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Review Numbers What are Numbers? -quantities -amounts What do we use numbers for? -math -measuring -time -money -speed -baking/cooking Why are numbers important? -to be accurate Natural numbers -whole numbers above zero Ex. 1, 2, 3, … Whole numbers -numbers not divided into parts. No decimals Ex. -1, 0, 1, 2, … Rational numbers -numbers that can be put into a fractional form. Numbers and thedecimals. 1 Ex. 1, , 1.33 3 Irrational numbers -decimals that go on forever with no pattern. Ex. π = 3.1415... pi goes on forever. Addition Combining values Order doesn’t matters: you can add them in any order you want. Ex. 5 + 7 = 7 + 5 Long Hand Addition 215 One Way: Add from left to right using place value. 176 So 200 + 100 = 300 10 + 70 = 80 5 + 6 = 11 Then 300 + 80 + 11 = 391 215 176 Another Way: Add from right to left and use regrouping (carrying) 1. You can only put one number in each column in the “answer row”. Put the last digit of your solution. Carry the first number to the next column. 2. Repeat Step 1, adding your original numbers and the “carried number”. 3. Repeat Step 2-3 until you have completed all the columns. Subtraction Taking a value away from another value Order DOES matter Ex. 5 – 7 ≠ 7 – 5 Long Hand Subtraction ** same rules as adding (one number per column until you hit the last column) 415 1. 236 2. a. b. Start in column furthest to the right. If the top number is greater than the bottom number simply subtract. If not, borrow ten from the column next and place a ‘1’ next to the top number. Now subtract. Move to next column and repeat Step 1. Do this until you have used all columns. Multiplication Repeated addition. A certain number of groups of a certain value. Order DOESN’T matter Ex. 2 + 2 + 2 = 6 2x3=6 3x2=6 Long Hand Multiplication 29 54 x 20 9 50 4 1000 450 80 36 1. 2. 3. Break the numbers into their place values. Ex. 29 becomes 20 and 9. Multiply each value, putting the answer in the corresponding grid. Add all the grids together in your head. 1000 450 80 36 = 1566 29 54 same rules as adding (one number per column until you hit the last column) 1. Multiply the numbers in the ones column farthest to the right. 2. Put the last digit of the solution and “carry” the first to the second column. 3. Multiply the tens on top with the ones on the bottom and ADD the “carried” number to your solution. 4. Continue multiplying the top row with the ones digit on the bottom until you are done with the top row. 5. Put a “zero (0)” as a place holder under the digit farthest to the right in your answer spot. 6. Multiply the tens digit on the bottom with the each of the digits on the top following Steps 2 and 3. 7. When finished with the tens on the bottom, you may need to continue into the hundreds, thousands, etc. putting a placeholder whenever you switch columns. 8. Add the solution rows together Division Repeated subtraction The opposite of Multiplication Splitting a number into EQUAL groups Order MATTERS!!! o Ex. Ex. 6 3 36 6 3 2 Divisibility Rule – how to tell if a number is divisible by the BIG 10 2, 4, 6, 8, 10 even number 3 sum of digits is divisible by 3 45 – 4 + 5 = 9 and 9 is divisible by 3…so 45 is divisible by 3 4 last two digits are divisible by 4 340 – 40 is divisible by 4…so 340 is divisible by 4 5 ends in 5 or 0 6 divisible by 2 AND 3 8 last three digits divisible by 8 (like divisibility rule for 4) 9 sum of digits are divisible by 9 (like divisibility rule for 3) 10 ends in 0 Long Division 45 3 Inside the “house” 3 45 Outside the “house” 1. Divide – outside # with first digit(s) possible inside. Put solution on top. 2. Multiply – solution digit(s) on top with outside #. Put solution under first digit(s) inside. 3. Subtract – first digits inside and solution under it. 4. Bring Down – next digit inside. 5. Repeat – until you have a remainder of zero OR three (3) decimal points. With Decimals 3 764 = 254.67 6. Divide – outside # with first digit(s) possible inside. Put solution on top. 7. Multiply – solution digit(s) on top with outside #. Put solution under first digit(s) inside. 8. Subtract – first digits inside and solution under it. 9. Bring Down – next digit inside. 10. Repeat – until you have a remainder of zero OR three (3) decimal points.