Whole Number PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter One Whole numbers Introduction Whole numbers are numbers that do not contain any fractional...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter One Whole numbers Introduction Whole numbers are numbers that do not contain any fractional or decimal parts. LY These numbers do not contain any negative numbers at all. Examples of whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and so on. In Standard Four, you learnt how to determine the place value of a digit in a number as well as to count, read, and N write numbers up to 99 999. In this chapter, you will learn how to determine the place value of a digit in a number, count, read, and write numbers up to one million O (1 000 000). This competence will help you to count things, measure quantities, price items for sale, do calculations and solve daily life problems. Exercise 1: Revision SE U Answer the following questions: 1. Study the following patterns of numbers and fill in the blanks: (a) 3 220, 3 230, 3 240, 3 250, 3 260, _____, _____, _____. E (b) ____, _____, _____, 99 996, 99 997, 99 998, 99 999. N (c) 59 100, 59 200, 59 300, 59 400, _____, _____, _____. (d) ____, _____, 30 000, 40 000, 50 000, _____, _____, _____, 90 000. LI N 2. Fill in the blanks by subtracting 1 from each of the following numbers: (a) 40 000, _______. O (b) 69 992, _______. (c) 11 145, _______. R 3. Fill in the blanks by subtracting 1 from each of the following numbers: FO (a) ______, 20 000. (b) ______, 51 202. (c) ______, 98 433. 1 MATH std 5.indd 1 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. Use each of the digits 7, 8, 3, 2 and 1 only once to write the following in numerals: (a) The smallest number to be formed. (b) The largest number to be formed. 5. How many hundreds are there in ten thousand? 6. Clearly, study the following figure and then write the total number of LY potatoes in numeral and in words: N O SE U E N LI N O R FO 2 MATH std 5.indd 2 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 7. Fill in the blanks by writing the following numbers in numerals or in words: Number in numerals Number in words 12 767 Thirty-five thousand and twenty-three 87 654 Twelve thousand seven hundred and eighty LY 56 789 Ten thousand and five N 8. Write down the place value of each digit in the following numbers: O (a) 27 256 (b) 35 268 (c) 17 890 (d) 97 871 (e) 82 337 SE 9. Study the numbers 19 574, 99 861, 65 439, 74 200, 45 617 and answer the following questions: (a) Which number has the digit 5 in the hundreds place? U (b) Which number has the digit 1 in the ones place? (c) Which number has the digit 4 in the thousands place? E (d) Which number has the digit 6 in the ten thousands place? (e) Which number has the digit 7 in the tens place? N 10. Write in numerals the numbers which correspond to the following place LI values: (a) Five ten thousands, two thousands, zero hundreds, three tens and N nine ones. O (b) One ten thousands, eight thousands, nine hundreds, zero tens and one ones. (c) Nine ten thousands, two thousands, zero hundreds, eight tens and R seven ones. (d) Seven ten thousands, eight thousands, four hundreds, six tens FO and eight ones. (e) Two ten thousands, three thousands, six hundreds, four tens and two ones. 3 MATH std 5.indd 3 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Counting by grouping Objects are counted either one by one or in groups. Counting objects one by one is possible if the number of objects is small. If the number of objects to be counted is large, counting is made simpler by grouping the objects. Counting up to 500 000 Example 1 LY Count the following number cards which are in ten thousand each: N 10 000 10 000 10 000 10 000 10 000 O 10 000 10 000 10 000 10 000 10 000 SE After counting, you will get a total of ten cards each having a value of ten thousand. The total of all the number cards is one hundred thousand. U Example 2 E N Study the following figures, and answer the question that follow: LI EN EN EN SPECIM SPECIM SPECIM N O EN EN EN SPECIM SPECIM SPECIM R EN EN EN SPECIM SPECIM SPECIM FO Figure 1: Ten thousand shillings notes 4 MATH std 5.indd 4 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE EN EN EN SPECIM SPECIM SPECIM EN EN EN SPECIM SPECIM SPECIM LY EN EN EN SPECIM SPECIM SPECIM N Figure 2: One thousand shillings notes O EN EN SPECIM SPECIM SE Figure 3: Five hundred shillings notes U Question E Count and write the total amount of money in all figures. N Solution LI 1. Count the ten thousand shillings notes in Figure 1. There are 9 notes with a total amount of 90 000 shillings. N 2. Count the one thousand shillings notes in Figure 2. There are 9 notes O with a total amount of 9 000 shillings. 