Fractions Operations

Operations on Fractions

Addition of Fractions

To add fractions, if the denominators are the same, simply add the numerators and keep the denominator. If the denominators are different, find a common denominator.

Example 1: 1/4 + 2/4

Since the denominators are the same (4), we add the numerators: 1 + 2 = 3.

So, 1/4 + 2/4 = 3/4.

Example 2: 1/3 + 1/6

Find a common denominator (6): 1/3 = 2/6.

Now, add the fractions: 2/6 + 1/6 = 3/6.

Simplify: 3/6 = 1/2.

Example 3: 3/5 + 4/5

The denominators are the same (5), so add the numerators: 3 + 4 = 7.

Thus, 3/5 + 4/5 = 7/5 = 1 2/5.

Example 4: 2/7 + 3/7

The denominators are the same (7), so add the numerators: 2 + 3 = 5.

Thus, 2/7 + 3/7 = 5/7.

Example 5: 5/6 + 1/3

Find a common denominator (6): 1/3 = 2/6.

Now, add the fractions: 5/6 + 2/6 = 7/6 = 1 1/6.

Example 6: 3/8 + 1/4

Find a common denominator (8): 1/4 = 2/8.

Now, add the fractions: 3/8 + 2/8 = 5/8.

Example 7: 7/10 + 2/5

Find a common denominator (10): 2/5 = 4/10.

Now, add the fractions: 7/10 + 4/10 = 11/10 = 1 1/10.

Example 8: 2/9 + 4/27

Find a common denominator (27): 2/9 = 6/27.

Now, add the fractions: 6/27 + 4/27 = 10/27.

Example 9: 1/5 + 1/3

Find a common denominator (15): 1/5 = 3/15 and 1/3 = 5/15.

Now, add the fractions: 3/15 + 5/15 = 8/15.

Example 10: 7/12 + 5/8

Find a common denominator (24): 7/12 = 14/24 and 5/8 = 15/24.

Now, add the fractions: 14/24 + 15/24 = 29/24 = 1 5/24.

Subtraction of Fractions

To subtract fractions, follow the same rules as addition. If the denominators are the same, subtract the numerators. If the denominators are different, find a common denominator.

Example 1: 3/4 – 1/4

The denominators are the same (4), so subtract the numerators: 3 – 1 = 2.

Thus, 3/4 – 1/4 = 2/4 = 1/2.

Example 2: 5/6 – 1/2

Find a common denominator (6): 1/2 = 3/6.

Now, subtract the fractions: 5/6 – 3/6 = 2/6 = 1/3.

Example 3: 7/8 – 3/8

The denominators are the same (8), so subtract the numerators: 7 – 3 = 4.

Thus, 7/8 – 3/8 = 4/8 = 1/2.

Example 4: 5/12 – 1/6

Find a common denominator (12): 1/6 = 2/12.

Now, subtract the fractions: 5/12 – 2/12 = 3/12 = 1/4.

Example 5: 4/5 – 2/3

Find a common denominator (15): 4/5 = 12/15 and 2/3 = 10/15.

Now, subtract the fractions: 12/15 – 10/15 = 2/15.

Example 6: 9/10 – 1/2

Find a common denominator (10): 1/2 = 5/10.

Now, subtract the fractions: 9/10 – 5/10 = 4/10 = 2/5.

Example 7: 5/9 – 2/7

Find a common denominator (63): 5/9 = 35/63 and 2/7 = 18/63.

Now, subtract the fractions: 35/63 – 18/63 = 17/63.

Example 8: 6/11 – 1/5

Find a common denominator (55): 6/11 = 30/55 and 1/5 = 11/55.

Now, subtract the fractions: 30/55 – 11/55 = 19/55.

Example 9: 7/12 – 5/8

Find a common denominator (24): 7/12 = 14/24 and 5/8 = 15/24.

Now, subtract the fractions: 14/24 – 15/24 = -1/24.

