Question

3) 2/5 * 6/13 + 1/4 * 6/13 4) 3 3/4 * 2/5 - 3 6/25 * 5/27 5) 3/5 - 3/5 * 2/7 6) 1/7 * 1/8 + 1/7 * 1/6

Answer 1

Ответ:

Пошаговое объяснение:

3) 2/5 ·6/13 +1/4 ·6/13=6/13 ·(2/5 +1/4)=6/13 ·(8/20 +5/20)=6/13 ·13/20=3/10=0,3

4) 3 3/4 ·2/5 -3 6/25 ·5/27=15/4 ·2/5 -81/25 ·5/27=3/2 -3/5=1,5-0,6=0,9

5) 3/5 -3/5 ·2/7=3/5 ·(1 -2/7)=3/5 ·(7/7 -2/7)=3/5 ·5/7=3/7

6) 1/7 ·1/8 +1/7 ·1/6=1/7 ·(1/8 +1/6)=1/7 ·(3/24 +4/24)=1/7 ·7/24=1/24

Answer 2

Let's solve each of these math problems step by step:

3. (2/5 * 6/13) + (1/4 * 6/13)

To add these fractions, you need a common denominator, which in this case is 20 (5 * 4 = 20). So, you'll need to convert both fractions to have a denominator of 20:

(2/5 * 6/13) = (2/5 * 6/13 * 4/4) = (48/65)

(1/4 * 6/13) = (1/4 * 6/13 * 5/5) = (30/65)

Now you can add them:

(48/65) + (30/65) = (48 + 30) / 65 = 78/65

Now, you can simplify this fraction:

78/65 = 6/5

4. (3 3/4 * 2/5) - (3 6/25 * 5/27)

First, convert the mixed numbers to improper fractions:

3 3/4 = (4 * 3 + 3)/4 = 15/4

3 6/25 = (25 * 3 + 6)/25 = 81/25

Now, calculate the products:

(15/4 * 2/5) - (81/25 * 5/27)

To multiply fractions, multiply the numerators and denominators separately:

(15 * 2) / (4 * 5) - (81 * 5) / (25 * 27)

(30/20) - (405/675)

Now, find a common denominator, which is 675:

(30/20) - (405/675) = (30/20) - (405/675 * 20/20)

(30/20) - (8100/13500)

Now, subtract:

(30/20) - (8100/13500) = (30/20) - (540/900)

(30/20) - (3/5)

To subtract, find a common denominator, which is 20:

(30/20) - (3/5) = (30/20 * 1/1) - (3/5 * 4/4)

(30/20) - (12/20)

Now, subtract:

(30 - 12) / 20 = 18/20

Simplify the fraction:

18/20 = 9/10

5. 3/5 - 3/5 * 2/7

First, calculate the product:

(3/5 * 2/7)

(6/35)

Now, subtract it from 3/5:

3/5 - 6/35

To subtract, find a common denominator, which is 35:

(3/5 * 7/7) - (6/35 * 5/5)

(21/35) - (30/35)

Now, subtract:

(21 - 30) / 35 = (-9/35)

6. (1/7 * 1/8) + (1/7 * 1/6)

Calculate the products:

(1/7 * 1/8) = (1/56)

(1/7 * 1/6) = (1/42)

Now, add them:

(1/56) + (1/42)

To add these fractions, find a common denominator, which is 168 (56 * 3 = 168 and 42 * 4 = 168):

(1/56 * 3/3) + (1/42 * 4/4)

(3/168) + (4/168)

Now, add:

(3 + 4) / 168 = 7/168

Simplify the fraction:

7/168 = 1/24

So, the results of the given expressions are:

3. 6/5
4. 9/10
5. -9/35
6. 1/24