## Topic outline

- General
- Unit1:Reading, Writing and Comparing Whole Numbers Beyond 1,000,000Unit1:Reading, Writing and Comparing Whole Numbers Beyond 1,000,000Label: 1Unit1:Reading, Writing and Comparing Whole Numbers Beyond 1,000,000
- Key unit competence: To be able to round off decimals, convert fractions to decimals and vice versa.
**Introduction**In counting and mathematical operations, some numbers may be found difficult to be memorized or used. These can be simplified to their nearest numbers which can be easily memorized or used. For example money used by different schools per year can be rounded to simple figures to summarize.

Let’s consider an example of school party where Primary 6 learners contributed to buy all items needed. After planning all needed items, they found that the quantity of rice needed for the party is 40.97 kg which is near 50 kg. Then they decided to buy 50 kg of rice instead of 49.97 kg.

(a) Why do you think Primary 6 learners prefer to buy 50 kg instead of 49.97 kg?

(b) Do you think both quantities: 50 kg and 49.97 kg are easily memorized?

(c) How is rounding off useful in daily life?

**1.1 Reading and Writing Numbers Beyond 1,000,000 in words****Activity**1. A chart shows 999,999.

(a) If you add 1 to 999,999, what will be your next number?

(b) How many digits will the next number have?

(c) Draw an abacus with 7 spikes. Starting from ones (right), fill in the

number you get in (a) above to the last place value on the left.

(d) What is the place value of 1 in the number you get in (a) above?

(e) What name would you give to the number you get in (a) above?2. Now match the number figures to their corresponding number words.

2,999,999 Fourteen million, one hundred forty

thousand, two hundred nineteen.1,259,000 Two million, nine hundred ninety-nine

thousand nine hundred ninety-nine.14,140,219 One million, two hundred fiftynine

(a) Explain the steps you took when matching the numbers.

thousand.(b) Use the same steps in (a) above to write the population of Rwanda 12,279,742 in words.

(c) Why is it necessary to know how to write in number words?

**Example 1**A country has a population of 5,600,002. Write the population in words.

**Solution**Group the population in digits of threes. (5),(600),(002)

Draw a place value table and fill in the digits.

Write in words the values in the three-digit groups below.

**Example 2**A water tank holds 82,999,555 litres of water. Write the litres in words.

**Solution**Eighty-two million nine hundred ninety-nine thousand, five hundred fifty-five litres.

**Study tip**When you add 1 to 999,999, you get 1,000,000. To write 1,000,000 in words:

- First group the given digits in threes starting from the right to the left side of the whole number.
- Each group of three digits is known as a period.
- Draw a place value table and then write each digit under its place value.
- Write the value of each period in words. Then write the names of the periods to separate one period from another.
- Use a comma to separate millions from thousands and thousands from units.
- The periods that are millions, thousands and units are written without ‘s’. So, not in plural form.

**Application 1.1**

(a) 12,456,678 (b) 9,700,956 (c) 59,648,200 (d) 721,569,216

2. Kalisa bought a cow at 456,700 Frw. Write the amount

in words and explain your working out.

3. Abeli collected 5,417,257 litres of milk from his

farm in five months. Write the number of litres he

collected in words.

4. Agatha deposited 4,565,090 Frw in the bank. Write the amount she

deposited in words.

5. A non-government organisation spent 12,468,250 Frw on educating

young people about the dangers of alcohol. Write the amount of money

they spent in words.

6. On the inauguration ceremony of a district chairperson, 4,412,567 people

were invited. Write the number of people invited in words.

7. A district planted 9,998,888 saplings. Write the number in words.**1.2 Reading and Writing Numbers Beyond 1,000,000 in Figures****Activity**1. A chart shows 999,999.

(a) If you add 1 to 999,999, what will be your next number?

(b) How many digits will the next number have?

(c) Draw an abacus with 7 spikes. Starting from ones (right), fill in the

number you get in (a) above to the last place value on the left.

(d) What is the place value of 1 in the number you get in (a) above?

(e) What name would you give to the number you get in (a) above?

2. Now match the number figures to their corresponding number words.

2,999,999 Fourteen million, one hundred forty

thousand, two hundred nineteen.

1,259,000 Two million, nine hundred ninety-nine

thousand nine hundred ninety-nine.