Example 10: 8/9 – 3/4

Find a common denominator (36): 8/9 = 32/36 and 3/4 = 27/36.

Now, subtract the fractions: 32/36 – 27/36 = 5/36.

Multiplication of Fractions

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

Example 1: 1/3 * 2/5

Multiply the numerators: 1 * 2 = 2. Multiply the denominators: 3 * 5 = 15.

Thus, 1/3 * 2/5 = 2/15.

Example 2: 4/7 * 3/5

Multiply the numerators: 4 * 3 = 12. Multiply the denominators: 7 * 5 = 35.

Thus, 4/7 * 3/5 = 12/35.

Example 3: 2/9 * 3/8

Multiply the numerators: 2 * 3 = 6. Multiply the denominators: 9 * 8 = 72.

Thus, 2/9 * 3/8 = 6/72 = 1/12.

Example 4: 5/6 * 2/3

Multiply the numerators: 5 * 2 = 10. Multiply the denominators: 6 * 3 = 18.

Thus, 5/6 * 2/3 = 10/18 = 5/9.

Example 5: 7/8 * 4/5

Multiply the numerators: 7 * 4 = 28. Multiply the denominators: 8 * 5 = 40.

Thus, 7/8 * 4/5 = 28/40 = 7/10.

Example 6: 3/4 * 5/6

Multiply the numerators: 3 * 5 = 15. Multiply the denominators: 4 * 6 = 24.

Thus, 3/4 * 5/6 = 15/24 = 5/8.

Example 7: 1/2 * 1/3

Multiply the numerators: 1 * 1 = 1. Multiply the denominators: 2 * 3 = 6.

Thus, 1/2 * 1/3 = 1/6.

Example 8: 3/5 * 7/8

Multiply the numerators: 3 * 7 = 21. Multiply the denominators: 5 * 8 = 40.

Thus, 3/5 * 7/8 = 21/40.

Example 9: 4/9 * 2/7

Multiply the numerators: 4 * 2 = 8. Multiply the denominators: 9 * 7 = 63.

Thus, 4/9 * 2/7 = 8/63.

Example 10: 5/6 * 3/4

Multiply the numerators: 5 * 3 = 15. Multiply the denominators: 6 * 4 = 24.

Thus, 5/6 * 3/4 = 15/24 = 5/8.

Division of Fractions

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

Example 1: 1/3 ÷ 2/5

Reciprocal of 2/5 is 5/2. Now, multiply: 1/3 * 5/2 = 5/6.

Example 2: 3/4 ÷ 1/2

Reciprocal of 1/2 is 2/1. Now, multiply: 3/4 * 2/1 = 6/4 = 3/2.

Example 3: 7/8 ÷ 4/5

Reciprocal of 4/5 is 5/4. Now, multiply: 7/8 * 5/4 = 35/32.

Example 4: 6/7 ÷ 3/5

Reciprocal of 3/5 is 5/3. Now, multiply: 6/7 * 5/3 = 30/21 = 10/7.

Example 5: 2/3 ÷ 4/9

Reciprocal of 4/9 is 9/4. Now, multiply: 2/3 * 9/4 = 18/12 = 3/2.

Example 6: 5/6 ÷ 1/2

Reciprocal of 1/2 is 2/1. Now, multiply: 5/6 * 2/1 = 10/6 = 5/3.

Example 7: 4/9 ÷ 2/3

Reciprocal of 2/3 is 3/2. Now, multiply: 4/9 * 3/2 = 12/18 = 2/3.

Example 8: 3/5 ÷ 7/8

Reciprocal of 7/8 is 8/7. Now, multiply: 3/5 * 8/7 = 24/35.

Example 9: 5/6 ÷ 3/4

Reciprocal of 3/4 is 4/3. Now, multiply: 5/6 * 4/3 = 20/18 = 10/9.

Example 10: 2/7 ÷ 5/3

Reciprocal of 5/3 is 3/5. Now, multiply: 2/7 * 3/5 = 6/35.

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