Slide 1 / 239 Slide 2 / 239 5th Grade Division 2015-11-25 www.njctl.org Slide 3 / 239 Slide 4 / 239 Division Unit Topics Click on the topic to go to that section Divisibility Rules · Patterns in Multiplication and Division · Division of Whole Numbers · Divisibility Rules Division of Decimals · Glossary & Standards · Return to Table of Contents Slide 5 / 239 Slide 6 / 239 Divisible Divisible two Divisible is when one number is divided by another, and the result is an exact whole number. BUT, 9 is not divisible by 2 because 9 ÷ 2 is 4 five four with one left over. Example: 15 is divisible by 3 three because 15 ÷ 3 = 5 exactly.
Slide 7 / 239 Slide 8 / 239 Divisibility Rules Divisibility Look at the last digit in the Ones Place! A number is divisible by another number when the remainder is 0. 2 Last digit is even-0,2,4,6 or 8 5 Last digit is 5 OR 0 There are rules to tell if a number is divisible by certain other numbers. 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4 Slide 9 / 239 Slide 10 / 239 Divisibility Practice Divisibility Rules Let's Practice! Is 34 divisible by 2? Yes, because the digit in the ones place is an even Click for Link number. 34 / 2 = 17 Divisibility Rules You Tube song Is 1,075 divisible by 5? Yes, because the digit in the ones place is a 5. 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a 0. 740 / 10 = 74 Slide 11 / 239 Slide 12 / 239 Divisibility Practice Divisibility Practice Is 6,237 divisible by 9? Is 258 divisible by 3? Yes, because the sum of its digits is divisible by 9. Yes, because the sum of its digits is divisible by 3. 6 + 2 + 3 + 7 = 18 Look 18 / 9 = 2 2 + 5 + 8 = 15 Look 15 / 3 = 5 6,237 /9 = 693 258 / 3 = 86 Is 520 divisible by 4? Is 192 divisible by 6? Yes, because the number made by the last two digits Yes, because the sum of its digits is divisible by 3 is divisible by 4. AND 2. 20 / 4 = 5 1 + 9 + 2 = 12 Look 12 /3 = 4 192 / 6 = 32 520 / 4 = 130
Slide 13 / 239 Slide 14 / 239 2 Is 315 divisible by 5? 1 Is 198 divisible by 2? Yes Yes No No Slide 15 / 239 Slide 16 / 239 3 Is 483 divisible by 3? 4 294 is divisible by 6. Yes True No False Slide 17 / 239 Slide 18 / 239 Divisibility 5 3,926 is divisible by 9. 9 Some numbers are divisible by more than 1 digit. Let's practice using the divisibility rules. True 18 is divisible by how many digits? False Let's see if your choices are correct. Click Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Click 6 Did you guess 3 and 5? 4
Slide 19 / 239 Slide 20 / 239 Divisibility Table Divisibility Complete the table using the Divisibility Rules. 28 is divisible by how many digits? (Click on the cell to reveal the answer) Let's see if your choices are correct. by2 by 3 by 4 by 5 by 6 by 9 by 10 Divisible Did you guess 2 and 4? Click 39 no yes no no no no no 156 yes yes yes no yes no no 530 is divisible by how many digits? no yes no no no no no 429 Let's see if your choices are correct. 446 yes no no no no no no Click Did you guess 2, 5, and 10? 1,218 yes yes no no yes no no 1,006 yes no no no no no no 28,550 yes no no yes no no yes Now it's your turn...... Slide 21 / 239 Slide 22 / 239 6 What are all the digits 15 is 7 What are all the digits 36 is divisible by? divisible by? Slide 23 / 239 Slide 24 / 239 8 What are all the digits 1,422 is 9 What are all the digits 240 is divisible by? divisible by?
Slide 25 / 239 Slide 26 / 239 10 What are all the digits 64 is divisible by? Patterns in Multiplication and Division Return to Table of Contents Slide 27 / 239 Slide 28 / 239 Number Systems Number Systems A number system is a systematic way of counting numbers. There are many different number systems that have been used throughout history, and are still used in different parts of the world today. Roman Numerals For example, the Myan number Sumerian system used a symbol for zero, a dot wedge = 10, line = 1 for one or twenty, and a bar for five. Slide 29 / 239 Slide 30 / 239 Base Ten Our Number System We have a base ten number system. This means that in a multi- digit number, a digit in one place is ten times as much as the place to its right. Generally, we have 10 fingers and 10 toes. Also, a digit in one place is 1/10 the value of the place to its left. This makes it very easy to count to ten. Many historians believe that this is where our number system came from. Base ten .
