Advanced Fraction Operations

Advanced Operations on Fractions

Addition of Fractions

To add fractions, find a common denominator if necessary, then add the numerators.

Example 1: 25/36 + 7/18

Find a common denominator (36): 7/18 = 14/36.

Now, add the fractions: 25/36 + 14/36 = 39/36 = 1 3/36 = 1 1/12.

Example 2: 19/20 + 3/5

Find a common denominator (20): 3/5 = 12/20.

Now, add the fractions: 19/20 + 12/20 = 31/20 = 1 11/20.

Example 3: 7/11 + 9/22

Find a common denominator (22): 7/11 = 14/22.

Now, add the fractions: 14/22 + 9/22 = 23/22 = 1 1/22.

Example 4: 35/48 + 17/24

Find a common denominator (48): 17/24 = 34/48.

Now, add the fractions: 35/48 + 34/48 = 69/48 = 1 21/48 = 1 7/16.

Example 5: 13/18 + 4/9

Find a common denominator (18): 4/9 = 8/18.

Now, add the fractions: 13/18 + 8/18 = 21/18 = 1 3/18 = 1 1/6.

Example 6: 29/45 + 11/15

Find a common denominator (45): 11/15 = 33/45.

Now, add the fractions: 29/45 + 33/45 = 62/45 = 1 17/45.

Example 7: 17/24 + 5/8

Find a common denominator (24): 5/8 = 15/24.

Now, add the fractions: 17/24 + 15/24 = 32/24 = 1 8/24 = 1 1/3.

Example 8: 8/13 + 11/26

Find a common denominator (26): 8/13 = 16/26.

Now, add the fractions: 16/26 + 11/26 = 27/26 = 1 1/26.

Example 9: 21/29 + 9/58

Find a common denominator (58): 21/29 = 42/58.

Now, add the fractions: 42/58 + 9/58 = 51/58.

Example 10: 17/25 + 13/50

Find a common denominator (50): 17/25 = 34/50.

Now, add the fractions: 34/50 + 13/50 = 47/50.

Subtraction of Fractions

To subtract fractions, find a common denominator, then subtract the numerators.

Example 1: 53/72 – 17/36

Find a common denominator (72): 17/36 = 34/72.

Now, subtract the fractions: 53/72 – 34/72 = 19/72.

Example 2: 29/45 – 7/9

Find a common denominator (45): 7/9 = 35/45.

Now, subtract the fractions: 29/45 – 35/45 = -6/45 = -2/15.

Example 3: 13/16 – 5/8

Find a common denominator (16): 5/8 = 10/16.

Now, subtract the fractions: 13/16 – 10/16 = 3/16.

Example 4: 29/32 – 7/16

Find a common denominator (32): 7/16 = 14/32.

Now, subtract the fractions: 29/32 – 14/32 = 15/32.

Example 5: 41/60 – 19/30

Find a common denominator (60): 19/30 = 38/60.

Now, subtract the fractions: 41/60 – 38/60 = 3/60 = 1/20.

Example 6: 22/45 – 8/15

Find a common denominator (45): 8/15 = 24/45.

Now, subtract the fractions: 22/45 – 24/45 = -2/45.

Example 7: 11/17 – 7/34

Find a common denominator (34): 11/17 = 22/34.

Now, subtract the fractions: 22/34 – 7/34 = 15/34.

Example 8: 63/100 – 17/50

Find a common denominator (100): 17/50 = 34/100.

Now, subtract the fractions: 63/100 – 34/100 = 29/100.

Example 9: 14/25 – 9/50

Find a common denominator (50): 14/25 = 28/50.

Now, subtract the fractions: 28/50 – 9/50 = 19/50.

Example 10: 9/14 – 5/7

Find a common denominator (14): 5/7 = 10/14.

Now, subtract the fractions: 9/14 – 10/14 = -1/14.

Multiplication of Fractions

To multiply fractions, multiply the numerators and multiply the denominators.

Example 1: 23/45 * 12/55

Multiply the numerators: 23 * 12 = 276. Multiply the denominators: 45 * 55 = 2475.

Thus, 23/45 * 12/55 = 276/2475 = 4/35.

Example 2: 9/14 * 7/18

Multiply the numerators: 9 * 7 = 63. Multiply the denominators: 14 * 18 = 252.

Thus, 9/14 * 7/18 = 63/252 = 1/4.

Example 3: 11/13 * 5/8

Multiply the numerators: 11 * 5 = 55. Multiply the denominators: 13 * 8 = 104.

Thus, 11/13 * 5/8 = 55/104.

Example 4: 17/24 * 8/35

Multiply the numerators: 17 * 8 = 136. Multiply the denominators: 24 * 35 = 840.

Thus, 17/24 * 8/35 = 136/840 = 17/105.

Example 5: 3/5 * 11/9

Multiply the numerators: 3 * 11 = 33. Multiply the denominators: 5 * 9 = 45.

Thus, 3/5 * 11/9 = 33/45 = 11/15.

Example 6: 5/7 * 6/11

Multiply the numerators: 5 * 6 = 30. Multiply the denominators: 7 * 11 = 77.

Thus, 5/7 * 6/11 = 30/77.

Example 7: 4/9 * 2/5

Multiply the numerators: 4 * 2 = 8. Multiply the denominators: 9 * 5 = 45.

Thus, 4/9 * 2/5 = 8/45.

Example 8: 6/17 * 5/6

Multiply the numerators: 6 * 5 = 30. Multiply the denominators: 17 * 6 = 102.

Thus, 6/17 * 5/6 = 30/102 = 5/17.

Example 9: 12/13 * 3/4

Multiply the numerators: 12 * 3 = 36. Multiply the denominators: 13 * 4 = 52.

Thus, 12/13 * 3/4 = 36/52 = 9/13.

Example 10: 10/17 * 5/8

Multiply the numerators: 10 * 5 = 50. Multiply the denominators: 17 * 8 = 136.

Thus, 10/17 * 5/8 = 50/136 = 25/68.

Division of Fractions

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Example 1: 23/45 ÷ 12/55

Reciprocal of 12/55 is 55/12. Now, multiply: 23/45 * 55/12 = 1265/540 = 17/7.

Example 2: 9/14 ÷ 7/18

Reciprocal of 7/18 is 18/7. Now, multiply: 9/14 * 18/7 = 162/98 = 81/49.

Example 3: 11/13 ÷ 5/8

Reciprocal of 5/8 is 8/5. Now, multiply: 11/13 * 8/5 = 88/65.

Example 4: 17/24 ÷ 8/35

Reciprocal of 8/35 is 35/8. Now, multiply: 17/24 * 35/8 = 595/192.

Example 5: 3/5 ÷ 11/9

Reciprocal of 11/9 is 9/11. Now, multiply: 3/5 * 9/11 = 27/55.

Example 6: 5/7 ÷ 6/11

Reciprocal of 6/11 is 11/6. Now, multiply: 5/7 * 11/6 = 55/42 = 5/6.

Example 7: 4/9 ÷ 2/5

Reciprocal of 2/5 is 5/2. Now, multiply: 4/9 * 5/2 = 20/18 = 10/9.

Example 8: 6/17 ÷ 5/6

Reciprocal of 5/6 is 6/5. Now, multiply: 6/17 * 6/5 = 36/85.

Example 9: 12/13 ÷ 3/4

Reciprocal of 3/4 is 4/3. Now, multiply: 12/13 * 4/3 = 48/39 = 16/13.

Example 10: 10/17 ÷ 5/8

Reciprocal of 5/8 is 8/5. Now, multiply: 10/17 * 8/5 = 80/85 = 16/17.

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