Equivalent Fractions

Fractions are simply equal pieces of something. Any object can be broken into equal pieces - even thousands or millions!

   3=Numerator==Part of whole
   4=Denominator==Whole

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same:

1/2  =  2/4  =  4/8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

Here is why those fractions are really the same:

       x2     x2
1/2 = 2/4 = 4/8

      x2      x2

3 ways to find equivalent fractions:

1. Model 

2.  Multiply    

   x2     x2
1/2 = 2/4 = 4/8

      x2      x2

What ever you do to the numerator...You do to the denominator.

3. Divide

(simplest form)

(reduce)

   divide by 2     
4/8 = 2/4 = 1/2

     divide by 2

What ever you do to the numerator...You do to the denominator.

3rd Grade Math Study Guide

3^rd Grade 2^nd 9 Weeks Math Study Guide:

Unknown Numbers:   7 x ? = 35          36 divided ? = 6

Properties of Operation:

Commutative Property      7 x 2=    2x7=                     order does not matter

Associative Property          (3 x 5) x 2 =      5 x (3 x 2)=        order does not matter

Distributive Property        8 x 9 =

Multiplication/Division:           7 x 7=     8 x 6 =        18 divided 2 =           48 divided 8 =

Two-Step Word Problems:    Tom went to the store and bought a box of cookies that cost $5.  He also picked up a bag of apples for $6 and a pack of meat for $9.  How much change did she get back if she paid with $40?

Patterns:  Find the rule and finish the pattern.

5, 10, 15,__,___,___                                     2, 4, 8, 16,___                        3, 8, 13,__,__

Multiply by Multiples of 10:          40 x 8=                      90 x 3=            60 x 7=

Area:    Find the area of each shape.    

         

Arithmetic Patterns

Pattern:
Things that are arranged following a rule or rules.

Example: there is a pattern in these numbers: 2, 7, 12, 17, 22, ... they follow a rule "start at 2 and add 5 each time"

What is a RULE?

A RULE is a set of directions on how to create a
pattern.

In other words: it tells you what to do with the
pattern.

EX: Rule--Start at 0 and add 2

Pattern: 0, 2, 4, 6, 8, 10, ___, ___, ____

Patterns can be found in addition, subtraction,
multiplication, and division.

• Addition-- start at 0 and add 3
• Pattern-- 0, 3, __, ___, ___

• Subtraction--take 5 away
• Pattern--- 25, 20, ___, ____, ____

• Multiplication--- count by 4

• Pattern--4, 8, ___, ___,____

• Division--Divide by 2
• Pattern-- 40, 20, ___,____