Simplify the following fraction (5/9x3/5)+6/7

1 4/21

Step-by-step explanation:

(5/9*3/5)+6/7

The 5's cancel

(3/9)+6/7

Cancel a 3 in the numerator and a 3 in the denominator

1/3 + 6/7

We need to get a common denominator of 21

1/3 *7/7  + 6/7 *3/3

7/21 + 18/21

25/21

This is an improper fraction

21 goes into 25 1 time with 4 left over

1 4/21

Step-by-step explanation:

The first step is to make the multiplication of the fractions inside the parentheses. To do this, you must multiply the numerator of the first fraction by de numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:

Now you can reduce the fraction  :

 And make the corresponding addition: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators.   Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then add the products. Therefore you get:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional