Question

А)(3/4+1/6)*3+(5/6-1/2):2/9 б) (1 1/5+2 3/10):1/2+(6 3/4-2 2/3):1 1/6

Answer 1

а) (3/4+1/6)*3+(5/6-1/2)÷2/9=4 1/4
1)3/4+1/6=9/12+2/12=11/12
2)5/6-1/2=5/6-3/6=2/6=1/3
3)11/12*3=11/4=2 3/4
4)1/3÷2/9=1/3×9/2=3/2=1 1/2
5)2 3/4+1 1/2=2 3/4+1 2/4=3 5/4=4 1/4

б)(1 1/5+2 3/10)÷1/2+(6 3/4-2 2/3)÷1 1/6=19 3/8
1)1 1/5+2 3/10=1 2/10+2 3/10=3 5/10=3 1/2
2)6 3/4-2 2/3=6 9/12-2 8/12=4 1/12
3)1/2÷1/2=1/2×2/1=1
4)4 1/12÷2/9=49/12×9/2=49/4×3/2=147/8=18 3/8
5)1+18 3/8=19 3/8

Answer 2

a) Let's solve the expression step by step:

(3/4 + 1/6) * 3 + (5/6 - 1/2) : (2/9)

First, let's simplify the addition and subtraction inside the parentheses:

(9/12 + 2/12) * 3 + (5/6 - 3/6) : (2/9)

Now, let's simplify the addition and subtraction further:

(11/12) * 3 + (2/6) : (2/9)

Multiplying 11/12 by 3:

33/12 + (2/6) : (2/9)

Now, let's simplify the division:

33/12 + (1/3) : (2/9)

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

33/12 + (1/3) * (9/2)

Now, let's simplify the multiplication:

33/12 + (9/6)

We need to find a common denominator for the fractions:

33/12 + (18/12)

Adding the fractions:

(33 + 18)/12

51/12

Simplifying the fraction:

17/4

So, the value of the expression is 17/4.

b) Let's solve the expression step by step:

(1 1/5 + 2 3/10) : (1/2) + (6 3/4 - 2 2/3) : (1 1/6)

First, let's convert the mixed numbers to improper fractions:

(6/5 + 23/10) : (1/2) + (27/4 - 8/3) : (7/6)

Now, let's simplify the addition and subtraction inside the parentheses:

(12/10 + 23/10) : (1/2) + (81/12 - 32/12) : (7/6)

Adding the fractions:

(35/10) : (1/2) + (49/12) : (7/6)

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

(35/10) * (2/1) + (49/12) * (6/7)

Now, let's simplify the multiplication:

(35/10) * (2/1) + (49/2) * (1/2)

Multiplying the fractions:

(70/10) + (49/4)

Simplifying:

7 + (49/4)

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator:

7 + (49/4) = 7 * (4/4) + (49/4) = 28/4 + 49/4

Adding the fractions:

(28 + 49)/4 = 77/4

So, the value of the expression is 77/4.