3. Count the five hundred shillings notes in Figure 3. There are 2 notes with a total amount of 1 000 shillings. R 4. If you add the values of all the notes in all the figures you will get a FO total of 100 000 shillings. Therefore, the total amount of money is 100 000 shillings. 5 MATH std 5.indd 5 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 Count and write down the number of pieces of chalk in the following counting basin: Thousands thousands Hundreds thousands Hundred Ones LY Tens Ten N O 3 5 2 8 6 2 Steps: SE 1. Count the pieces of chalk in the ones place. There are 2 pieces of chalk. Write 2 in the ones place. U 2. Count the pieces of chalk in the tens place. There are 6 pieces of chalk. Write 6 in the tens place. 3. Count the pieces of chalk in the hundreds place. There are 8 pieces E of chalk. Write 8 in the hundreds place. N 4. Count the pieces of chalk in the thousands place. There are 2 pieces of chalk. Write 2 in the thousands place. LI 5. Count the pieces of chalk in the ten thousands place. There are 5 pieces of chalk. Write 5 in the ten thousands place. N 6. Count the pieces of chalk in the hundred thousands place. There are O 3 pieces of chalk. Write 3 in the ten thousands place. The result of the steps above is the number written under the counting R basin. It is read as three hundred fifty-two thousand eight hundred and FO sixty-two. This number can be written in numeral as 352 862. 6 MATH std 5.indd 6 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Answer the following questions: 1. Fill in the blanks by subtracting 2 from the previous number. (a) 1 200, _______, _______, _______. (b) 2 153, _______, _______, _______. LY 2. Write down three numbers after each of the following numbers by adding 1 successively: N (a) 99 995 (b) 34 628 (c) 222 222 (d) 102 100 O 3. Complete the following table by writing each digit in its place value: Number Hundred Ten thousands thousands SE Thousands Hundreds Tens Ones U (a) 100 000 (b) 65 232 (c) 364 207 E (d) 200 001 (e) 42 761 N 4. Write down three consecutive numbers obtained by subtracting one LI thousand from each of the following: N (a) 400 000 (b) 300 107 (c) 290 050 (d) 165 000 O 5. Fill in the blanks by adding 5 to the following numbers in numerals successively: R (a) 12 456, _____, _____, _____. FO (b) Two hundred thousand, _____, _____, _____. (c) _____, _____, _____, 305 005. (d) Fifteen thousand, _____, _____, _____. (e) Four hundred and fifteen thousand, _____, _____, _____. 7 MATH std 5.indd 7 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 6. Write down all the numbers from 300 000 up to 500 000 by adding forty thousand to the previous number. Counting up to 1 000 000 Example 1 LY Carefully, study Figure 4 which shows ten thousand shillings notes bound in packages of one hundred thousand each, then count the number of N packages and their total. O SPECIM EN SPECIM EN SPECIM EN SE SPECIM EN SPECIM EN U EN EN EN EN EN E SPECIM SPECIM SPECIM SPECIM SPECIM N Figure 4: Ten packages of 100 000 shillings LI Solution N O In Figure 4, there are ten packages of one hundred thousand shillings, which altogether give a total of one million shillings as shown in Figure 5. Therefore, one million shillings is equal to ten groups of one hundred thousand shillings. R FO 8 MATH std 5.indd 8 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE EN EN SPECIM SPECIM LY EN EN SPECIM SPECIM N Figure 5: A package of one million shillings O Example 2 SE The following drug containers have the number of tablets in them written on the label of each container. Count the number of containers and then, U write the total number of tablets in all the containers. E 100000 100000 100000 100000 100000 100000 100000 100000 100000 N LI N 10 0 00 10 0 00 10 0 00 10 0 00 10 0 00 10 0 00 10 0 00 10 0 00 10 0 00 O R 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 1 0 00 FO 9 MATH std 5.indd 9 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Steps: 1. Count the containers with a label of 100 000, there are 9 containers, with a total number of 900 000 tablets. 2. Count the containers with a label of 10 000, there are 9 containers, with a total number of 90 000 tablets. 3. Count the containers with a label of 1 000, there are 10 containers, LY with a total number of 10 000 tablets. 