UNIT 2:Addition and subtraction of integers►

UNIT 1: Reading, writing, comparing and calculating whole numbers up to 1 000 000

  • UNIT 1: Reading, writing, comparing and calculating whole numbers up to 1 000 000

    1.1 Reading and writing numbers in words up to 1 000 000

    (a) Reading and writing in words

    Activity 1.1
    • Study these numbers:
    100 001        280 465       405 230     729 111         999 999
    • Write each of them on little slips of papers. Pick a slip of paper.
    • Now, arrange yourselves according to your numbers.

    • Read your number aloud then write your number in words.

    Tip:
    When writing a number in words, group the digits of the number. Look at

    the example below.

    Example 1.1
    Write 976 946 in words.

    Solution
    We can group 976 946 as:
    976 000 – nine hundred seventy six thousand
    900 – nine hundred
    40 – forty
    6 – six
    Therefore 976 946 is nine hundred seventy six thousand nine hundred and forty six.
    Practice Activity 1.1
    1. Read and write each of the following numbers in words.
    (a) 671 379       (b) 286 748       (c) 910 842        (d) 263 450
    2. Discuss how to write the followings numbers in words.
    (a) 716 809       (b) 604 382      (c) 862 059        (d) 345 671
    3. A factory packed 447 313 text books in cartons for sale. Write this in words. Explain the steps you used to arrive at your answer.
    4. A Green Belt Movement planted 527 174 tree seedlings. Write this in words. Explain steps to your answer.

    (b) Reading and writing numbers in figures
    Activity 1.2
    (a) Write these numbers in figures.
    (i) Six hundred thirty three thousand four hundred and five.
    (ii) One hundred thousand and eleven.
    (iii) Nine hundred seven thousand one hundred and seven.

    (b) Now match these numbers in figures to the correct number in words.

    n

      Make a class presentation to explain your answer.

    Example 1.2
    Write eight hundred twenty five thousand two hundred and thirty four in figures:
    Solution
    Thousands 825 000
    Hundreds          200
    Tens                    30
    Ones            +      4

                       825 234

    Practice Activity 1.2
    1. Write each of the following numbers in figures.
    (a) Seven hundred and six thousand five hundred and eighteen.
    (b) One hundred and three thousand six hundred and four.
    (c) Nine hundred thousand nine hundred and nine.
    (d) Five hundred thousand and five.
    2. Discuss how to write the following in figures.
    (a) Six hundred and fifty thousand.
    (b) Eight hundred and eight thousand eight hundred and eight.
    (c) Two hundred thirty four thousand one hundred and eleven.
    (d) Four hundred seventy one thousand two hundred and thirty five.
    3. I had three hundred ninety eight thousand seven hundred and sixty
    six Rwandan Francs. Write the amount I had in figures..
    4. During an election, five hundred forty seven thousand seven hundred and fifty voted for the winning MP. How many votes in figures did she get? Explain your steps to answer.

    1.2 Place value and comparing numbers

    (a) Place value of numbers up to 7 digits


    Activity 1.3
    • Study these numbers.
    (a) 100 000         (b) 473 625         (c) 999 999
    Write the numbers on paper cutouts.
    Name the place value of each digit.
    Write the place value of each digit.
    Say the place value of each digit. Present your findings.
    • What is the next number after 999 999? What is the place value of digit 1 in your answer? Discuss your answer.
    Example 1.3

    Write the place value of each digit in the number 235 176.

    d

    Solution
    2 – Hundred Thousands
    3 – Ten Thousands
    5 – Thousands
    1 – Hundreds
    7 – Tens

    6 – Ones

    Practice Activity 1.3

    1. Identify the place value of each digit in the number.
    (a) 560 438       (b) 189 274 dam2       (c) 908 346
    2. Identify the digit in the place value of hundred thousands. Justify your answer.
    (a) 964 815        (b) 321 456               (c) 811 943 kg
    3. Write the place value of the coloured digit. Discuss and present your answer.

    (a) 198 065        (b) 746 138 l             (c) 640 404         (d) 245 689

    (b) Comparing numbers using <, > or =

    Activity 1.4
    • Write the following numbers on small paper cutouts.
    6 , 2 , 4 , 8 , 9 , 1
    Arrange the numbers to form:
    – the largest number.
    – the smallest number.
    (i) Use > to compare the numbers you have formed.
    (ii) Use < to compare the numbers you have formed.
    • Repeat the activity above with other digits. Explain your answers.

    • Where do you compare quantities? Discuss how you do it.

    Example 1.4
    By using <, = or > compare: 356 481 —— 353 4

    Solution
    Step 1: Write the two numbers   
          on place value chart
    m

    Step 2: Compare the digits from the left towards the right.
    The hundred thousands digits are the same. So are the ten thousands digits. Thousands digits are 6 and 3, but 6 > 3.
    Therefore, 356 481 > 353 406

    Tip:
    • To compare whole numbers: Check digits of numbers at the same place values. Start at the left and compare the digits in the greatest place value position. The greater number has a greater digit at the greatest place value.

