Question

(1) 4 7/15+2 7/30-5 1/30 (2)5 1/2+4 13/14-6 23/24 (3)13 11/12-1 3/4+2 5/6​

Answer 1

Пошаговое объяснение:

1)

4 7/15+2 7/30-5 1/30=

=(4+2-5)+(14/30+7/30-1/30)=

=1+20/30=1+2/3=1 2/3

2)

5 1/2+4 13/14-6 23/24=

=(5+4-6)+(84/168+156/168-161/168)=

=3+79/168=3 79/168

3)

13 11/12-1 3/4+2 5/6=

=(13-1+2)+(11/12-9/12+10/12)=

=14+12/12=14+1=15

Answer 2

Let's solve the three expressions step by step:

(1) 4 7/15 + 2 7/30 - 5 1/30:

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

4 7/15 can be written as (4 * 15 + 7)/15 = 67/15. 2 7/30 can be written as (2 * 30 + 7)/30 = 67/30. 5 1/30 can be written as (5 * 30 + 1)/30 = 151/30.

Now we can rewrite the expression:

67/15 + 67/30 - 151/30

To add or subtract fractions, we need to find a common denominator. In this case, the common denominator is 30.

(67/15) * (2/2) = 134/30 (67/30) (151/30)

Now we can rewrite the expression with the common denominator:

134/30 + 67/30 - 151/30

Now we can add and subtract the fractions:

(134 + 67 - 151)/30 = 50/30 = 5/3

Therefore, the result of the expression is 5/3.

(2) 5 1/2 + 4 13/14 - 6 23/24:

Following the same steps as above:

5 1/2 can be written as (5 * 2 + 1)/2 = 11/2. 4 13/14 can be written as (4 * 14 + 13)/14 = 57/14. 6 23/24 can be written as (6 * 24 + 23)/24 = 167/24.

Now we can rewrite the expression:

11/2 + 57/14 - 167/24

To find the common denominator, we multiply the denominators: 2 * 14 * 24 = 672.

(11/2) * (336/336) = 1848/672 (57/14) * (48/48) = 2736/672 (167/24) * (28/28) = 4672/672

Now we can rewrite the expression with the common denominator:

1848/672 + 2736/672 - 4672/672

Now we can add and subtract the fractions:

(1848 + 2736 - 4672)/672 = -88/672 = -11/84

Therefore, the result of the expression is -11/84.

(3) 13 11/12 - 1 3/4 + 2 5/6:

Following the same steps as above:

13 11/12 can be written as (13 * 12 + 11)/12 = 167/12. 1 3/4 can be written as (1 * 4 + 3)/4 = 7/4. 2 5/6 can be written as (2 * 6 + 5)/6 = 17/6.

Now we can rewrite the expression:

167/12 - 7/4 + 17/6

To find the common denominator, we multiply the denominators: 12 * 4 * 6 = 288.

(167/12) * (24/24) = 4008/288 (7/4) * (72/72) = 504/288 (17/6) * (48/48) = 816/288

Now we can rewrite the expression with the common denominator:

4008/288 - 504