14,140,219 One million, two hundred fiftynine

thousand.**Activity****Match the following cards accordingly:**

Four million, five hundred sixty-five 1,900,999thousand, two hundred seventy.

One million, nine hundred thousand, 1,300,860

nine hundred ninety-nine.One million, three hundred 4,565,270

thousand, eight hundred sixty.1. Explain the steps you took when matching the cards.

2. Why is it necessary to know how to write numbers in figures?**Study tip**When writing whole number in figures:

- First, group the number words in threes starting from the right of the whole numbers.
- Write the digits of each period in numbers.
- Read and write each period separately.
- Use a comma to separate millions from thousands and units.
- Add the values to get the right figure.

**Application 1.2**Write the following numbers in figures:

1. Fifteen million, three hundred fifty-six thousand, four hundred thirteen.

2. Eighty-three million, sixty- six thousand, two hundred thirty.

3. Eight hundred million, eighteen thousand, seven hundred seventeen.

4. A school collected four hundred fifty-six million, five hundred forty-five thousand, two hundred Rwandan francs as school fees from its learners. Write the amount in figures.

5. Five hundred twelve million, five hundred forty-nine thousand Rwanda francs was spent by a school in a year. Write the amount in figures.

6. Nineteen million Rwanda francs was spent by a company to print books. Write the amount in figures.

##### 1.3 Finding Place Value and Values of Numbers up to 7 Digits

##### Activity

1. Look at the cards below and form a number.

2. Draw a place value table in your exercise book.

3. Fill in the digits of the number 7,830,591 in the correct place values in

the place value table.

4. Write down the place value of each digit from the table.

5. Use the place value table to write 7,830,591 in words.

6. In which areas of your life can you apply place values?**Example 1**What is the place value of each digit in 8,356,421?

**Solution****Method 1**Count the digits in the number. There are 7 digits, now draw a place value table as shown below.

- The place value of 8 is millions.
- The place value of 3 is hundred thousands.
- The place value of 5 is ten thousands.
- The place value of 6 is thousands.
- The place value of 4 is hundreds.
- The place value of 2 is tens.
- The place value of 1 is ones

**Study tip**- The place values of numbers are the positions of Ones, Tens, Hundreds,Thousands, Ten thousands, Hundred thousands, Millions, Ten millions and Hundred millions.
- To find the place values of digits, draw the place value table and place the digits in it from the right.
- To find the value of digits, find the product of the digits and their place values.

**Application 1.3**1. Write the place value of each digit in the following:

(a) 2,312,983 (b) 7,676,405 (c) 10,101,899 (d) 853,925,732

2. Write the place value of the underlined digits in the following:

(a) 3,459,874 (b) 356,295,712 (c) 7,879,631 (d) 54,382, 345

3. Write the value of each digit in the following:

(a) 24,567,400 (b) 894,500,678 (c) 208,567,120 (d) 120,394,456

4. Write the value of the underlined digits in the following:

(a) 34,475,576 (b) 687,034,239 (c) 126,687,893 (d) 653,592,721

5. Describe how you can identify the value of 6 in 4,567,890

#### 1.4 Comparing Numbers Using <, > or =

(a) Which one is bigger than the other?

(b) Explain your answer.

(c) Complete the sentence using either <, > or =. That is A ...... B.

2. Count the total number of learners in your class.

(a) Use <, > or = to compare the number of boys to girls in your class.

(b) How can you apply comparison in your daily life situations?**Example 1**Compare 6,312,542 and 6,312,452 using <, > or =.

**Solution**Draw a place value table and fill in the numbers.

Compare the digits in each place value from left to right.

6 = 6, 3 = 3, 1 = 1, 2 = 2, 5 > 4 in the hundreds of units place value.

Therefore, 6,312,542 > 6,312,452

**Example 2**Compare 42,635,989 and 42,543,129 using <, > or =.

**Solution**Draw a place value table and fill in the numbers.

Compare the digits in each place value from left to right.

4 = 4, 2 = 2, 6 > 5 in the hundred thousands place value.

Therefore, 42,635,989 > 42,543,129.

Imanirere sold clothes worth 2,560,320 Frw in 2015. She sold clothes worth 4,576,670 Frw in 2016. Compare the sales over the two years using <, > or=.

