Lesson 5: Lesson Five--Adding Fractions
Lesson Five-Adding fractions and mixed numbers (like and unlike denominators, with carrying over in cases of improper fractions).
Section One-Review of improper fractions- to- mixed numbers
Before we learn how to add fractions with or without common denominators, let's review a concept that will turn out to be a necessity when using fractions in all operations: turning an improper fraction into a mixed number and vice versa.
Remember, an improper fraction is one where the numerator is bigger than the denominator, for example, 5/4. All improper fractions can be turned into whole (4/4 = 1) or mixed numbers by dividing the denominator into the numerator, then turning the remainder into a fraction.
For instance:
13/7 is an improper fraction. To make it a mixed number, divide 13 by 7, you get 1 remainder 6, which becomes 1 6/7. Any remainder can be made into a fraction by putting the remainder over the divisor, the number you are dividing by.
One more example:
45/4. Divide 45 by 4 and you get 11, remainder 1. Thus, the answer is 11 1/4.
Undo this process to turn mixed numbers into improper fractions (this is vital for multiplying and dividing fractions, because the old-fashioned way, multiplying by mixed numbers, is too cumbersome--further, I haven't done this since the 4th grade!).
Take the mixed number 5 3/4. To make this an improper fraction, multiply the whole number by the denominator, then add the numerator, putting everything over the denominator.
Thus, 5 3/4: 5 x 4 = 20. Add 3, 20 + 3 = 23. So the fraction is 23/4. ALWAYS use the denominator you started with!
One more:
6 2/5: 6 x 5 = 30, then 30 + 2 = 32, so the fraction becomes 32/5.
