MATHEMATICS 5 QUARTER 1 WEEK 1 DIVISIBILITY RULES

MATHEMATICS 5 QUARTER 1 WEEK 1

DIVISIBILITY RULES

WHAT I NEED TO KNOW? v. To find the common factors of a number using the divisibility rules of 2, 5 , and 10 v. To find the common factors of a number using the divisibility rules of 3, 6, and 9.

WHAT I KNOW? I. Circle the numbers that are divisible by the number given. a. Divisible by 2? 2191 8, 243 5, 534 6, 331 2, 282 8, 046 5, 990 9, 055 5, 160 4, 528 7, 303 8, 797 2, 454 1, 253 2, 780 2, 454 1, 905 7, 892 b. Divisible by 5? 4, 455 1, 800 3, 721 9, 124 1, 023 1, 725 9, 267 9, 508 1, 820 7, 896 2, 870 1, 745 3, 265 1, 270 4, 902 1, 069 2, 456 2, 900

c. Divisible by 10? 5, 020 4, 125 4, 900 7, 634 1, 700 3, 986 6, 200 4, 782 9, 108 5, 600 4, 700 1, 725 8, 823 1, 640 5, 015 3, 620 1, 902 5, 890 d. Divisible by 2 and 5? 6, 588 6, 244 7, 330 5, 020 6, 364 2, 900 6, 100 7, 508 7, 200 9, 603 8, 500 3, 897 8, 156 5, 090 1, 725 8, 240 4, 800 1, 903 e. Divisible by 5 and 10? 6, 367 8, 300 7, 050 4, 891 2, 890 1, 784 1, 350 2, 178 6, 142 5, 090 1, 800 1, 456 5, 902 2, 560 3, 620 2, 784 1, 256 1, 670

• 3 3, 039 114 375 61, 145 156 324 15, 948 7, 425 453 58, 302 6 9

LESSON 1: At the end of lesson 1, you are expected to recognize the numbers that is divisible by 2, 5, and 10. Divisible means that a number divides equally into another number. Let’s see what this means. Alexandra has 90 collected stamps. Can she shared that equally to her 2 friends? 5 friends? Or 10 friends? To solve the problem, you need to know if 2, 5, and 10 are factors of 90 or if 90 is divisible by 2, 5, and 10. To see if the number is divisible by 2, 5, and 10, test it by checking the ones digit. DIVISIBILITY TEST 90 Divisibility rule for 2: given number is ending in 0, 2, 4, 6, 8 or all even YES numbers Divisibility rule for 5: given number is ending in 0 and 5 YES Divisibility rule for 10 : given number is ending in zero (0) YES

WHAT’S IN? Write YES or NO if the number is divisible by the given number. 1, 620 2, 425 1, 980 3, 600 By 2: _______ By 5: _______ By 10: _______ 9, 050 4, 985 7, 010 8, 100 By 2: _______ By 5: _______ By 10: _______ 7, 120 7, 904 12, 980 25, 875 By 2: _______ By 5: _______ By 10: _______

WHAT’S NEW? • 2 80 234 3755 5680 54150 912 5660 2700 2655 5 10

B. Determine whether the first number is divisible by the second number. Write YES or NO on the blank. 1. 25 : 5 ______ 6. 4080 : 5 ______ 2. 60 : 10 ______ 7. 90 : 5 ______ 3. 575 : 5 ______ 8. 2150 : 10 ______ 4. 465 : 10 ______ 9. 325 : 10

WHAT IS IT? We are trying to focus in learning the divisibility rules for easy finding the common factors. Divisibility means that there are no remainder left when we are dividing a number by another number. And that determining the factors of a bigger number is not so easy. And using the divisibility rules will help you to understand whether a number is exactly divisible by another number. The rules are the shortcuts for finding out whether numbers are exactly divisible without doing a division calculations.