**Solution**Draw a place value table and fill in the numbers.

Compare the digits in each place value from left to right.

2 < 4 in the millions place value.

Therefore 2,560,320 < 4,576,670**Study tip**- Compare numbers using place values. Check the biggest number against the smallest number.
- You can compare numbers by counting the number of digits of the whole numbers given.

- For numbers with the same number of digits, compare the digits with the same place value from the left. The number with the bigger digit is greater than the other. The number with the smaller digit is lesser than the othe
- For numbers with a different number of digits, the one with the highest number of digits is greater that the one with the lowest number of digits.
- If two numbers have different place values, compare them looking for the biggest or the smallest.
- If two numbers have the same place values and the same number of digits,compare them starting from the left until you get two different digits to tell the biggest or the smallest number.
- Order pairs of cards in ascending order.
- Write the order on slips of paper.
- Change to ordering cards in descending order.
- Write down the order.
- Start comparing from the highest place value to the lowest place value.
- In ones of millions, 1 = 1, 3 = 3, but 1 < 3 and 3 > 1.
- In hundred thousands, 7 = 7, 0 < 2, so, 3,205,446 > 3,025,446; 3,025,446> 1,770,550; 1,770,550 > 1,707,055.
- Also, 1,707,055 < 1,770,550; 1,770,550 < 3,025,446 and 3,025,446 < 3,205,444.
- Ascending order is the arrangement from the smallest to the biggest. So,the ascending order is 1,707,055; 1,770,550; 3,025,446; 3,205,446.
- Descending order is the arrangement from the biggest to the smallest. So,the descending order is 3,205,446; 3,025,446; 1,770,550; 1,707,055.
- A number is greater than another if its corresponding digit of another number in the same place value is smaller if they have the same number of digits.
- A number is smaller than another if its corresponding digit of another number in the same place value is bigger.
- A number with more digits is bigger than the other.
- A number with fewer digits is smaller than the other.
- Write two 7-digit numbers on flash cards.
- Arrange them in vertical order by the place value of their digits.
- Work out their sum.
- What answers do you get?
- Compare the answers in your groups.
- Add ones: 4 + 8 = 12. Write 2 under ones and carry 1 to tens.
- Add tens: 0 + 7 + 1 = 8. Write 8 under tens.
- Add hundreds:9 + 9 = 18. Write 8 under hundreds and carry 1 to thousands.
- Add thousands: 5 + 4 + 1 = 10. Write 0 under thousands and carry 1 to
- Add ten thousands: 2 + 3 + 1 = 6. Write 6 under ten thousands.
- Add hundred thousands: 3 + 8 = 11. Write 1 under hundreds thousands
- Add Millions: 1 + 6 + 2 = 9 write 9 under millions.
- Add ones: 8 + 4 + 3 = 15. Write 5 under ones and carry 1 to tens.
- Add tens: 0 + 0 + 5 + 1 = 6. Write 6 under tens.
- Add hundreds: 2 + 0 + 2 = 4. Write 4 under hundreds.
- Add thousands: 9 + 3 + 7 = 19. Write 9 under thousands and carry 1 to
- Add ten thousands: 2 + 2 + 8 + 1 = 13. Write 3 under ten thousands and
- Add hundred thousands: 6 + 8 + 9 = 24. Write 4 under hundreds thousands
- Add millions: 4 + 2 + 5 + 2 = 13. Write 13 under millions.
**When adding whole numbers, start from right to left. That is, from ones, to****Words used for addition include; total, sum, altogether, combined.**- Add thousands: 2 + 8 + 1 = 11. Write 1 under thousands and carry 1 to ten thousands.
- Add ten thousands: 6 +2 + 1 = 9. Write 9 under ten thousands.
- Add hundred thousands: 7 + 0 = 7. Write 7 under hundreds thousands.
- Add Millions: 5 + 3 = 8 write 8 under millions.
- First read and interpret the question correctly.
- When adding whole numbers, arrange the digits in the table according to place values.
- If numbers do not have the same number of digits, use zeros to act as place holders to ensure proper alignment of each digit according to place values.
- Start adding from right to the left, that is from ones to tens, thousands, ten thousands,hundred thousands and millions.
- Calculate the difference between the bigger and the smaller number.
- What is the most suitable method you can use to work out the difference?
- Subtract ones: 5 - 4 = 1, write 1 under ones.
- Subtract tens: 2 - 0 = 2, write 2 under tens.
- Subtract hundreds: 6 - 3 = 3, write 3 under hundreds.
- Subtract thousands: 5 - 4 = 1, write 1 under thousands.
- Subtract ten thousands: 4 - 2 = 2, write 2 under ten thousands.
- Subtract hundred thousands: 3 - 1 = 2, write 2 under hundred thousands.
- Subtract Millions: 6 - 2 = 4, write 4 under millions.
- Subtract ones: 0 - 0 = 0, write 0 under ones.
- Subtract tens: 2 - 5 = (not possible), borrow 1 from hundreds, then regroup with tens to get 12 - 5 = 7. Now write 7 under tens.
- Subtract hundreds: 5 - 5 = 0, write 0 under hundreds.
- Subtract thousands: 5 - 9 (not possible), borrow 1 from ten thousand, then regroup with thousands to get 15 - 9 = 6. Now write 6 under thousands.