    • We use: < for “less than”, > for “greater than” and = for “equal to”.

    Practice Activity 1.4
    1. By using <, = or > compare the following pair of numbers.
    (a) 440 040 — 440 040                  (b) 657 000 — 675 000
    (c) 649 362 — 639 462                  (d) 831 647 — 861 347
    2. Use <, = or > to compare the following. Discuss your answers.
    (a). 531 926 — 513 926                 (b) 100 000 — 1 000 000
    (c) 210 034 — 201 034                  (d) 245 689 — 245 689
    3. The number of adults in a certain district was 136 895. The number of children was 136 989 for the same district.
    (i) Were there more adults or children?
    (ii) Were there fewer adults or children? Discuss your answers.
    4. Anne is a coffee farmer. Anne made 550 000 Frw from sales of her coffee over four months. Musabe is a business person. Musabe made 630 000 Frw from sales in his shop over four months. Who made more money? Explain your answer.
    1.3 Addition of 3 or more whole numbers of 7 digits
    with/without carrying
    Activity 1.5
    Use an abacus or objects of different colours to add the following:
    (a) 100 204 + 551 480 + 226 102.
    (b) 128 539 + 300 856 + 15 210. Explain your answer.

    What did you observe while carrying out the addition?

    Example 1.5
    Work out:

    (a) 272 142 + 203 512 + 402 123 (b) 472 598 + 284 706 + 163 075

    d

    Practice Activity 1.5
    1. Work out:
    (a) 430 526 + 323 250 + 122 102 =
    (b) 252 143 + 235 322 + 400 312 =
    (c) 283 054 + 3 002 + 415 621 =
    (d) 311 052 + 203 932 + 132 003 =

    2. Work out the following. Present your answers.
    (a) 39 845 + 105 523 + 351 214 =
    (b) 193 584 + 258 907 + 391 358 =
    (c) 552 797 + 25 895 + 188 253 =
    (d) 340 020 + 215 322 + 104 052 + 340 606 =

    3. A poultry farmer sold 252 797 chickens in one year. The next year he sold 391 358 chicken. The third year he sold 193 583 chickens. How many chickens did he sell in 3 years?

    4. A business man invested 442 300 Frw in the first year of business.
    The second year he invested 442 100 Frw. The third year he invested 115 600 Frw. How much money did he invest in total?
    Explain your answer.

    5. At a peace campaign rally, there were 8 430 women. Men were 5 660     and children were 7 200. How many people attended the rally? Discuss the steps involved in calculating your answer.
    d

    1.4 Subtraction of 2 whole numbers of 7 digits with/     without borrowing

    Activity 1.6
    Use an abacus to subtract:
    (a) 398 450 – 352 150 (b) 852 757 – 193 583 (c) 710 534 – 40 203
    What do you notice in subtracting a, b and c? Explain the borrowing
    from one place value to the next to carry out subtraction in b and c.
    (d) A company packed 763 389 packets of milk on Monday. 539 897
    packets were sold the same day. How many packets of milk remained
    to be sold on Tuesday?
    z
    Practice Activity 1.6
    Subtract
    1. (a) 808 210 – 205 210 =            (b) 394 930 – 192 620 =
        (c) 888 980 – 56 360 =               (d) 393 588 – 372 475 =

    2. Subtract the following numbers and explain your answer.
        (a) 855 157 – 398 480 =              (b) 875 864 – 557 993 =
        (c) 480 734 – 469 372 =               (d) 736 425 – 463 758 =

    3. A farmer harvested 404 040 kilograms of maize. He sold 345 678
    kilograms. How many kilograms of maize did he remain with? Discuss
    the steps involved in calculating your answer.

    4. A school uses 840 020 litres of water in a term. The school was closed a
    week earlier. They had used 710 229 litres of water. How many litres
    of water was not used? Discuss the steps involved in calculating your
    answer.

    1.5 Quick multiplication of a 3 digit number by 5, 9,

    11, 19, 25, 49 and 99

    Activity 1.7
    • Compose 3 digit numbers and quick multiply by 5, 9, 11, 19, 25, 49
    and 99. Solve them and make a presentation to the class.
    • Solve this problem. We are 5 in our group. Each of us has 520 Frw.
    How much money do we have?
    • Now compose problems related to real life. Solve and present them

    to class.

