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