- Subtract ten thousands: 7 - 9 (not possible), borrow 1 from hundred thousand, then regroup with ten thousands to get 17 - 9 = 8. Write 8 under ten thousands.
- Subtract hundred thousands: 8 - 8 = 0, write 0 under hundred thousands.
- When subtracting large numbers, arrange the numbers in vertical order, placing each digit in its correct place value.
- Subtract ones: 3 - 0 = 3, write 3 under ones.
- Subtract tens: 5 - 0 = 5, write 5 under tens.
- Subtract hundreds: 4 - 0 = 4, write 4 under hundreds.
- Subtract thousands: 3 - 4 (not possible), borrow 1 from millions, then first regroup with hundred thousands, then later regroup with ten thousands to get 13 - 4 = 9. Write 9 under thousands.
- Subtract ten thousands: 9 - 5 = 4, write 4 under ten thousands.
- Subtract hundred thousands: 9 - 6 = 3, write 3 under hundred thousands.
- First read and interpret the question correctly.
- When subtracting whole numbers, arrange the digits in the table according to place values. Make sure the larger number is on top of the smaller number.
- If numbers do not have the same number of digits, use zeros to act as place holders to ensure proper alignment of each digit according to place values.
- Start subtracting from the right (ones) as you go to the left side. Make sure you borrow and re-group where you find that the top digit is smaller than the bottom digit.
- Words to mean subtraction are; take away, minus, reduce and difference.
- To subtract, means to reduce a given number by a certain number. The result of subtraction is called difference.
- Write 1,235,265 on a sheet of paper.
- Multiply the number by 4. Note the answer.
- Multiply the number by 20. Write the answer.
- Now multiply 1,235,263 by 100. What do you get?
- When multiplying, arrange numbers in vertical order placing each digit in its correct place value.
- Multiplication is done by multiplying ones, tens, and hundreds.
- Arrange the whole number according to its place value.
- Then multiply the lower value by all of the upper values starting from ones to the left. Write your answer.
- Next multiply the second lowest number by all of the upper values from ones (right side) all through to the left side. Write your answer by skipping one place value from the right.
- Lastly add the two answers from multiplication to get a product.
- Explain to the class the procedure.
- When dividing, start with the digits in the highest place value.
- Estimate the nearest number of times a number can be divided.
- Carry the remainder to the next place value if it does not divide exactly.
- Align the digits in order to subtract correctly.
- First read and interpret the question correctly. This will help you to apply the right operation.
- When dividing, start with the digits in the highest place value.
- Estimate the nearest number of times a number can be divided. If it does not divide exactly, carry the remainder to the next place value.
- Then multiply and subtract.
- To round off whole numbers, use the place values and the value of digits.
- To round off to the nearest ten, first look at the digit in the place value of tens in the whole number.
- If the digit on the right of the required place value is greater or equal to 5, (that is, 5, 6, 7, 8, 9), you round up. Add 1 to the digit in the required place value.
- If the digit on the right of the required place value is less than 5, (that is, 0,1, 2, 3, 4), you round down. The digit in the required place value doesn’t change but all digits to the left change to 0.
**Application 1.14**- In pairs, pick four number cards from the pack.
- Look keenly at the digits in each particular place value.
- Write on the sheets of paper the approximate numbers to hundred.
- Now round off 39,289 to the nearest hundred. Explain your working.
**Study tip****To round off whole numbers to the nearest hundred, consider the number****in the tens place value.****To round off whole numbers to the nearest thousand, consider the number****in the hundreds place value.****If the digit is greater or equal to 5, it is converted to one hundred or thousand****then added to the place value of hundreds or thousands according to the****required place value.****If the digit is less than 5, it is converted to zero hundred or zero thousand****and then added to the required place value.**- To round off to the nearest ten thousand, consider the digit in the thousands place value.
- To round off to the nearest hundred thousand, consider the digit in the ten thousands place value.
- To round off to the nearest million, consider the digit in the hundred thousands place value.
- If the digit is greater or equal to 5, it is converted to one ten thousand, one hundred thousand, one million respectively, the added to the required place value.
- If the digit is less than 5, it is converted to zero ten thousand, zero hundred thousand, zero million respectively, then added to the required place value.

