Ms. Scott's SchoolNotes
For all my students, parents, and fellow teachers, here is my SchoolNotes link. I will post homework, assignments, and resources, etc. on this website. Enjoy!
Saturday, April 12, 2008
Multiplying and Dividing and Fractions, oh my!
Review - the top number of a fraction is called the numerator and the bottom number of a fraction is called the denominator. The reciprocal of a fraction is just switching the numerator and the denominator or in easier terms, flip-flopping the numbers.
Fractions - we all learn about them at some point in elementary school. We learn that it is wrong to leave a fraction as an improper fraction and we should always convert them to mixed numbers. When you get to algebra, it is the other way around. Wouldn't it be a pain to have to constantly convert fractions from mixed numbers into improper fractions and back again?
Lesson #1: Leave your fraction as an improper fraction instead of converting it to a mixed number. It will save you a lot of time and brain energy for the multiplying and dividing.
Multiplying Fractions - while we may think of this as difficult, it is really quite easy. All you have to do is multiply the numerators and multiply the denominators. You will just look at your two (or three, or four, etc.) fractions and multiply straight across. It is important to remember to leave everything where it is supposed to be - keep your numerators in the numerator and your denominators in the denominator.
Lesson #2: You multiply fractions across - multiply the numerators and multiply the denominators.
Dividing Fractions - if you can multiply fractions, then you can divide them too. Let's start talking about dividing with two fractions. Say your first fraction is 1/2 and your second fraction is 3/4. You will keep your first number, 1/2 as 1/2, you will change the division sign between 1/2 and 3/4 to a multiplication sign, and you will take the reciprocal of 3/4, which is 4/3, and put that as your second fraction. You will then have 1/2 times (or multiplied by) 4/3 and if you use the rules for multiplying you will get 4/6, which we can divide both the numerator and denominator by 2 and get 2/3. This last part where we divide both the numerator and denominator is called simplifying. Easy enough right? As one student in my class called it, keep, change, change. You could also use keep, change, flip - meaning you keep the first number, you change the division sign to multiplication, and you flip the numbers.
Lesson #3: To divide fractions, you keep the first number, change the division sign to multiplication and flip the second number.
I hope that this online lesson is helpful in understanding how to multiply and divide fractions. And that it's not too long. Don't forget, I'm always available to help you if you just ask!
Fractions - we all learn about them at some point in elementary school. We learn that it is wrong to leave a fraction as an improper fraction and we should always convert them to mixed numbers. When you get to algebra, it is the other way around. Wouldn't it be a pain to have to constantly convert fractions from mixed numbers into improper fractions and back again?
Lesson #1: Leave your fraction as an improper fraction instead of converting it to a mixed number. It will save you a lot of time and brain energy for the multiplying and dividing.
Multiplying Fractions - while we may think of this as difficult, it is really quite easy. All you have to do is multiply the numerators and multiply the denominators. You will just look at your two (or three, or four, etc.) fractions and multiply straight across. It is important to remember to leave everything where it is supposed to be - keep your numerators in the numerator and your denominators in the denominator.
Lesson #2: You multiply fractions across - multiply the numerators and multiply the denominators.
Dividing Fractions - if you can multiply fractions, then you can divide them too. Let's start talking about dividing with two fractions. Say your first fraction is 1/2 and your second fraction is 3/4. You will keep your first number, 1/2 as 1/2, you will change the division sign between 1/2 and 3/4 to a multiplication sign, and you will take the reciprocal of 3/4, which is 4/3, and put that as your second fraction. You will then have 1/2 times (or multiplied by) 4/3 and if you use the rules for multiplying you will get 4/6, which we can divide both the numerator and denominator by 2 and get 2/3. This last part where we divide both the numerator and denominator is called simplifying. Easy enough right? As one student in my class called it, keep, change, change. You could also use keep, change, flip - meaning you keep the first number, you change the division sign to multiplication, and you flip the numbers.
Lesson #3: To divide fractions, you keep the first number, change the division sign to multiplication and flip the second number.
I hope that this online lesson is helpful in understanding how to multiply and divide fractions. And that it's not too long. Don't forget, I'm always available to help you if you just ask!
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