ØDivisibility Rule for 2: All the numbers that are ending in 0, 2, 4, 6, and 8 are divisible by 2 or all the even numbers are divisible by 2. Example: 1 7 8 : look at the last digit Is it 0, 2, 4, 6, or 8? If it is, then the number is divisible by 2. ØDivisibility Rule for 5: A number is divisible by 5 if the numbers is ending in 0 or 5. Example : 8 5 5 : look at the last digit If it is a 5 or a 0 then the number is divisible by 5. ØDivisibility Rule for 10: A number is divisible by 10 only if it is ending in zero ( 0 ). Example : 1 , 7 6 0 : look at the last digit If it is a 0 then the number is divisible by 10.

WHAT’S MORE? ACTIVITY 1 Encircle the answer that makes each statement correct. 1. Ten thousand, four hundred two is ( divisible, not divisible ) by two. 2. Eighty is ( divisible, not divisible ) by ten. 3. Five hundred, thirty four is ( divisible, not divisible ) by five. 4. Two hundred fifty- five is ( divisible, not divisible ) by ten. 5. Forty-nine thousand, six hundred ninety is ( divisible, not divisible ) by five and 10.

ACTIVITY 2 For each number on the left, place a check mark under the numbers it is divisible by. Number 4520 7495 2562 8290 5464 2 5 10

ACTIVITY 3 Select the divisibility that applies for the following. Encircle the letter of the correct answer. 1. 21, 432 a. Divisibility 2 b. Divisibility 5 c. Divisibility 10 d. Divisibility 2 and 5 2. 85, 975 a. Divisibility 2 b. Divisibility 5 c. Divisibility 10 d. Divisibility 2 and 5 3. 57, 890 a. Divisibility 2 b. Divisibility 5 c. Divisibility 10 d. Divisibility 2 and 5 4. 356, 000 a. Divisibility 2 b. Divisibility 5 c. Divisibility 10 d. Divisibility 2 and 5 5. 35, 728 a. Divisibility 2 b. Divisibility 5 c. Divisibility 10 d. Divisibility 2 and 5

WHAT I HAVE LEARNED? I learned that: v. All numbers ending in 0, 2, 4, 6 and 8 are divisible by 2. v. A number is divisible by 5 if the number ends in 0 or 5. v. A number is divisible by 10 only if it end in zero ( 0 ).

WHAT I CAN DO? ACTIVITY 4 Find the divisibility of the following numbers by 2 , 5 , and 10. 1. 6735 ________ 6. 750 ________ 2. 270 ________ 7. 6275 ________ 3. 6478 ________ 8. 75, 926 ________ 4. 35, 890 ________ 9. 15, 240

ASSESSMENT A. Write YES if the first number is divisible by the second number or NO if not. _____1. 842 : 10 _____6. 12, 421 : 2 _____2. 6570 : 5 _____7. 43, 905 : 5 _____3. 12, 785 : 5 _____8. 20, 450 : 2 _____4. 90, 540 : 10 _____9. 34, 208 : 5

chart. B. Write the number under the proper divisibility column in the 648 1245 2390 2 640 1256 426 535 832 124 5 740 520 145 635 8100 7590 10

C. Encircle the answer that makes each statement true. 1. 23, 680 is ( divisible , not divisible ) by 5. 2. 52, 160 is ( divisible , not divisible ) by 10. 3. 4, 656 is ( divisible , not divisible ) by 5. 4. 36, 782 is ( divisible , not divisible ) by 2. 5. 32, 758 is ( divisible , not divisible ) by 10.

• 2 450 544 675 1900 468 9150 2400 458 852 5 10

Additional Activity A. Encircle the correct answer. 1. Which of the following numbers are divisible by 2, 5, and 10? a. 149 b. 19, 400 c. 720, 345 d. 125, 370 e. 30, 000 2. Which of the following numbers are divisible by 2? a. 16, 786 b. 12, 655 c. 27, 900 d. 35, 584 e. 14, 457 3. In each of the following numbers without doing actual division, determine whether the first number is divisible by the second number. a. 15, 246 : 2 b. 21, 560 : 5 c. 189 : 5 d. 15, 578 : 10 e. 24, 560 : 5 4. Is 5 a factor of the following? a. 26, 580 b. 13, 754 c. 15, 982 d. 46, 650 e. 25, 785 5. Which of the following numbers are divisible by 5? a. 18, 240 b. 34, 652 c. 17, 900 d. 27, 545 e. 14, 457

