1. Numerator: it is the number of parts you have Denominator: it is the number of parts the whole is divided into. Proper Fraction: has a top number (numerator) less than its bottom number (denominator) Improper Fraction : The numerator is greater than (or equal to) the denominator Mixed Fraction: A whole number and proper fraction together Equivalent Fractions: Equal fractions with the same value - it is best reduce or simplify an answer. (a.k.a. Bennett Method) Numerator Denominator Ex: ¾ means -We have 3 parts -Each part is a quarter (1/4) if a whole Ex: 3/8 (Three-Eighths) Smaller 3 Larger 8 Ex: 4/3 (Four-thirds) Larger (or equal) 4 Smaller (or equal) 3 Ex: 1 1/3 (One and one-third) 3x3 5x2 Ex: 9 3 = 2 10 5 3 Therefore: 3/5 is less than 2/3 or 2/3 is greater than 3/5 FRACTIONS

2. There are 3 Simple Steps to add fractions: Step 1: Make sure the bottom numbers (the denominators) are the same, If the DENOMINATOR is DIFFERENT, you must follow the steps to find the LCD. Step 2: Add the top numbers (the numerators), put the answer over the denominator Step 3: Simplify the fraction (if needed). Example 1: 1 + 1 44 Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2. Step 2. Add the top numbers and put the answer over the same denominator: 1 + 1 = 1 + 1 = 2 4 4 4 4 Step 3. Simplify the fraction: 2 = 1 4 2 ADDING FRACTIONS

3. Adding Fractions with like denominators: - Add the numerators and keep the denominator the same. -Simplify or reduce Adding Fractions with unlike denominators: -If the denominators are not the same, you must make the denominators the same. 2 methods” 1) Common Denominator: Simple answer is to multiply the current denominators together: Ex: 1/4 + 1/4 = 2/4 =1/2 Ex: 1/3+1/6=? 1/3 +1/6=? 3 x 6 = 18 1 x 6 + 1 x 3 = 6 + 3 = 9 = 1 3 x 6 6 x 3 18 18 18 2 Keep in mind, what you do to the denominator you must do to the numerator.

4. Adding Fractions with unlike denominators: Continue 2) Least Common Denominator: List the multiples of the numerator and denominatorMultiples of 3: 3, 6, 9, 12, 15, 18 …Multiples of 6: 6: 6, 12, 18... Then find the smallest number that is the same multiples of 3:3, 6, 9, 12, 15, 18 …multiples 6: 6, 12, 18... -The answer is 6, and that is the Least Common Denominator. Then multiply both by the LCD. 1/3 +1/6=? 1 x 2 + 1 = 2 + 1 = 3 = 1 3 x 2 6 6 6 6 2 * When we multiply top and bottom of 1/3 by 2 we get 2/6 * 1/6 already has a denominator of 6

5. There are 3 Simple Steps to subtract fractions: Step 1: Make sure the bottom numbers (the denominators) are the same, If the DENOMINATOR is DIFFERENT, you must follow the steps to find the LCD. Step 2: Subtract the top numbers (the numerators), put the answer over the denominator Step 3: Simplify the fraction (if needed). Example 1: 3 - 1 44 Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2. Step 2. Subtract the top numbers and put the answer over the same denominator: 3 - 1 = 3 - 1 = 2 4 4 4 4 Step 3. Simplify the fraction: 2 = 1 4 2 SUBTRACTING FRACTIONS

6. There are 3 Simple Steps to multiply fractions: 1.Multiply the top numbers (the numerators). 2.Multiply the bottom numbers (the denominators). 1.Simplify the fraction if needed. Example 1: 1 X 2 2 5 Step 1. Multiply the top numbers: Go to step 2. 1 X 2 = 1 X 2 = 2 2 5 Step 2. Multiply the denominators (bottom numbers) 1 X 2 = 1 X 2 = 2 2 5 2 X 5 10 Step 3. Simplify the fraction: 2 = 1 10 5 MULTIPLY FRACTIONS

7. There are 3 Simple Steps to divide fractions: Step 1. Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal)reciprocal) Step 2. Multiply the first fraction by the reciprocal. Step 3. Simplify the fraction (if needed) Example 1: 1÷ 1 = 2 6 Step 1. Turn the second fraction upside-down (it becomes a reciprocal): 1 becomes 6 6 1 Step 2. Multiply the first fraction by that reciprocal: 1 ×6= 1 × 6 =6 212 × 12 Step 3. Simplify the fraction: 6 = 3 2 DIVIDE FRACTIONS

8. Multiplication Table Tricks To multiply byTrick 2add the number to itself (example 2×9 = 9+9) 5The last digit always goes 5,0,5,0,.., is always half of 10× (Example: 5x6 = half of 10x6 = half of 60 = 30) is half the number times 10 (Example: 5x6 = 10x3 = 30) 6f you multiply 6 by an even number, they both end in the same digit. Example: 6×2=12, 6×4=24, 6×6=36, etc 9is 10× the number minus the number. Example: 9×6 = 10×6 - 6 = 60-6 = 54 The last digit always goes 9,8,7,6,.. if you add the answer's digits together, you get 9. Example: 9×5=45 and 4+5=9. (But not with 9×11=99) 10put a zero after it 11up to 9x11: just repeat the digit (Example: 4x11 = 44) for 10x11 to 18x11: write the sum of the digits between the digits (Example: 15x11 = 1(1+5)5 = 165) Note: this works for any two-digit number, but if the sum of the digits is more than 9, you will have to"carry the one"carry the one" (Example: 75x11 = 7(7+5)5 = 7(12)5 = 825). 12is 10× plus 2×