(a) 260,340………60,430,730.

(b) 8,855,631……..8,855,136

(c) 302,831,547 …… 30,283,154.

(d) 9,991,999 …… 9,991,999

2. Camille harvested 5,562 tonnes of beans and Kajile

harvested 5,256 tonnes of beans. Who harvested

more beans?

3. Mukagasana deposited 2,506,590 Frw in the bank.

His son deposited 259,000 Frw. Who deposited

more money? Explain your answer.

4. A school received a donation of 67,957,800 Frw while another school

received 67,854,590 Frw. Find the difference. Which school received

less money?

5. Hospital A admitted 45,679 patients in 2016

while hospital B admitted 67,890 patients

in the same year. Which hospital admitted

more patients? Explain your answer.

6. A district collected 4,853,825 Frw in taxes

while another district collected 4,197,900Frw. Which district collected more money?

##### 1.5 Arranging Numbers in Ascending and Descending Order

Activity

Use cards below.**942,704 942,407 1,496,066 1,496,606**

procedure to the class.**Example**Arrange the following numbers in ascending and descending order.

1,707,055 1,770,550 3,025,446 3,205,446

**Solution**Use a place value table to compare the digits.

**Study tip****Application 1.5**Use a place value table to compare and arrange numbers in ascending and descending order

**.**1. Order the following numbers in ascending order.

(a) 1,673,421; 1,065,345; 1,671,241; 1,065,234

(b) 2,303,874; 2,033,874; 2,330,874; 2,874,303

(c) 9,827,623; 6,827,623; 8,279,625; 9,623,829

(d) 11,046,305; 11,460,305; 4,116,305; 4,611,530

2. Order the following numbers in descending order.

(a) 4,963,427; 4,427,963; 4,369,427; 4,724,963

(b) 8,306,396; 8,693,306; 8,369,306; 8,063,963

(c) 12,042,994; 12,420,994; 12,994,609; 12,499,906

(d) 3,625,113; 625,113; 6,253,311; 652,311

**1.6 Adding Numbers Beyond 1,000,000****Activity****Example 1**

Add: 6,325,904 and 2,834,978.

Solution

Arrange the digits according to place values.Then add the two whole numbers starting from the right (ones) to the left.

**Units****Thousands****Millions****Example 2**

Find the sum of 4,629,208; 2,823,004 and 5,987,253.

Solution

Arrange the digits according to place values.

Then add the two whole numbers starting from the right (ones) to the left.**Units****Thousands****Millions****Study tip****tens, thousands, ten thousands, hundred thousands and millions.****Application 1.6**Add the following:

(a) 4,985,670 + 2,322,502 =

(b) 2,069,012 + 2,625,044 =

(c) 6,232,343 + 2,432,234 + 1,067,103 =

(d) 3,807,233 + 2,067,943 + 6,723,623 =

(e) 9,088,033 + 9,000,046 =

(f) 1,602,444 + 2,622,433 + 5,789,987 =

(g) 8,421,982 + 3,723,848 + 3,921,982 =**1.7 Solving Problems Involving Addition of Numbers Beyond 1,000,000****Activity****In a country, there are 12,000,000 males and 3,000,000 females.****1. What should you do to know the total number of people in the country?****2. Compare the number of males to that of females.****3. Create a list of instances where addition is applied in your daily life.****4. How is addition relevant to you?****Example**bricks to put up walls of the house. Find the total number of bricks that were used to complete the house.

