or “Half of one, Six twelfths of the other” Equivalent Fractions or “Half of one, Six twelfths of the other”

What is a fraction? A fraction is part of a whole that is made up of equal parts.

Multiply by 1 5 x 1 = 235 x 1 = 2/3 x 1 = a x 1 = 5 235 2/3 a

What is 1?

Was there something else? Yes, it could also be part of a whole group of items. Here is a group of cookies. We could say 1/5 of these cookies are chocolate chip. We could also say that 4/5 are Oreos. 1 5 4 5 3 4 Oops, let’s make that 3/4 are Oreos.

Say, what? Okay, try this. Let’s take a rectangle and divide it into 8 parts. Now, if we color 2 parts, we say that 2/8 of the rectangle are shaded. 2 8

I’m with you. What’s next? Now, let’s take that same rectangle and divide it into 16 parts. If we color 4 parts, we say that 4/1 of the rectangle are shaded. 4 16

So that means? So that means 2/8 is equivalent to 4/1 . 16 And we write it this way: = 2 8 4 16

Give us another example. Okay, how about: 3 9 1 3 3 9 1 3 =

Vocabulary Equivalent fractions are fractions that represent the same amount. 2 4 = 8 4

Creating Equivalent Fractions Multiply the numerator and denominator by the same number. Divide the numerator and denominator by the same number (it has to be a common factor to work with division) We can choose any number to multiply by. Let’s multiply by 2. 3 x 2 6 So, 3/5 is equivalent to 6/10. = 5 x 2 10

How do you find equivalent fractions? You can multiply (or divide), but you must multiply (or divide) both the numerator AND denominator by the same number. 1 4 3 12 x3 = x3 2 5 4 10 x2 = x2

What about dividing? Here’s how. 4 20 1 5 ÷ 4 = ÷ 4 4 14 2 7 ÷ 2 = ÷2

What if you’re not sure? Here is how you can check to see if two fractions are equivalent. You can “cross-multiply.” 5 x 2 = 10 1 5 2 10 = 1 x 10 = 10 Since both products are the same, these two fractions are equivalent.

How do you know if they’re not equivalent? Here is an example. You still “cross-multiply.” 3 x 4 = 12 2 3 4 5 = 2 x 5 = 10 Since both products are NOT the same, these two fractions are NOT equivalent.

Vocabulary: Simplest Form Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1. Examples of fractions that are in simplest form: 4 2 3 5 11 8

Vocabulary: Simplify Simplify means to reduce a fraction to it’s simplest form.

Writing Fractions in Simplest Form. Find the greatest common factor (GCF) of the numerator and denominator. Divide both numbers by the GCF.

Example: 20 5 ÷ 4 = Simplest Form 28 ÷ 4 7 20 28 20: 1, 2, 4, 5, 10, 20 We will divide by 4. 28: 1, 2, 4, 7, 14, 28 1 x 20 2 x 10 4 x 5 1 x 28 2 x 14 4 x 7 Common Factors: 1, 2, 4 GCF: 4