- 1). Write down the denominator of the fraction. For the fraction 11/12, for example, write down "12." For 5/8, write down "8."
- 2). Write down two numbers that when multiplied together equal the denominator number (these numbers are called "multiplies"). Two multiples of 12, for instance, are "2" and "6" because 2 times 6 equals 12. Two multiples of 8 are "4" and "2."
- 3). Circle the multiple(s) you just wrote down if it is a prime number. A prime number is an integer that is only divisible by 1 and itself. The first five prime numbers are: 2, 3, 5, 7 and 11. Of the two multiples of 12 (2 and 6), circle the number "2." Of the two multiples of 8 (4 and 2) you would also circle the number "2."
- 4). Write down two numbers that when multiplied together equal the number(s) not circled in Step 3. For instance, since the "6" wasn't circled for the "12" factor tree, underneath "6" you would write "2 * 3" because 2 times 3 equals 6. Since "4" wasn't circled for the "8" factor tree, underneath 4 write "2 * 2."
- 5). Circle the number(s) written down in Step 4 if it is a prime number. Continue the pattern of writing down multiples and circling prime numbers until the only multiples left are prime numbers. All the new multiples written down in Step 4 are prime numbers, therefore you've reached the end of the factor tree for those numbers.
- 6). List all the prime numbers in your factor tree. For the "12" factor tree, write down "2, 2, 3." For the "8" factor tree, write down "2, 2, 2."
- 7). List all of the prime numbers the two denominators have in common. Using the numbers "12" and "8" shown in Step 6, the prime numbers you would write down are "2" and "2." Then add the prime numbers the two denominators do not have in common to the list. In this case, you would write down "2, 2, 2, 3."
- 8). Multiply all the numbers listed in the final list, from Step 7, together. The result is the least common denominator that can be used to subtract the fractions (also referred to as the "least common multiple.")
Example: 2 * 2 * 2 * 3 = 24 - 9). Multiply the denominator of the first fraction by whatever will result in the product of the least common denominator found in Step 8.
Example: 2 * 12 = 24
Multiply the numerator of the first fraction by the same number. The result is the new version of the first fraction.
Example: 2 * 11 = 22
Therefore the new fraction in this example is 22 / 24. - 10
Repeat for the second fraction.
Example:
3 * 8 = 24
3 * 5 = 15
Therefore the new fraction in this example is 15 / 24 - 11
Subtract the numerator of the second fraction from the numerator of the first fraction. Leave the denominator the same. The result is the difference between the two fractions.
An example: 22/24 - 15/24 = 7/24.
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