**Solution**Arrange the digits according to place values.

Then add the two whole numbers starting from the right (ones) to the left.

**Units**Add ones: 6 + 7 = 13. Write 3 under ones and carry 1 to tens.

Add tens: 2 + 8 + 1 = 11. Write 1 under tens and carry 1 to hundreds.

Add hundreds: 4 + 9 + 1 = 14. Write 4 under hundreds and carry 1 to thousands.

**Thousands****Millions**The total bricks that were used to complete the house are 8,791,413.

**Study tip**. Other words used for addition include total,sum, altogether and combined.

**Application 1.7****1**. A dairy cooperative sold 1,123,456 and 8,467,619 litres of milk on Monday and Tuesday respectively. How much milk was sold in the two days?**2**. Publishing companies A, B and C supplied the following number of textbooks to primary schools in the same district last month. A supplied 1,345,346 copies, B supplied 1,206,460 copies and C supplied 1,600,400 copies. What is the total number of books supplied by all three publishing companies?3. 3,460,782 people participated in a Run for Water marathon organised by a telecom company. About 5,525,448 people participated in a cancer marathon organised by the same telecom company. How many people participated in both marathons?

4. Kayitesi sold 1,625,255 kg of maize flour in one year and 3,268,450 kg of maize flour in another year. What was her total sales in the two years?

**1.8 Subtracting Numbers Beyond 1,000,000****Activity**Explain your procedure to the class.

Now try out this: Mukangarambe went to the shop with 20,000 Frw, she spent 17,240 Frw. How much was her balance?

**Example 1**Subtract: 6,345,625 - 2,124,304

**Solution**Arrange the digits according to place values. Put the larger number at the top of the table followed by the smaller number.

Subtract the two whole numbers starting from the right to the left. Remember to borrow then re-group where necessary as you subtract.

**Units****Thousands****Millions**Therefore, 6,345,625 - 2,124,304 = 4,221,321.

**Example 2**Subtract 1,899,550 litres from 2,985,620 litres.

**Solution**Arrange the digits in the table according to place values.

Put the larger number at the top of the smaller number.

Subtract the two whole numbers starting from the right to the left.

Remember to borrow then re-group where necessary.

**Units****Thousands****Millions**Subtract Millions: 2 - 1 = 1, write 1 under millions.

Therefore, 2,985,620 litres - 1,899,550 litres = 1,086,070 litres.

**Study tip****Application 1.8****Subtract the following**:**1**. 6,000,101 – 4,999,011 =**2**. 6,291,569 – 4,687,263 =**3**. 3,562,560 – 1,670,340 =**4**. 9,003,087 – 6,334,050 =**5**. 3,642,110 kg – 1,039,042 kg =**6**. 6,334,050 trees from 9,003,087 trees =**7**. 9,008,200 Frw – 8,000,200 Frw =**8**. 6,326,428 books from 8,040,249 books =**9**. 9,462,490 – 5,233,982 =**1.9 Solving Problems Involving Subtraction of Numbers Beyond 1,000,000****Activity****1.**Determine the amount of money Gabiro still owes the bank.**2.**Give instances where subtraction is applied in your daily life.**3.**How is subtraction relevant to you?**Example**A juice company produced 7,003,453 litres last week. It sold only 5,654,000 litres in the week. How many litres of juice remained unsold?

**Solution**Arrange the digits in the table according to place values.

Put the larger number at the top of the smaller number.

Subtract the two whole numbers starting from the right to the left.

Remember to borrow then re-group wherenecessary.

**Units****Thousands****Millions**Subtract Millions: 6 - 5 = 1, write 1 under millions. 1,349,453 litres of juice remained.

