Question

Г) (3 1/2 : 4 2/3 + 4 2/3 : 3 1/2) * 4 4/5 д) (11 5/11 - 8 21/22) : 1 2/3 е) ((1 1/2) - 3/4) : 7/8

Answer 1

(3 1/2:4 2/3+4 2/3:3 1/2)*4 4/5=(7/2:14/3+14/3:7/2)*24\5=7/2*3/14+14/3*2/7)*24/5=

=(21/28+28/21)*24/5=(3/4+4/3)*24/5=(9/12+16/12)*24/5=25/12*24/5=600/60= 10

Д) (11  5/11-8  21/22) :1  2/3=(126/11-197/22):5/3=(252/22-197/22):5/3=

=55/22:5/3=55/22*3/5=5/2*3/5=15/10=3/2=1 1/2

Е)(1  1/2 -3/4):7/8= (3/2-3/4):7/8=(6/4-3/4):7/8=3/4*8/7=24/21=8/7=1 1/7

Answer 2

Г)

First, we need to simplify the fractions within the parentheses:

3 1/2 = 7/2

4 2/3 = 14/3

4 2/3 = 14/3

3 1/2 = 7/2

Next, we can add the two fractions within the parentheses and then divide 3 1/2 by the sum:

(7/2 : 14/3 + 14/3 : 7/2) * 4 4/5

To add the two fractions within the parentheses, we need to find a common denominator. The least common multiple of 2 and 3 is 6, so we can convert the fractions as follows:

7/2 : 14/3 = (7/2 * 3/3) : (14/3 * 2/2) = 21/6 : 28/6 = (21 - 28)/6 = -7/6

14/3 : 7/2 = (14/3 * 2/2) : (7/2 * 3/3) = 28/6 : 21/6 = (28 - 21)/6 = 7/6

Substituting these values back into the original expression, we get:

(-7/6 + 7/6) * 4 4/5

which simplifies to:

0 * 4 4/5 = 0

Therefore, the value of the expression is 0.

д)

We need to convert the mixed numbers to improper fractions and then perform the subtraction and division:

11 5/11 = (11 * 11 + 5)/11 = 126/11

8 21/22 = (8 * 22 + 21)/22 = 185/22

1 2/3 = (1 * 3 + 2)/3 = 5/3

Now we can substitute these values into the expression:

(126/11 - 185/22) : 5/3

To divide by a fraction, we can multiply by its reciprocal:

(126/11 - 185/22) * 3/5

To subtract the two fractions, we need to find a common denominator. The least common multiple of 11 and 22 is 22, so we can convert the fractions as follows:

126/11 = (126 * 2)/22 = 252/22

185/22 = 185/22

Substituting these values back into the expression, we get:

(252/22 - 185/22) * 3/5 = (67/22) * 3/5 = 201/110

Therefore, the value of the expression is 201/110.

е)

We need to simplify the fractions within the parentheses and then perform the division:

1 1/2 = (1 * 2 + 1)/2 = 3/2

3/4 = 0.75

7/8 = 0.875

Substituting these values into the expression, we get:

(3/2 - 0.75) : 0.875

Simplifying the subtraction, we get:

0.75 : 0.875

To divide by a decimal, we can multiply by its reciprocal:

0.75 * 1.142857 = 0.857142857

Therefore, the value of the expression is approximately 0.857.