I forgot how to add and subtract mixed # fractions. How do you do it?
ex) 3/7+5/6=1 11/42- How did they get this answer??
ex) 5 6/13-2 8/13=2 11/13- How did they get this answer??
ex) 3/7+5/6=1 11/42
You need to find a common denominator when adding or subtracting fractions.
3/7 = 18/42
5/6 = 35/42
18/42 + 35/42 = 53/42 = 1 11/42
ex) 5 6/13-2 8/13=2 11/13
5 6/13 = 4 19/13
4 19/13 - 2 8/13 = 2 11/13
What are a unlike denominators with 2/5 +3/7
It's easy to add and subtract like fractions, or fractions with the same denominator. You just add or subtract the numerators and keep the same denominator. The tricky part comes when you add or subtract fractions that have different denominators. Since only like fractions can be added or subtracted, we first have to convert unlike fractions to equal like fractions. We want to find the smallest, or least, common denominator, because working with smaller numbers makes doing the math easier. The least common denominator, or LCD, of two fractions is the smallest number that can be divided by both denominators. Rewrite the fractions as equivalent fractions with the LCM as the denominator. Then add or subtract only the numerators and keep the denominator the same. For mixed numbers, you add the whole numbers and add the fractions separately, or change them to improper fractions then find the LCD. Then, add or subtract and simplify.
I prefer to write the multiples of both denominators until I find a common multiple.
Let’s solve the problem: ¾ + 1/6
Simply start writing all the multiples of both denominators, beginning with the numbers themselves. For example: Multiples of 4 are 4, 8, 12, 16, and so on (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12, …-- wait, stop! That's the number we're looking for, 12, because it's the first one that appears in both lists of multiples. It's the least common multiple, which we'll use as our least common denominator.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.
Yeah!
To subtract mixed number fractions, you need to convert each mixed number to an improper fraction and then find a common denominator. Once you have a common denominator, simply subtract the numerators and keep the same denominator. If the numerator is larger than the denominator, you'll end up with a mixed number again.
To add or subtract mixed number fractions, you need to follow these steps:
1. Convert the mixed numbers to improper fractions: To do this, multiply the whole number by the denominator of the fraction, then add the numerator. This will give you the numerator of the new fraction, and the denominator remains the same.
2. Find a common denominator: Look at the denominators of the fractions you are adding or subtracting. If they are the same, great! You can skip this step. If they are different, you need to find a common denominator. To do this, you need to find the least common multiple (LCM) of the denominators. Once you have the LCM, you can convert the fractions to have the same denominator.
3. Add or subtract the fractions: Once you have the fractions with the same denominator, you can add or subtract the numerators while keeping the same denominator.
4. Simplify the fraction (if necessary): If the resulting fraction is an improper fraction (where the numerator is larger than the denominator), you can simplify it by dividing the numerator by the denominator. The whole number part will be the quotient, and the remainder over the denominator will be the fraction part.
Now, let's go through the examples you provided:
Example 1: 3/7 + 5/6 = 1 11/42
- Convert the mixed numbers to improper fractions:
3/7 = 3 * 7/7 + 3/7 = 21/7 + 3/7 = 24/7
5/6 = 5 * 6/6 + 5/6 = 30/6 + 5/6 = 35/6
- Find a common denominator: Both fractions already have different denominators, so we need to find the LCM, which is 42 in this case.
- Convert the fractions to have the same denominator:
24/7 = 24 * 6/7 * 6 = 144/42
35/6 = 35 * 7/6 * 7 = 245/42
- Add the fractions:
144/42 + 245/42 = 389/42
- Simplify the fraction (if necessary):
389/42 = 9 11/42
Example 2: 5 6/13 - 2 8/13 = 2 11/13
- Convert the mixed numbers to improper fractions:
5 6/13 = 5 * 13/13 + 6/13 = 65/13 + 6/13 = 71/13
2 8/13 = 2 * 13/13 + 8/13 = 26/13 + 8/13 = 34/13
- Find a common denominator: Both fractions already have the same denominator, which is 13.
- Subtract the fractions:
71/13 - 34/13 = 37/13
- Simplify the fraction (if necessary):
37/13 = 2 11/13
I hope this explanation helps you understand how to add and subtract mixed number fractions.