    ds

    Practice Activity 1.7
    1. Quick multiply the following:
    (a) 883 × 5       (b) 827 × 9       (c) 618 × 11        (d) 704 × 19
    2. Use quick multiplication to solve the following. Discuss the steps to your answers.
    (a) 567 × 25      (b) 430 × 49       (c) 525 × 99
    (d) 629 × 5        (e) 449 × 9
    3. A library has 113 shelves with 99 books each. How many books are in the library?
    4. 25 schools have 215 pupils each in a certain province. How many pupils are in those 25 schools? Explain your answer.
    5. A school bought 19 boxes of pencils. Each box had 144 pencils. How many pencils are there? Explain and present your answer.
    6. A school farm collected 99 eggs daily. Each egg was sold at 110 Frw.
    Calculate the money the school got from sale of eggs daily.
    7. There are 49 pupils in the P5 class. During a mathematics lesson, each pupil brought 125 counters. How many counters were brought altogether?
    8. 25 pupils in a school are given milk. Milk is in 500 millilitre packets.
    The pupils take a packet of milk every day. How many packets are required in 7 weeks? Discuss and present your answer.

    n

    1.6 Multiplication of whole numbers by a 3 digit number

    Activity 1.8
    • Solve this problem.
    A shopkeeper had 112 bottles of juice. He sold each of them at 350 Frw. How much money did he get?
    • Now compose problems related to real life. Solve and present them to the class.
    Example 1.8

    Multiply 365 × 241

    b

    Practice Activity 1.8
    Work out:
    1. (a) 833 × 410      (b) 581 × 611       (c) 648 × 212
    (d) 439 × 326          (e) 788 × 423       (f) 373 × 465
    Solve the following problems and discuss your answers.
    2. (a) 349 × 247      (b) 943 × 333       (c) 317 × 149      (d) 623 × 261
    3. There are 258 hotels in a certain country. In one holiday season, each hotel received 415 visitors. How many visitors were there during that season? Explain your answer.
    4. 135 rings are needed to decorate the ceiling of each room in a hotel.
    The hotel has 221 similar rooms. Explain how many rings are needed?
    5. A district received 375 cartons of exercise books. Each carton holds 180 exercise books. How many exercise books were received? Explain your answer.
    6. A wholesaler received 247 cartons of juice. Each carton costs 950 Frw.
    Explain how much money he paid?
    7. The government gave 790 textbooks to each of the 183 primary schools in a district. Explain how many textbooks were given altogether?
    1.7 Division without a remainder of a 3 digit number by a 2 digit number
    Activity 1.9
    (a) A teacher had 120 exercise books. The books are to be equally shared by 24 pupils. How many books did each pupil get (b) During a birthday party a packet of sweets with 120 sweets was shared equally by 15 pupils. Discuss how many sweets each pupil got.
    • Now explain situations where sharing occurs in daily life.

    • Name some items or things that are often shared.

    x

    Practice Activity 1.9
    1. Divide the following:
    (a) 792 ÷ 18     (b) 768 ÷ 32       (c) 391 ÷ 23
    (d) 858 ÷ 22     (e) 405 ÷ 15       (f) 390 ÷ 30
    2. Work out the following and discuss your answer.
    (a) 688 ÷ 43      (b) 714 ÷ 17      (c) 759 ÷ 23      (d) 861 ÷ 21
    3. Margaret has 180 eggs. She packs them in trays of 30 eggs each. How many trays did she fill? Explain your answer.

    m

    4. A farmer had 468 seedlings planted in 18 rows. Each row had an equal number of seedlings. Explain how many seedlings were in each row?
    5. The teacher shared 516 books equally among 43 pupils. How many books did each pupil get? Explain your answer.

    Revision Activity 1

    1. Write the numbers below in words.
    (a) 382 640 (b) 942 108
    2. Write the numbers below in figures.
    (a) Nine hundred seventy seven thousand six hundred thirty one.
    (b) Four hundred eighty two thousand seven hundred sixty five.
    3. What is the place value of the coloured digits?
    (a) 981 555 (b) 436 914
    4. Use <, = or > to compare
    (a) 677 931 _______ 977 631
    (b) 848 756 _______ 848 657
    5. To conserve environment, members of community planted trees during rainy season. In the first region, they planted 187 255 trees.
    In the second region, they planted 320 316 trees. In the third region they planted 439 230 trees.
    (a) Find the total number of trees planted in the three regions.
    (b) Calculate the difference of the highest and lowest number of trees they planted. Justify your answer.
    (c) Discuss the importance of conserving our environment.
    6. In a certain village, 840 kg of maize seeds were donated by a certain firm. Thirty five families shared them equally and planted in their farms. How many kilograms of maize seeds did each family get?
    7. A distributor delivered 99 cartons of books to each of 265 schools.
    This was during book delivery program. Each carton had 25 books.
    (a) Using multiplication, find the number of cartons of books delivered to the schools.
    (b) Suppose one carton was to be given to each school. How many books would have to be delivered to 228 schools? Why should we have books?
    Word list
    Place values Numerals Addition Subtraction
    Multiplication Division Digits Abacus
    Compare Calculate
    Task
    Do the following.
    (i) Read each word aloud to your friend.
    (ii) Write the meaning of each of the words above. Discuss with your friend.

    (iii) Write sentences using each of the words above. Read with your friend.

UNIT 2:Addition and subtraction of integers►