**Study tip****Application 1.9****1**. What is the difference between 2,798,576 pens and 2,745,568 pens?**2**. 3,567,342 babies were born in a country in 2016. Of these, 1,593,599 babies were girls. Find the number of boys.**3**. A farmer harvested 12,000,500 kg of maize in the first season. By the end of the first month, he had sold 6, 400,400 kg of maize. How many kilograms are still in his store?**4**. A truck carrying 2,560,000 litres of milk was in an accident. 1,756,950 litres were split. How much milk remained?**5**. There are nine million three hundred twelve thousand six hundred eight animals in a park. Of these, three million six hundred nine thousand, three hundred twenty-three are zebras. How many are not zebras?**6**. Gitego harvested twenty-five million, five thousand two hundred fifty kilograms of Irish potato. He took away sixteen million, four hundred twenty-eight thousand, five hundred kilograms to distribute to schools. How many kilograms remained?**1.10 Multiplying Numbers Beyond 1,000,000****Activity****Example****Example****Work out the following:****(a)**986,342 x 76**(d)**896,234 x 121**(b)**1,112,025 x 111**(e)**Multiply 2,316,310 by 99.**(c)**Multiply 1,076,033 by 104.**(f)**What is the product of 1,404,055 and 121?**1.11 Solving Problems Using Calculation Strategies on Multiplication****Activity**In January, a school admitted 500 learners. Each learner paid 30,000 Frw in school fees to the bursar.

**1.**How would you find the total school fees paid by all learners?**2.**Describe the steps you take to get the answer.**3.**What mathematics operation are you likely to use to carry out the calculation easily?**4.**In what other ways can you use the operation in your daily life?**Study tip****Application 1.11****1**. A non-government organisation was supposed to deposit five hundred thousand five hundred Rwanda francs as tuition fees for each of the students it sponsors at university. If it sponsors 25 students, how much money should it deposit?**2**. Habimana wanted to save tuition fees for her daughter to study at University. At university the tuition fees are 400,000 Frw per year. How much money must she save in order for her daughter to complete three years?**3**. In a store, there are 382,324 bags of mangoes. Each bag contains 250 mangoes. How many mangoes are in the store?**4**. 44 drums of the same capacity contain 2,200,000 litres of oil each. How many litres are there altogether?**5**. If light travels 300,000,000 metres in one second, how far does light travel in one minute?**6**. A private school has 617 learners. If one learner pays 10,000 Frw in school fees per term, how much money do they pay altogether?**7**. A shoe factory makes 600,000 pairs of shoes per day. How many pairs of shoes can the same factory produce in 15 days if they work at the same rate?**1.12 Dividing Numbers Beyond 1,000,000****Activity****Study tip****Application 1.12**Work out the following.

(a) 2,026,648 ÷ 26 =

(b) 8,123,518 ÷ 34 =

(c) 7,562,296 ÷ 56 =

(d) 9,561,978 ÷ 73 =

(e) Share equally 8,164,904 saplings among 124 villages.

(f) Distribute equally 7,827,831 kg of maize among 333 parishes. How many kilograms does each parish get?

**1.13 Solving Problems Using Calculation Strategies on Division****Activity**Get 300 sticks and share them among 10 learners.

(a) How many sticks does each learner get?

(b) What operation have you carried out?

(c) Write the operation statement and work it out.

(d) Present your working out to the class.

**Study tip****Application 1.13**Divide the following:

1. Share equally 2,026,800 Frw among 24 employees.How much does each get!

2. 500 members of the congregation contributed equally 5,501,000 Frw. How much did each contribute?

3. A soda bottling company packed 8,462,376 bottles of soda in crates each containing 24 bottles. Find the number of crates that were packed.

4. A school paid its employees 28,559,925 Frw salary for the month just ended. If there are 135 employees who get the same salary, how much money does each employee receive?

5. A sugar factory manufactured 12,960,648 kgs of sugar in a year. How many kgs of sugar were produced every month if the factory produces equal amounts of sugar monthly?

**1.14 Rounding off Whole Numbers to the Nearest Ten****Activity**Study the number cards shown and answer the questions that follow.

(a) Write all the number cards in whole numbers.

(b) Describe the steps you took to write the above number cards as whole numbers.

(c) What do you refer to during the process of converting a decimal number

into a whole number?

(d) Round off the following numbers to the nearest ten.

(i) 2345 (ii) 8703

(e) Of what importance is rounding off in daily life?**Example 1****Solution****Study tip**1. Round off to the underlined place value.