4. The number of tablets in all the containers is 900 000 plus 90 000 plus N 10 000, giving a total of 1 000 000, which is read as one million. O SE Therefore, all the containers contain a total of one million tablets. U Exercise 3 Answer the following questions: E 1. Count the counters in the following counting basin, then write the result in the blank spaces provided both in words and in numerals. N LI Thousands thousands thousands Hundreds Hundred N Ones Tens Ten O R FO 10 MATH std 5.indd 10 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Write the place value of the digit 1 in the number 1 000 000. 3. Fill in the blanks with the missing numbers: (a) 100 000, _______, 300 000, 400 000, _______. (b) 729 600, 729 590, _______, _______, _______, 729 550, 729 540. (c) _______, _______, _______, 141 000, 142 000, _______, 144 000. LY 4. Write down three numbers in the following patterns by adding one hundred to the previous number: (a) 699 200, _______, _______, _______. N (b) 300 000, _______, _______, _______. (c) 100 480, _______, _______, _______. O (d) 899 000, _______, _______, _______. SE 5. Use each of the digits 4, 2, 9, 7, 8 and 1 only once to write; (a) The largest number to be formed. (b) The smallest number to be formed. U 6. Count and write down in numeral the number represented by the following abacus: E Thousands thousands thousands N Hundreds Hundred Ones Tens LI Ten N O R FO 11 MATH std 5.indd 11 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 7. If counting is done by adding one thousand, write the next five numbers after five hundred thousand. 8. Form a number pattern from two hundred and seventy thousand to three hundred and fifty thousand by adding ten thousand to a previous number to obtain the next number. 9. Write in numerals the number shown by the counters in the following LY counting basin. Thousands thousands thousands Hundreds N Hundred Ones Tens O Ten SE U Total value of a digit in a number E Total value of a digit in a number shows how much is that digit worth. N For example, the total value of each digit in the number 479 651 is as follows: LI 4 7 9 6 5 1 1 N 50 O 600 9 000 R 70 000 400 000 FO 12 MATH std 5.indd 12 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example Write the total value of 9 in 89 670. Answer The total value of 9 in 89 670 is 9 000. Expanded form LY A number is in expanded form if it is written as the sum of the total values of its digits. This form identifies the total value of each digit in the number. N Example O Write down the following numerals in expanded form: (a) 26 713 (b) 41 023 SE (c) 129 567 Solution U Number in numerals Number in expanded form (a) 26 713 20 000 + 6 000 + 700 + 10 + 3 (b) 41 023 40 000 + 1 000 + 0 + 20 + 3 E (c) 129 567 100 000 + 20 000 + 9 000 + 500 + 60 + 7 N Exercise 4 LI Answer the following questions: N 1. Write down the total value of each digit in the following numbers: (a) 461 585 (b) 147 295 O (c) 947 231 (d) 417 293 (e) 531 278 R 2. Write down the following numbers in expanded form: FO (a) 401 627 (b) 561 894 (c) 300 002 (d) 261 578 (e) 987 351 13 MATH std 5.indd 13 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Use the digits in the following numbers to fill in the blanks: (a) 724 564 has _____ hundred thousands, _____ ten thousands, _____ thousands, _____ hundreds, _____ tens and _____ ones. (b) 612 702 has _____ hundred thousands, _____ ten thousands, _____ thousands, _____ hundreds, _____ tens and _____ ones. (c) 394 189 has _____ hundred thousands, _____ ten thousands, _____ thousands, _____ hundreds, _____ tens and _____ ones. (d) 100 364 has _____ hundred thousands, _____ ten thousands, _____ thousands, _____ hundreds, _____ tens and _____ ones. LY (e) 999 998 has _____ hundred thousands, _____ ten thousands, _____ thousands, _____ hundreds, _____ tens and _____ ones. N 4. Which number is greater than the other numbers among the following? O 444 144, 444 444, 444 441, 434 444, 414 444 SE 5. Which number is smaller than the other numbers among the following? 