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How to Make Equivalent Fractions Step One: Choose any number to multiply against the numerator and denominator. *IT MUST BE THE SAME NUMBER YOU MULTIPLY ON THE TOP AND BOTTOM. Step Two: Multiply straight across. This is your equivalent fraction. EXAMPLE: Find an equivalent fraction for 2 is the chosen number 3 5 3 5 x 2 2 = 6 10 How to Identify Equivalent Fractions OPTION ONE: Change the fractions to a common denominator Option A: Check to see if your smaller denominator can be multiplied by another number to turn into your larger denominator. -If so, follow these steps (If not, go to Option B): -Multiply the fraction with the smaller denominator by the same number on the top and the bottom so that both denominators will be the same. -Compare the numerators once the denominators are the same. If they are equal, then the fractions are equivalent. Example: Are 2 6 and 4 12 equivalent? Think: Can 6 be multiplied by a number to turn into 12? YES (by 2). So, multiply the numerator AND denominator of that fraction by the number (2). 2 6 x 2 = 2 4 12 Now, compare your new fraction with the other fraction to determine if they are equivalent. 2 6 4 12 and 4 12 and : Are these equivalent? 4 12 YES Option B: If your smaller denominator cannot be changed into your larger denominator by multiplication, you need to find a common denominator. (Any common denominator will do.) -Multiply each fraction on the top and bottom by whatever number you need to in order to make each denominator the common denominator. -Once the denominators are the same, compare the numerators. If they are the same, then they are equivalent. Example: Are 3 5 and 4 6 equivalent? Think: -Can 5 be multiplied by a number to turn into 6? NO. -Find a multiple that 5 and 6 have in common. (An easy way is to multiply 5 by 6.) (Common multiple: 30) -Turn each fraction (through multiplication) into one that has 30 as the new denominator. 3 5 4 6 x x Are Are 6 6 5 5 3 5 18 30 = = and and 18 30 20 30 4 6 equivalent? 20 30 equivalent? NO OPTION TWO: Draw a picture *Do this option ONLY if you must. It is the least reliable. Tips for drawing fractions: -Draw RECTANGULAR boxes (not circles). -Draw the boxes on top of each other to easily compare and ensure the boxes are the same size. -Split the sections into EQUAL pieces…erase and try again if they aren’t equal the first time! Example: Are 3 5 and NO 4 6 equivalent? OPTION THREE: Cross multiply Example: Are 1. Circle the OPPOSITE numerator and denominator together. 2. Multiply the numbers you’ve circled together. Write the product ABOVE the NUMERATOR. 3. If the products written above the numerators are the same, then the fractions are equivalent. If not, whichever product written above the numerator is bigger, that represents the bigger fraction. 3 5 and 4 6 3 4 5 6 18 20 3 4 5 6 Example: Are 3 5 and NO. 4 6 equivalent? equivalent?