(a) 4,856,796 (b) 6,789,735 (c) 2,234,587

(d) 3,654,867 (e) 62,453,792 (f) 5,459,599

2. The average number of goats on a farm is 6,753,927, round off this number to the nearest ten.

3. Find the product of 23,000 and 30. Round off your answer to the nearest ten.

4. A school used 100,000 Frw to buy computers and 598,999 Frw to buy books for its library. How much money did it spend altogether? Round off the answer to the nearest ten.

5. A restaurant sells food at 3,000 Frw per plate. On the first day it sold 413 plates, on the second day it sold 123 plates. Round off the plates sold in the two days to nearest ten.

**1.15 Rounding off Whole Numbers to the Nearest Hundred and Thousand****Activity****example 1**Round off 6,773,543 to the nearest hundred.

**Solution****example 2**Round off 1,257,654 to nearest thousand.

**Solution****Study tip****Application 1.15**(a) 3,654,597 (b) 22,987,635 (c) 564,323,990

(d) 3,890,909 (e) 4,361,367 (f) 12,642,298

2. Round off the following numbers to the nearest thousand.

(a) 6,068,602 (b) 8,523,174 (c) 64,565,438

(d) 70,309,985 (e) 4,236,201 (f) 17,099,924

**1.16 Rounding off Whole Numbers to the Nearest Ten Thousand, Hundred****Thousand and Million****Activity**Study the number cards and answer the questions that follow:

2,345,789 3,604,800 5,687,231 1,342,798

(a) Identify the digits to the right of the ten thousands place value.

Round it up or down.

(b) Add the rounded digit to the ten thousands place value.

(c) Replace all the digits to the right of the ten thousands place value with

zeros. What do you notice?**example 1**Round off 1,576,798 to the nearest ten thousand.

**Solution****example 2**Round off 3,540,750 to the nearest hundred thousand.

**Solution**E

**xample 3**Round 7,398,500 to the nearest million.

**Solution****Study tip****Application 1.16**1. Round off the following numbers to the nearest ten thousand:

(a) 4,546,401 (b) 2,560,456 (c) 1,564,670

2. A farmer sold ten of his cows and earned 4,687,300 Frw. Round off his earned money to the nearest ten thousand.

3. Round off the following numbers to the nearest hundred thousand.

(a) 8,576,700 (b) 61,223,789 (c) 7,890,650

4. Mutesi paid 1,520,500 Frw in tuition fees for her first semester at university. Round off her tuition fees to the nearest hundred thousand.

5. Round off the following numbers to the nearest million:

(a) 3,120,600 (b) 8,670,798 (c) 7,456,982

6. Agatesi bought her car for 9,561,000 Frw. Round off the money she paid to the nearest million.

**End of Unit 1 Assessment**1. Write the place value of the underlined digits?

(a) 76,767,709 (b) 5,999,999 (c) 1,808,064

2. Compare the following using >, < or =.

(a) 1,121,277......1,121,207

(b) 9,876,534...... (3,232,456 + 1,087,653)

(c) 92,268 ÷ 2...... 7,689 x 12

3. Round off to the underlined digits:

(a) 8,765,423 (b) 6,545,677 (c) 98,776,113

(d) 45,367,789 (e) 9,999,958 (f) 32,694,689

4. Round off 1,140,038 to the nearest million.

5. A company printed 19,884,345 books last year and 26,326,150 books this year. How many books were printed altogether over the two years?

6. A farmer’s hens gave him 16,764 eggs per day. How many eggs will he get in 30 days?

7. An NGO released five million four hundred and seventy-two thousand six hundred fifty francs to an organisation that rehabilitate street children.Write the amount in figures.

8. A total of nine million, seven hundred and ninety-six thousand, eight hundred and seventeen text books were bought by a library in the past few years. Write the total number of books in figures.

9. Kamali collected 5,678,950 Frw from milk sales in this month. Write the amount in words.

10. Muhire has 8,434,579 tea shrubs on his tea estate. Write the number in words.

11. Complete the table below.

12. A bottling company produced 10,964,329 bottles of soda in January, 12,726,455 bottles in February, 18,612,900 bottles in March and 5,046,500 bottles in April.

(a) How many bottles of soda did the company produce over the four months?

(b) If the company sold 20,892,600 bottles bottled during those four months, how many bottles of soda remained?