Question

(5/21+2/15)+2/21= (2/35+3/28)+1/28= (7/30+8/45)+(2/45+1/30)= (5/24+11/60)+(13/60+1/24)=

Answer 1

1) 7/21+2/15=(7*15+2*21)/315=147/315

2) 2/35+4/28=2/35+5/35=1/5

3) 8/30+10/45=(8*1,5+10)/45=22/45

4) 6/24+24/60=1/4+6/15=(15+6*4)/60=39/60

Answer 2

To simplify the given expressions, we need to find a common denominator for each set of fractions and then perform the addition. Let's go step by step:

1. (5/21 + 2/15) + 2/21: To add these fractions, we need a common denominator. The least common multiple (LCM) of 21 and 15 is 105. So, we'll convert each fraction to have a denominator of 105:

(5/21) = (5/21) * (5/5) = 25/105 (2/15) = (2/15) * (7/7) = 14/105 2/21 = 2/21

Now, the expression becomes: (25/105 + 14/105) + 2/21

Adding the fractions: (25/105 + 14/105) = 39/105

The expression is now: (39/105) + 2/21

To add these fractions, we again need a common denominator. The LCM of 105 and 21 is 105. So, we'll convert 2/21 to have a denominator of 105:

2/21 = (2/21) * (5/5) = 10/105

Now, the expression becomes: (39/105) + (10/105)

Adding the fractions: (39/105 + 10/105) = 49/105

So, the result of the first expression is 49/105.

2. (2/35 + 3/28) + 1/28: To add these fractions, we need a common denominator. The least common multiple (LCM) of 35 and 28 is 140. So, we'll convert each fraction to have a denominator of 140:

(2/35) = (2/35) * (4/4) = 8/140 (3/28) = (3/28) * (5/5) = 15/140 1/28 = 1/28

Now, the expression becomes: (8/140 + 15/140) + 1/28

Adding the fractions: (8/140 + 15/140) = 23/140

The expression is now: (23/140) + 1/28

To add these fractions, we again need a common denominator. The LCM of 140 and 28 is 140. So, we'll convert 1/28 to have a denominator of 140:

1/28 = (1/28) * (5/5) = 5/140

Now, the expression becomes: (23/140) + (5/140)

Adding the fractions: (23/140 + 5/140) = 28/140

Since 28/140 can be simplified, we divide both the numerator and denominator by 28 (the greatest common divisor): 28 ÷ 28 = 1, and 140 ÷ 28 = 5.

So, the result of the second expression is 1/5.

3. (7/30 + 8/45) + (2/45 + 1/30): We'll start by adding the fractions within the parentheses first:

(7/30 + 1/30) = 8/30 = 4/15 (8/45 + 2/45) = 10/45 = 2/9

Now, the expression becomes: (4/15) + (2/9)

To add these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 9 is 45. So, we'll convert each fraction to have a denominator of 45:

(4/15) = (4/15) * (3/3) = 12/45 (2/9) = (2/9) * (5/5) = 10/45

Now, the expression becomes: (12/45) + (10/45)

Adding the fractions: (12/45 + 10/45) = 22/45

So, the result of the third expression is 22/45.

4. (5/24 + 11/60) + (13/60 + 1/24): We'll start by adding the fractions within the parentheses first:

(5/24 + 1/24) = 6/24 = 1/4 (11/60 + 13/60) = 24/60 = 2/5

Now, the expression becomes: (1/4) + (2/5)

To add these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 5 is 20. So, we'll convert each fraction to have a denominator of 20:

(1/4) = (1/4) * (5/5) = 5/20 (2/5) = (2/5) * (4/4) = 8/20

Now, the expression becomes: (5/20) + (8/20)

Adding the fractions: (5/20 + 8/20) = 13/20

So, the result of the fourth expression is 13/20.

In summary, the results of each expression are as follows:

1. (5/21 + 2/15) + 2/21 = 49/105
2. (2/35 + 3/28) + 1/28 = 1/5
3. (7/30 + 8/45) + (2/45 + 1/30) = 22/45
4. (5/24 + 11/60) + (13/60 + 1/24) = 13/20