661 256, 663 666, 666 166, 666 646, 616 666 U 6. Write down the total value of 9 in each of the following numbers: (a) 392 527 (b) 579 711 (c) 418 692 E Reading and writing numbers up to 1 000 000 Reading numbers N A number is read by considering the place value of its digits, starting with the LI leftmost digit to the rightmost digit. N Example 1 O Read loudly the following numbers: Number in R Number in words numerals 105 202 One hundred five thousand two hundred and two FO 254 000 Two hundred fifty-four thousand 100 006 One hundred thousand and six 14 MATH std 5.indd 14 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 Read the following numbers: (a) 311 008 Three hundred eleven thousand and eight. (b) 101 008 One hundred one thousand and eight. (c) 411 000 Four hundred eleven thousand. (d) 500 709 Five hundred thousand seven hundred and nine. (e) 1 000 000 One million. LY Exercise 5 N Answer the following questions: O 1. Read the following numbers loudly: (a) 99 999, 100 000, 100 001, 100 002, 100 003, 100 004, 100 005. SE (b) 100 010, 100 020, 100 030, 100 040, 100 050, 100 060, 100 070. (c) 200 200, 200 400, 200 600, 200 800, 201 000, 201 200, 201 400. U (d) 113 999, 199 922, 497 007, 931 311, 100 003. E 2. Read loudly the numbers in the following table and write them in words: N Number in Numeral Number in words LI 128 749 338 952 N 876 187 997 000 O 872 006 984 901 R 888 888 440 690 FO 300 003 772 024 15 MATH std 5.indd 15 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Writing numbers in words and in numerals Example 1 Write down the following numbers in numerals: 1. One hundred seven thousand five hundred and five 2. Seven hundred eighty-nine thousand 3. Two hundred sixty-six thousand and eight LY Solution N 1. One hundred seven thousand five hundred and five = 107 505. 2. Seven hundred eighty-nine thousand = 789 000. O 3. Two hundred sixty-six thousand and eight = 266 008. Example 2 SE Write and read the number represented by the following abacus: U Thousands thousands thousands Hundreds Hundred Ones E Tens Ten N LI N O R 3 7 2 0 5 6 FO The number which is represented by the abacus is 372 056 and is read as three hundred seventy-two thousand and fifty-six. 16 MATH std 5.indd 16 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 6 Answer the following questions: 1. Read loudly the numbers in the following table and write them in numerals: Number in Number in words numerals LY (a) One million (b) Five hundred thousand four hundred and thirty (c) Nine hundred eighty thousand and forty-two N (d) One hundred twenty-seven thousand, nine hundred (e) Four hundred thousand O (f) Four hundred thousand and four (g) Three hundred seventy thousand and twenty SE (h) Eight hundred thousand, five hundred and fifty-seven (i) One hundred thousand and one U 2. Write the number represented by the following abacus both in words and in numerals: Thousands E thousands thousands Hundreds Hundred N Ones Tens Ten LI N O R FO 17 MATH std 5.indd 17 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 7 Answer the following questions: 1. Fill in the blanks: (a) 234 566,_______,_______,234 569, _______, _______, 234 572. (b) 359 000, 358 000 _______, _______, _______, 354 000. (c) _______, _______, _______, 400 000, 500 000, 600 000. (d) 155 600, _______,_______,155 300, 155 200, _______, _______. LY (e) _______,_______,_______,840 000, _______, 860 000, 870 000. 2. Count and write the numbers represented by the following abacus: N (a) Thousands thousands thousands Hundreds Hundred O Ones Tens Ten SE U E N (b) LI Thousands thousands thousands Hundreds Hundred N Ones Tens Ten O R FO 18 MATH std 5.indd 18 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Write the number 300 110 in words. 4. Write the following numbers in numerals: Number in Number in words numerals LY (a) Two hundred ninety-five thousand seven hundred and fifty (b) Three hundred thousand and sixty-five N (c) Nine hundred ninety-nine thousand, nine hundred and ninety-nine O (d) One hundred fifty thousand (e) Seven hundred eighty-seven thousand and seven SE 5. Write the number 763 631 in its expanded form. U 6. Write the number 900 000 + 30 000 + 1 000 + 300 + 50 + 4 in numeral. E 7. Write the place value of 7 in each of the following numbers: N (a) 867 652 (b) 879 543 LI (c) 236 374 (d) 374 964 N (e) 721 603 O 8. Write the following numbers in words: (a) 311 321 R (b) 401 719 FO (c) 572 900 (d) 200 535 (e) 145 130 19 MATH std 5.indd 19 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. To obtain the place value of a digit in a number, you have to identify the position of that digit in the number. 2. Groups of objects to be counted may be of different sizes and colours. 3. To write a number in its expanded form, start with the digit with the LY largest place value going down to the digit with the smallest place value. N O SE U E N LI N O R FO 20 MATH std 5.indd 20 30/07/2021 14:49