What are the steps involved in subtracting mixed numbers?
To subtract mixed numbers, we follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
A mixed number is a combination of a whole number and a fraction. To subtract mixed numbers, it's easier to work with improper fractions. To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. Place the result over the denominator.
For example, if we have the mixed number 3 1/2, we multiply 3 (whole number) by 2 (denominator) and add 1 (numerator), resulting in 7/2.
Step 2: Find a common denominator.
Since we are subtracting two fractions, the next step is to find a common denominator. If the denominators are the same, we can skip this step. Otherwise, we need to determine the least common multiple (LCM) of the two denominators.
For example, if we are subtracting 5/6 from 3/4, the LCM of 4 and 6 is 12.
Step 3: Rewrite each fraction with the common denominator.
To rewrite each fraction with the common denominator, we need to multiply the numerator and denominator of each fraction by a factor that will make the denominator equal to the common denominator found in Step 2.
Using the example of 3/4 - 5/6, we multiply the numerator and denominator of 3/4 by 3, resulting in 9/12. Similarly, we multiply the numerator and denominator of 5/6 by 2, giving us 10/12.
Step 4: Subtract the fractions.
Now that both fractions have the same denominator, we can subtract them. Simply subtract the numerators while keeping the common denominator the same.
Continuing with the example, we subtract 10/12 from 9/12, resulting in -1/12.
Step 5: Simplify if necessary.
If possible, simplify the resulting fraction. In our example, -1/12 cannot be further simplified.
Step 6: Convert back to a mixed number (if required).
If the answer needs to be in mixed number form, we can convert the improper fraction back to a mixed number. To do this, divide the numerator by the denominator. The quotient becomes the whole number, while any remainder becomes the numerator of the fraction.
For the example -1/12, we divide -1 by 12, obtaining a quotient of 0 and a remainder of -1. Thus, the mixed number form of -1/12 is 0 - 1/12 or simply -1/12.
That's it! We have successfully subtracted the mixed numbers.
Step 1: Convert the mixed numbers to improper fractions.
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, place the sum over the original denominator.
Step 2: Find a common denominator.
- To subtract mixed numbers, you need to have the same denominator for both fractions. Find the least common multiple (LCM) of the denominators.
Step 3: Rewrite the fractions with the common denominator.
- Multiply the numerator and denominator of each fraction by the same factor so that they both have the common denominator.
Step 4: Subtract the fractions' numerators.
- Subtract the numerators of the fractions, leaving the common denominator unchanged.
Step 5: Simplify the resulting fraction, if needed.
- If the resulting fraction can be simplified further, divide both the numerator and denominator by their greatest common divisor (GCD).
Step 6: Determine if the resulting fraction is a proper or improper fraction, or a mixed number.
- If the numerator is larger than the denominator, the fraction is improper. Convert it to a mixed number if necessary.
Step 7: Write the final answer in the form of a mixed number, if applicable.
- If the resulting fraction is improper, convert it to a mixed number, if required.
These steps will guide you through the process of subtracting mixed numbers.