B. Write YES or NO if the number is divisible by the given number. 1. 9, 450 2. 14, 208 3. 67, 205 4. 2, 560 By 2: _______ By 5: _______ By 10: _______ 5. 17, 806 6. 24, 400 7. 15, 855 8. 13, 100 By 2: _______ By 5: _______ By 10: _______ 9. 3, 788 10. 67, 532 11. 16, 850 12. 13, 240 By 2: _______ By 5: _______ By 10: _______

LESSON 2: At the end of lesson 1, you are expected to recognize the numbers that is divisible by 3, 6, and 9. Have you ever wondered why some numbers will divide evenly (without a remainder) into a number, while others will not? The Divisibility Rules help us to determine if a number will divide into another number without actually having to divide. There is a divisibility rule for every number. Let us see what does it means. Annabel’s garden has 549 vegetable plants. She wants to arrange then in either rows of 3 , 6, or 9. And to solve the problem, you need to know if 3, 6, or 9 are factors of 549 or if it is divisible by 3, 6, or 9.

Let us recall the rules of divisibility. v. Divisibility rule for 3: the sum of digits of the number is divisible by 3 549 = 5 + 4 +9 = 18, 18 is divisible by 3, therefore 549 is divisible by 3 v. Divisibility rule for 6: the sum of the digits both divisible by 2 and 3 549 is divisible by 2 and 3, therefore 549 is divisible by 6 v. Divisibility rule for 9: the sum of the digits of the number is divisible by 9 549 = 5 + 4 +9 = 18, 18 is divisible by 9, therefore 549 is divisible by 9

WHAT’S IN? • Number 1. 45 2. 70 3, . 62 4. 115 5. 276 6. 550 7. 1195 8. 444 9. 900 10. 645 Divisible by 2 Divisible by 5 Divisible by 10

B. Cross out the box of the correct answer. 1. Is 72 divisible by 3 ? YES NO 2. Is 117 divisible by 9? YES NO 3. Is 84 divisible by 6? YES NO 4. Is 153 divisible by 9? YES NO 5. Is 92 divisible by 6? YES NO

WHAT’S NEW? A. Determine whether the first number is divisible by the second number. Write YES or NO on the blank. 1. 360 : 3 ______ 6. 864 : 6 ______ 2. 342: 6 ______ 7. 792 : 9 ______ 3. 621 : 9 ______ 8. 855 : 9 ______ 4. 477 : 3 ______ 9. 336 : 6 ______ 5. 816 : 9 ______ 10. 933 : 9 ______

B. Use the divisibility rules to put a check or cross in each box 3 12 66 72 54 30 6 9

WHAT’ IS IT? We are trying to focus in learning the divisibility rules for 3, 6, and 9 in easy way in finding the common factors. The rules are the shortcuts for finding out whether numbers are exactly divisible without doing a division calculations.

WHAT’ MORE? ACTIVITY 1 A. Circle the number that are divisible by 3. 561 85, 634 1, 605 764, 593 6, 710 26, 823 27, 365 80, 469 4, 567 1, 353 9, 132 25, 788 B. Circle the number that are divisible by 6. 4, 728 627 72 54 13, 224 5, 844 57 163 35, 766 82, 356 15, 269 6, 360 C. Circle the number that are divisible by 9. 477 750, 413 643 1, 499 2, 469 267, 786 34, 796 86, 823 681, 435 520 59, 994 4, 597 507, 888 6, 777 7, 901 365 78 241 73, 062 3, 708 98, 631

ACTIVITY 2 Write YES or NO if the number is divisible by the given number. 1, 620 42 65, 483 1, 680 By 3: _______ By 6: _______ By 9: _______ By 9: 39 ____ By 9: ____ 81 By 9: 1008 ____ 34, 911 By 3: _______ By 6: _______ By 9: ____ By 9: 45, 799 ____ By 9: 10. 540 ____ By 9: 92, 745 ____ 12. 66 By 3: _______ By 6: _______ By 9: ________

WHAT I HAVE LEARNED? I learned that: v. A number is divisible by 3 if the sum of its digit is a multiple of 3 or divisible of 3. v. A number is divisible by 6 if it is divisible by both 2 and 3. It is an even number and the sum of the digits is divisible by 3. v. A number is divisible by 9 if the sum of the digit is divisible by 9.

