.

70/28 = (14 * 5) / (14 * 2) = 5/2

Now, we need to add 1/4 to the result.

5/2 + 1/4 = (5 * 2 + 1) / 2 = 11/4

Therefore, the solution to the expression 1 3/4 : 7/10 + 1/4 is 11/4.

в) (27 + 9/10 - 17 + 4/5) * 3

To solve this expression, we need to simplify the expression inside the parentheses first and then multiply the result by 3.

Let's simplify the expression inside the parentheses:

27 + 9/10 - 17 + 4/5

To add or subtract mixed numbers, we need to convert them to improper fractions.

27 = 27/1 9/10 = 9/10 17 = 17/1 4/5 = 4/5

Now, let's add and subtract the fractions:

27/1 + 9/10 - 17/1 + 4/5

To add or subtract fractions, we need to have a common denominator. The least common multiple of 1, 10, and 5 is 10.

27/1 + 9/10 - 17/1 + 4/5 = (27 * 10)/ (1 * 10) + (9 * 1) / (10 * 1) - (17 * 10) / (1 * 10) + (4 * 2) / (5 * 2) = 270/10 + 9/10 - 170/10 + 8/10 = (270 + 9 - 170 + 8) / 10 = 117/10

Now, let's multiply the result by 3:

117/10 * 3 = (117 * 3) / (10 * 1) = 351/10

Therefore, the solution to the expression (27 + 9/10 - 17 + 4/5) * 3 is 351/10.

г) 23/81 * 3 + 6/7

To solve this expression, we need to multiply the fraction 23/81 by 3 and then add 6/7 to the result.

Let's multiply the fraction 23/81 by 3:

23/81 * 3 = (23 * 3) / (81 * 1) = 69/81

Now, let's add 6/7 to the result:

69/81 + 6/7

To add fractions, we need to have a common denominator. The least common multiple of 81 and 7 is 567.

69/81 + 6/7 = (69 * 7) / (81 * 7) + (6 * 81) / (7 * 81) = 483/567 + 486/567 = (483 + 486) / 567 = 969/567

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3.

969/567 = (3 * 323) / (3 * 189) = 323/189

Therefore, the solution to the expression 23/81 * 3 + 6/7 is 323/189.

д) 7/8 : 1 + 5/16 * 3 + 1/2

To solve this expression, we need to divide the fraction 7/8 by 1, then multiply the fraction 5/16 by 3, and finally add the results together with the fraction 1/2.

Let's start with the division:

7/8 : 1 = 7/8

Next, let's multiply the fraction 5/16 by 3:

5/16 * 3 = (5 * 3) / (16 * 1) = 15/16

Now, let's add the results together with the fraction 1/2:

7/8 + 15/16 + 1/2

To add fractions, we need to have a common denominator. The least common multiple of 8 and 16 is 16.

7/8 + 15/16 + 1/2 = (7 * 2) / (8 * 2) + 15/16 + (1 * 8) / (2 * 8) = 14/16 + 15/16 + 8/16 = (14 + 15 + 8) / 16 = 37/16

Therefore, the solution to the expression 7/8 : 1 + 5/16 * 3 + 1/2 is 37/16.

е) (9 + 1/5 - 3 + 17/25) * 2 + 1/2

To solve this expression, we need to simplify the expression inside the parentheses first, then multiply the result by 2, and finally add 1/2 to the result.

Let's simplify the expression inside the parentheses:

9 + 1/5 - 3 + 17/25

To add or subtract mixed numbers, we need to convert them to improper fractions.

9 = 9/1 1/5 = 1/5 3 = 3/1 17/25 = 17/25

Now, let's add and subtract the fractions:

9/1 + 1/5 - 3/1 + 17/25

To add or subtract fractions, we need to have a common denominator. The least common multiple of 1, 5, and 25 is 25.

9/1 + 1/5 - 3/1 + 17/25 = (9 * 25) / (1 * 25) + (1 * 5) / (5 * 5) - (3 * 25) / (1 * 25) + 17/25 = 225/25 + 5/25 - 75/25 + 17/25 = (225 + 5 - 75 + 17) / 25 = 172/25

Now, let's multiply the result by 2:

172/25 * 2 = (172 * 2) / (25 * 1) = 344/25

Finally, let's add 1/2 to the result:

344/25 + 1/2

To add fractions, we need to have a common denominator. The least common multiple of 25 and 2 is 50.

344/25 + 1/2 = (344 * 2) / (25 * 2) + (1 * 25) / (2 * 25) = 688/50 + 25/50 = (688 + 25) / 50 = 713/50

Therefore, the solution to the expression (9 + 1/5 - 3 + 17/25) * 2 + 1/2 is 713/50.