Perform the indicated operations. Reduce the answers to lowest terms....

1.) 7 3/5 + 2 4/7 = _______________
2.) 8 5/9 + 15 5/6 =________________
3.) 14 5/10 + 8 3/5 = ________________
4.) 5/6 x 3/4 = _____________________

Reduce each fraction to lowest terms. Write improper fractions as mixed numbers.

1.) 15/4 = ______________
2.) 100/12 = _______________
3.) 36/40 = ________________
4.) 73/7 = ________________
5.) 180/32 = ________________
6.) 54/80 =_________________
7.) 49/42 =_________________
8.) 205/50 =_________________
9.) 63/108 =_________________

I'll be glad to show you how to do three of these problems. Which three do you want me to do?

1.) To add mixed numbers, we need to first add the whole numbers and then the fractions separately.

7 3/5 + 2 4/7

First, add the whole numbers: 7 + 2 = 9.

Now, let's add the fractions: 3/5 + 4/7

To find a common denominator, we multiply the denominators: 5 * 7 = 35.

Next, we convert the fractions to have a common denominator of 35:
(3/5) * (7/7) = 21/35
(4/7) * (5/5) = 20/35

Now, we can add the fractions: 21/35 + 20/35 = 41/35.

Since the fraction is improper, we need to convert it back to a mixed number:
41/35 = 1 6/35

Therefore, 7 3/5 + 2 4/7 = 9 1 6/35.

2.) Similar to the previous problem, let's add the whole numbers first:

8 5/9 + 15 5/6

8 + 15 = 23

Next, let's add the fractions: 5/9 + 5/6

To find a common denominator, we multiply the denominators: 9 * 6 = 54.

Next, we convert the fractions to have a common denominator of 54:
(5/9) * (6/6) = 30/54
(5/6) * (9/9) = 45/54

Now, we can add the fractions: 30/54 + 45/54 = 75/54.

Since the fraction is improper, we need to convert it back to a mixed number:
75/54 = 1 21/54.

Therefore, 8 5/9 + 15 5/6 = 23 1 21/54.

3.) Let's follow the same steps as the previous problems:

14 5/10 + 8 3/5

14 + 8 = 22

Next, let's add the fractions: 5/10 + 3/5

To find a common denominator, we multiply the denominators: 10 * 5 = 50.

Next, we convert the fractions to have a common denominator of 50:
(5/10) * (5/5) = 25/50
(3/5) * (10/10) = 30/50

Now, we can add the fractions: 25/50 + 30/50 = 55/50.

Since the fraction is improper, we need to convert it back to a mixed number:
55/50 = 1 5/50.

Therefore, 14 5/10 + 8 3/5 = 22 1 5/50.

4.) To multiply fractions, we simply multiply the numerators together and the denominators together:

5/6 x 3/4 = (5 * 3)/(6 * 4) = 15/24.

To reduce the fraction to its lowest terms, we divide both the numerator and denominator by their greatest common divisor, which in this case is 3:

15/24 ÷ 3/3 = 5/8.

Therefore, 5/6 x 3/4 = 5/8.

Now, let's reduce the given fractions to their lowest terms:

1.) 15/4 can be simplified further. The greatest common divisor of 15 and 4 is 1.

Therefore, 15/4 is already in its lowest terms.

2.) 100/12 can be simplified further. The greatest common divisor of 100 and 12 is 4.

Dividing both the numerator and denominator by 4 we get: (100 ÷ 4)/(12 ÷ 4) = 25/3.

Therefore, 100/12 in its lowest terms is 25/3.

3.) 36/40 can be simplified further. The greatest common divisor of 36 and 40 is 4.

Dividing both the numerator and denominator by 4 we get: (36 ÷ 4)/(40 ÷ 4) = 9/10.

Therefore, 36/40 in its lowest terms is 9/10.

4.) 73/7 is already in its lowest terms as there is no common divisor greater than 1.

Therefore, 73/7 is already in its lowest terms.

5.) 180/32 can be simplified further. The greatest common divisor of 180 and 32 is 4.

Dividing both the numerator and denominator by 4 we get: (180 ÷ 4)/(32 ÷ 4) = 45/8.

Therefore, 180/32 in its lowest terms is 45/8.

6.) 54/80 can be simplified further. The greatest common divisor of 54 and 80 is 2.

Dividing both the numerator and denominator by 2 we get: (54 ÷ 2)/(80 ÷ 2) = 27/40.

Therefore, 54/80 in its lowest terms is 27/40.

7.) 49/42 can be simplified further. The greatest common divisor of 49 and 42 is 7.

Dividing both the numerator and denominator by 7 we get: (49 ÷ 7)/(42 ÷ 7) = 7/6.

Therefore, 49/42 in its lowest terms is 7/6.

8.) 205/50 can be simplified further. The greatest common divisor of 205 and 50 is 5.

Dividing both the numerator and denominator by 5 we get: (205 ÷ 5)/(50 ÷ 5) = 41/10.

Therefore, 205/50 in its lowest terms is 41/10.

9.) 63/108 can be simplified further. The greatest common divisor of 63 and 108 is 9.

Dividing both the numerator and denominator by 9 we get: (63 ÷ 9)/(108 ÷ 9) = 7/12.

Therefore, 63/108 in its lowest terms is 7/12.

To solve the given operations and reduce the answers to lowest terms, we will follow the steps below:

1. Addition of Mixed Numbers:
- Convert each mixed number to an improper fraction.
- Find a common denominator for the fractions.
- Add the fractions and simplify the result, if required.
- Express the answer as a mixed number, if necessary, by dividing the numerator by the denominator and writing the remainder as a fraction.

Let's solve the given addition problems:

1.) To add 7 3/5 and 2 4/7:
- Convert both mixed numbers to improper fractions:
7 3/5 = (7*5 + 3)/5 = 38/5
2 4/7 = (2*7 + 4)/7 = 18/7

- Find the common denominator: The least common multiple of 5 and 7 is 35.

38/5 + 18/7 = (38/5)*(7/7) + (18/7)*(5/5) = 266/35 + 90/35 = 356/35

- Simplify the result if required: The numerator and denominator, 356 and 35, have a common factor of 71. We can divide both by 71 to simplify the fraction.

356/35 = (356/71)/(35/71) = 4/1 = 4

Therefore, 7 3/5 + 2 4/7 = 4

2.) To add 8 5/9 and 15 5/6, follow the same process as above and simplify the result.

3.) To add 14 5/10 and 8 3/5, follow the same process as above and simplify the result.

4.) To multiply 5/6 and 3/4:
- Simply multiply the numerators and denominators of the two fractions:

5/6 * 3/4 = (5*3)/(6*4) = 15/24

- Simplify the fraction if needed: Both the numerator and denominator are divisible by 3.

15/24 = (15/3) / (24/3) = 5/8

Therefore, 5/6 multiplied by 3/4 = 5/8

Now, let's solve the fraction reduction problems:

1.) To reduce 15/4:
- Divide the numerator (15) by the denominator (4):
15 ÷ 4 = 3 remainder 3

- Write the result as a mixed number:
15/4 = 3 and 3/4

2.) To reduce 100/12, follow the same process as above.

3.) To reduce 36/40, follow the same process as above.

4.) To reduce 73/7, follow the same process as above.

5.) To reduce 180/32, follow the same process as above.

6.) To reduce 54/80, follow the same process as above.

7.) To reduce 49/42, follow the same process as above.

8.) To reduce 205/50, follow the same process as above.

9.) To reduce 63/108, follow the same process as above.

Please provide the fractions for problems 5-9 so that I can guide you through the calculations and reduction process.