Understanding Fractions By Bob Snyder 2007

Writing Fractions Fractions can be written two ways: 1.With a flat line - ⅝ 2.With a slanted line – 5 / 8

Definition of a Fraction A fraction shows parts of a whole. In this group of puzzle pieces ¼ of the puzzle is green. One piece is green, and the puzzle has four pieces in all.

Parts of a Fraction The top number in a fraction is called the numerator. It tells how many you have. ¼ The bottom number in a fraction is called the denominator. It tells how many parts there are in all.

The Three Types of Fractions 1.Proper fraction: the numerator is smaller than the denominator – ½ 2.Improper fraction: the numerator is larger than the denominator – 7 / 3 (we’ll talk more about this later) 3.Mixed number: a combination of a whole number and a fraction - 1⅝ (we’ll talk more about this later, too) There are three types of fractions, which are:

Parts of a Whole Fractions show parts of a whole. You might eat one slice of this pizza, which has six equal parts.

Parts of a Set Fractions can also show parts of a set. For example, in this set of crayons one of the six crayons is purple, and the other five are not. We would say therefore that 1 / 6 of the set of crayons is purple.

Ordering Fractions Just like with whole numbers, we can order fractions from least to greatest or greatest to least. ¼ ½ ¾ These fractions are ordered from least to greatest: ¼ is smaller than ½, which is smaller than ¾.

Comparing Fractions We can also compare fractions to see if one is less than the other, one is greater than the other, or if they’re equal. Here we can say that 2 / 8 is equal to 1 / 4. We would write that like this 2 / 8 = 1 / 4.

Here we can see that ¼ is less than ½. We would write that like this: ¼ ‹ ½. We can also say that 5 / 6 is greater than 2 / 3. We would write that like this: 5 / 6 › 2 / 3.

Equivalent Fractions 3 / 9, 1 / 3, and 2 / 6 are all equal, so we call them equivalent fractions. Definition of equivalent fractions: fractions that are equal.

Fractions on the Number Line Numbers like 0, 1, and 2 are whole numbers. Fractions represent parts of a whole and they always fit between whole numbers on a number line. ½1½2½

Fraction Rules 1.If two fractions have the same numerator, the fraction with the smaller denominator is larger. 1 / 3 > 1 / 9 >

2. If two fractions have the same denominator, the fraction with the larger numerator is larger. 4 / 5 > 2 / 5 >

3. The larger the denominator, the smaller the fraction. 1 / 36 1/21/2 Would you rather have 1 / 36 of a cake or 1 / 2 ?

4. If the numerator and denominator are equal, then the fraction is equal to one whole. 6/66/6 1 If Drew ate 6 / 6 of a pie, he ate the whole thing!

5. A fraction with a numerator of zero is equal to zero. If someone offered you 0 / 4 of a pie, you would get nothing!

Mixed Numbers & Improper Fractions Let’s start with mixed numbers. All of you have used mixed numbers before but you just never realized it! You may have said, “I spent a day and a half at camp”. A day and a half is a mixed number! It’s one whole day plus part of another day.

Let’s represent a day and a half like this: 1 day ½ day We could also use an improper fraction to represent the same thing. Instead of a day and a half, let’s think of it as three half days. Let’s represent it like this instead: ½ day

Since each day is split into halves, we could say we have three halves and write it like this: 3 / 2. The denominator tells us how many parts each day is cut into; the numerator tells us how many parts we have in all.

1 day ½ day = Now we know that a day and a half is the same thing as three half days. We would write it like this: 1 ½ = 3 / 2

Fractional Parts of a Whole Number It is very important to know both multiplication and division when working with fractions! What if you need to find ¼ of 16?? Sometimes it’s easy, and you can just visualize what the answer would be, but…

other times it’s not so easy! What if you need to find 2 / 7 of 28? We use multiplication and division to help us! Here’s how it works: Step 1: divide 28 by the denominator (in this case 7). 28 ÷ 7 = 4. Step 2: multiply the answer to step 1 (in this case 4) by the numerator. 4 x 2 = 8 Step 3: Since 4 x 2 = 8, the answer is 8. 2 / 7 of 28 = 8

Let’s look at that one more time! To find 2 / 7 of 28, we first divide 28 by the denominator then multiply the quotient by the numerator. It is very important to remember the order of operations and do what is in the parentheses first! (28 ÷ 7) x 2 = 8 Order of Operations*: 1.Please (parentheses) 2.My - multiply 3.Dear - divide 4.Aunt - add 5.Sally – subtract *Always work left to right!