WHAT I CAN DO? ACTIVITY 3 Find the divisibility of the following numbers by 3 , 6 , and 9. 1. 144 ________ 6. 156 ________ 2. 180 ________ 7. 366 ________ 3. 198 ________ 8. 3411 ________ 4. 243 ________ 9. 801 ________ 5. 171 ________ 10. 258 ________

ACTIVITY 4 Circle the numbers that are divisible by the given number. 1. Divisible by 3? 459 163 642 246 473 241 265 275 904 2. Divisible by 6? 320 116 100 759 607 531 543 594 631 267 947 585 563 717 367 710 931 208 939 116 315 563 289 148 282 536 516 181 920 969 935 920 478 831 861 476 772 935 534

3. Divisible by 9? 695 352 408 631 315 378 805 457 684 819 567 662 881 501 340 755 585 524 297 888 526 296 819 194 4. Divisible by 3 and 6? 212 879 825 445 633 548 188 789 446 353 484 549 196 531 308 976 986 392 516 209 262 660 257 5. Divisible by 3 and 9? 823 557 590 247 818 521 261 634 586 962 208 598 750 573 253 281 697 291 635 433 386 985 869 165

ASSESSMENT? A. Supply the smallest digit that will make the number divisible by the number on the right side. 1. ____2, 469 3 6. ___2468 3 2. 34 ___ 6 7. 2___475 3 3. 26, 73 ___ 9 8. 391 ___ 6 4. 85, ___28 9 9. 932, 1 ___1 9 5. ___2364 6 10. 13 ___ 3

B. YES or NO. Tell whether the given number is divisible by: A. Divisible by 3 _____1. 4, 528 _____2. 3, 642 _____3. 9, 633 B. Divisible by 6 _____1. 2, 070 _____2. 27, 522 _____3. 12, 745 C. Divisible by 9 _____1. 60, 192 _____2. 24, 587 _____3. 310, 743 _____4. 4, 157 _____5. 5, 427 _____4. 7, 710 _____5. 17, 125 _____4. 54, 278 _____5. 38, 313

C. Encircle 3, 6, and 9 if the number is divisible by these numbers. 1. 630 3 6 9 6. 4, 275 3 6 9 2. 702 3 6 9 7. 22, 122 3 6 9 3. 1, 572 3 6 9 8. 10, 356 3 6 9 4. 2, 400 3 6 9 9. 32, 922 3 6 9 5. 13, 488 3 6 9 10. 7, 713 3 6 9

ADDITIONAL ACTIVITY 1. 2. 3. A. Are these numbers divisible both by 3 and 6? Write Yes or No. 630 ______ 4. 6, 312 ______ 3, 402 ______ 5. 54, 873 ______ 23, 541 ______ B. Are these numbers divisible both by 6 and 9 ? Write Yes or No. 38, 952 ______ 4. 14, 742 ______ 2, 748 ______ 5. 32, 562 ______ 31, 113 ______ C. Are these numbers divisible both by 3, 6 and 9 ? Write Yes or No. 2, 286 ______ 4. 32, 868 ______ 20, 574 ______ 5. 22, 113 ______ 52, 512 ______

D. Put a √ in the column if the given numbers is divisible by the number in the top row. Put an X if it is not. NUMBER 11, 205 13, 184 618, 759 27, 126 9, 351 3 6 9

D. Write the letter of the correct answer on the blank. _______1. 6 is a factor of a. 840 b. 760 c. 530 _______2. Which of the following is divisible by 3? a. 127 b. 360 c. 238 _______3. 9 is a factor of a. 675 b. 280 c. 854 _______4. Which of the following is divisible by 6 ? a. 71 b. 134 c. 234 _______5. Which of the following is divisible by 9? a. 108 b. 100 c. 124