Introduction to Place Values

Each place in a number has a value.

Ones

The ones place tells how many ones there are.

3 means 3 ones.

9 is the largest amount that we can express (write or say) with one digit.

Tens

The tens place shows how many tens there are. The ones place must have a digit in it before there can be a digit in the tens place.

Every ten is ten ones.

43 means 4 tens and 3 ones

99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits.

Hundreds

The place to the left of the tens place is the hundreds place. It shows how many hundreds there are. A number written using three whole digits has a hundreds place, a tens place, and a ones place.

Every hundred is ten tens — every hundred is the same as one hundred ones.

100                     100                       100

425 means 4 hundreds, 2 tens, and 5 ones.

Thousands

The place to the left of the hundreds place is the thousands place.

One thousand is the same as ten hundreds.

One thousand is the same as one hundred tens.

One thousand is the same as one thousand ones. (You will have to imagine the picture of the one thousand ones!)

Ten thousands

The place value to the left of thousands is ten thousands. As you can tell by the name, one ten thousand is ten thousands. You are not going to get a sketch of these large place values because the page isn’t big enough!

Hundred thousands

Have you heard the expression, “They have a 6 figure salary.” That means they earn at least one hundred thousand dollars, which takes six digits to write! The place value to the left of ten thousands is hundred thousands. There is definitely not room on the page for a picture of this place value! Ten ten thousands makes one hundred thousand.

Millions

And if we look one more place to the left, the place value is millions. One million is 1 with six zeros after it: 1 000 000.

A space is left between the millions place and the hundred thousands place. A space is left between the thousands place and the hundreds place.

• 2368100
• 3150213
• 14263942
• 5521671

Place values overview

This place value chart may help you to remember the place values.

Notice the groups of three digits. Look at the pattern for the three places which is repeated in each place value group – the pattern is hundreds, tens, ones.

… and so on.

Our number system is very tidy. When you learn to use the metric measurement system, you will see the metric system is based on ten just like the number system.

Reading and Writing Numerals

You know that the digits are 0 1 2 3 4 5  6  7  8  9  and that digits are arranged in different places so we can count larger amounts than our ten fingers!

When we use digits, we call what we write the “numeral.”

• 328 is a numeral
• 46 is a numeral
• 3 is a numeral

We use numerals to represent numbers.

Numerals under 1000

The numerals from 1 to 12 have special words. These are

• 0    zero
• 1     one
• 2    two
• 3    three
• 4    four
• 5    five
• 6    six
• 7    seven
• 8    eight
• 9    nine
• 10  ten
• 11   eleven
• 12   twelve

The numerals from 13 to 19 are

• 13    thirteen
• 14    fourteen
• 15    fifteen
• 16    sixteen
• 17    seventeen
• 18    eighteen
• 19    nineteen

The word names for the numbers 20 to 90 are

• 20 twenty
• 30 thirty
• 40 forty
• 50 fifty
• 60 sixty
• 70 seventy
• 80 eighty
• 90 ninety

The names for the numbers between groups of tens also follow a pattern. The first number tells us how many tens. The second number tells us how many ones.

The written names for numbers that have tens and ones are written with a hyphen (-) between them. This pattern with the hyphen continues up to ninety-nine (99).

When we write hundreds in words, we need two words. The first word tells us how many hundreds. The second word tells us we are counting hundreds.

200     two hundred

You now know how to write numbers in words up to 999.

Remember:

• hyphen (-) between the tens and units no hyphen anywhere else
• no “s” on the hundred
• no “and” between the hundreds place and the tens place

Here is another example.  Watch out for the empty space!

Here is another example.  Watch out for the empty space!

Example E

Here is another example. Watch out for the empty spaces!

Example F

Remember: empty spaces are not written in words.

Numerals over 1000

Large numerals are read in the place value groups of three that you noticed in the place value chart. You have been practicing reading numerals with three digits or less. Now practice reading the thousands group.

26 201 is twenty-six thousand two hundred one.

400 000 is four hundred thousand.

Now, just for fun, take a look at these very large numerals.  Say ―million for the group to the left of the thousands group.

Work on reading these numerals with someone else and then ask your instructor to listen as you read them.

• 241962107
• 483450
• 27800
• 2345409
• 164231
• 260164342
• 138000
• 410623
• 912050
• 24900
• 227695
• 105576

Topic A: Self-Test

Mark / 17     Aim 14/17

1. Write the place value for the underlined digit. (6 marks)
   1. 8765 the place value of 6
   2. 930 the place value of 0
   3. 47932 the place value of 4
   4. 85421 the place value of 5
   5. 279673 the place value of 2
   6. 397 the place value of 3
2. Write the word names for these numerals. (6 marks)
   1. 59
   2. 942
   3. 7378
   4. 8200
   5. 4005
   6. 58310
3. Write the numerals for these word names. (5 marks)
   1. eight hundred forty-seven
   2. four thousand three hundred eighty
   3. two hundred seventy-five thousand eighty-seven
   4. sixty thousand four hundred sixteen
   5. fifteen thousand twenty

Answers to Topic A Self-Test

1. 1. tens
   2. ones
   3. ten thousands
   4. thousands
   5. hundred thousands
   6. hundreds
2. 1. fifty-nine
   2. nine hundred forty-two
   3. seven thousand three hundred seventy-eight
   4. eight thousand two hundred
   5. four thousand five
   6. fifty-eight thousand three hundred ten
3. 1. 847
   2. 4 380
   3. 275 087
   4. 60 416
   5. 15 020

When we write a number in expanded form, each digit is written with its place value.