Slide 31 / 239 Slide 32 / 239 Base 10 Powers of 10 Numbers can be VERY long. $100,000,000,000,000 Wouldn't you love to have one hundred trillion dollars? Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of 10 . How do you think things would be different if we had six fingers on each hand? Slide 33 / 239 Slide 34 / 239 Powers of 10 Powers of 10 Numbers like 10, 100 and 1,000 are called powers of 10. 10 3 They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or 10 2 . The raised digit is called the exponent . The exponent tells how many tens are multiplied. 1,000 can be written as 10 x 10 x 10 or 10 3 . Slide 35 / 239 Slide 36 / 239 Powers of 10 Powers of 10 Powers of 10 (greater than 1) A number written with an exponent, like 10 3 , is in exponential Standard Product Exponential notation . Notation of 10s Notation 10 10 10 1 A number written in a more familiar way, like 1,000 is in standard 100 10 x 10 10 2 notation . 1,000 10 x 10 x 10 10 3 10,000 10 x 10 x 10 x 10 10 4 100,000 10 x 10 x 10 x 10 x 10 10 5 1,000,000 10 x 10 x 10 x 10 x 10 x 10 10 6
Slide 37 / 239 Slide 38 / 239 Multiplying Powers of 10 Powers of 10 To multiply by powers of ten, keep the placeholders by adding on as many 0s as Remember, in powers of ten appear in the power of 10. like 10, 100 and 1,000 the zeros are placeholders. Examples: Each place holder represents a value ten 28 x 10 = 280 Add on one 0 to show 28 tens times greater than the place to its right. 28 x 100 = 2,800 Add on two 0s to show 28 hundreds Because of this, it is easy to MULTIPLY a whole number by a 28 x 1,000 = 28,000 Add on three 0s to show 28 thousands power of 10. Slide 39 / 239 Slide 40 / 239 Multiplying Powers of 10 Multiplying Powers of 10 If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. Steps 60 x 400 = _______ 1. Multiply the digits to the left of the 50 x 100 = 5,000 zeros in each factor. steps 50 x 100 5 x 1 = 5 1. Multiply the digits to the left of the zeros in each 2. Count the number of zeros in each factor. factor. 6 x 4 = 24 50 x 100 2. Count the number of zeros in each factor. 3. Write the same number of zeros in the product. 3. Write the same number of zeros in the product. 5,000 50 x 100 = 5,000 Slide 41 / 239 Slide 42 / 239 Multiplying Powers of 10 Multiplying Powers of 10 60 x 400 = _______ 60 x 400 = _______ steps steps 1. Multiply the digits to the left of the zeros in each factor. 1. Multiply the digits to the left of the zeros in each 6 x 4 = 24 factor. 2. Count the number of zeros in each factor. 6 x 4 = 24 60 x 400 2. Count the number of zeros in each factor. 60 x 400 3. Write the same number of zeros in the product. 60 x 400 = 24,000 3. Write the same number of zeros in the product.
Slide 43 / 239 Slide 44 / 239 Multiplying Powers of 10 Multiplying Powers of 10 500 x 70,000 = _______ 500 x 70,000 = _______ steps steps 1. Multiply the digits to the left of the zeros in each 1. Multiply the digits to the left of the zeros in each factor. factor. 5 x 7 = 35 5 x 7 = 35 2. Count the number of zeros in each factor. 2. Count the number of zeros in each factor. 500 x 70,000 3. Write the same number of zeros in the product. 3. Write the same number of zeros in the product. Slide 45 / 239 Slide 46 / 239 Multiplying Powers of 10 Practice Finding Rule Your Turn.... 500 x 70,000 = _______ Write a rule. steps Input Output 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 35 15,000 50 Rule 2. Count the number of zeros in each factor. 2,100 7 multiply by 300 500 x 70,000 click 90,000 300 6,000 20 3. Write the same number of zeros in the product. 500 x 70,000 = 35,000,000 Slide 47 / 239 Slide 48 / 239 Practice Finding Rule 11 30 x 10 = Write a rule. Input Output 20 18,000 Rule 6,300 7 multiply by 900 9,000 8,100,000 click 72,000 80
Slide 49 / 239 Slide 50 / 239 12 800 x 1,000 = 13 900 x 10,000 = Slide 51 / 239 Slide 52 / 239 14 700 x 5,100 = 15 70 x 8,000 = Slide 53 / 239 Slide 54 / 239 16 40 x 500 = 17 1,200 x 3,000 =
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