Example:

Example:

Example:

Topic B: Self-Test

Mark / 12    Aim   10/12

1. Write each number in expanded form. (6 marks.)
   1. 643
   2. 759
   3. 4821
   4. 94205
   5. 367542
   6. 1850643
2. Write each number from its expanded form. (6 marks.)
   1. 300 + 60 + 9 =
   2. 700 + 5 =
   3. 1000 + 400 + 90 + 1 =
   4. 20000 + 1000 + 500 + 80 + 4 =
   5. 500000 + 40000 + 2000 + 700 + 30 + 9 =
   6. 3000000 + 900000 + 60000 + 8000 + 400 + 30 + 1 =

Answers to Topic B Self-Test

1. 1. 600 + 40 + 3
   2. 700 + 50 + 9
   3. 4000 + 800 + 20 + 1
   4. 90000 + 4000 + 200 + 5
   5. 300000 + 60000 + 7000 + 500 + 40 + 2
   6. 1000000 + 800000 + 50000 + 600 + 40 + 3
2. 1. 369
   2. 705
   3. 1491
   4. 21584
   5. 542739
   6. 3968431

In this topic you will learn to arrange numerals in order from smallest to largest. Sorting numbered papers such as order forms, arranging items by the date and comparing prices are examples of the ways you use this skill. First look at pairs of numerals. Look at two numerals and tell which one is larger. How do you do this?

To compare numerals, look at the place with the largest value.

Note: Numerals with one digit are always less than numerals with two digits. Numerals with two digits are always less than numerals with three digits, and so on.

• 9 is less than 15
• 87 is less than 107
• 999 is less than 1 001

Now use the same ideas to arrange more than two numerals in order.

For example, to arrange 6, 616, 1, 66, 666, 61, and 16 in order from smallest to largest, use the following method:

1. First, sort the numerals with the same number of digits into groups.
   • 6, 1
   • 66, 16, 61
   • and 616, 666
2. The group of one digit numerals contains 6 and 1. As 1 is smaller than 6, the list starts with 1, then 6.
3. The group of two-digit numerals contains 66, 61, and 16. Use your skills in ordering numerals to see that 16 is smallest, then 61, and 66 is the largest of this group. The list now reads, 1, 6, 16, 61, 66.
4. Finally, look at the three-digit numerals, 616 and 666. As 616 is smaller than 666, it will come first. The list now reads:
   • 1, 6, 16, 61, 66, 616, 666.

Greater Than, Less Than, Equal

The sign < means is less than (smaller than).

The sign > means is greater than (bigger than).

The greater than and less than signs always point to the smaller number (that is, the small part of the sign is close to the small number.)

5  < 12           5 is less than 12

6  > 3             6 is greater than 3

The sign = means equals and is used when two amounts are the same.

The sign ≠ means not equal to and is used when two amounts are not the same.

Topic C: Self-Test

Mark /12          Aim 10/12

1. Box the larger number of each pair. (6 marks)
   1. 9784; 7892
   2. 56663; 56566
   3. 13204; 14420
   4. 721011; 721101
   5. 461300; 416003
   6. 2879921; 2987721
2. Arrange these numerals in order from smallest to largest. (2 marks)
   1. 75; 754; 475; 47; 5747; 5774; 77575
   2. 18; 23070; 429; 7824; 37; 994; 1120
3. Write >, <. or = in each blank to make a true statement. (4 marks)
   1. 3678         3768
   2. 14002         14000
   3. 38463         3846
   4. 10010         10010

Answers to Topic C: Self-Test

1. 1. 9784
   2. 56663
   3. 14420
   4. 721101
   5. 461300
   6. 2987721
2. 1. 47, 75, 475, 754, 5747, 5774, 77575
   2. 18, 37, 429, 994, 1120, 7824, 23070
3. 1. <
   2. >
   3. >
   4. =

We use numbers a lot in our everyday lives. List some of the ways you use numbers.

You may have written money, shopping, time, and counting as part of your answer.

Think about time. Let’s say it takes eight minutes to walk to the bus. If someone asks you how long it takes, you will probably say, “About ten minutes.”

If you buy a sweater that costs $29, you may say, “Oh, it was around thirty dollars.”

How far is it from Vancouver to Prince George? The map says 796 km, but we would probably say, “About 800 kilometres.”

You have just read examples of rounding numbers.

We round numbers for many reasons:

• We may not know the exact number.
• The exact number may not be important for what we are doing.
• We may need a quick way to figure something out.

When you are rounding numbers, use zeros to hold the places at the end of the number. Work through the following examples and exercises carefully. Rounding is an important skill.

Rounding to the Nearest Hundred

A number rounded to the nearest hundred will have zeros in the ones place and in the tens place. The number will end with 000, 100, 200, 300, 400, 500, 600, 700, 800, or 900.

When rounding to the nearest 100, we are looking for the closest group of 100.

Remember: The rounded number has zeroes in the tens and ones places.

Remember: The rounded number has zeroes in the tens and ones places.

Now look at a shorter method to round to the nearest 100.

When rounding to the nearest hundred, do this:

Step 1: Underline the hundreds place.

468

Step 2: Look at the digit following in the tens place.

Step 3: If the digit in the tens place is less than 5,

• write a zero in the tens place and the ones place.
• leave the hundreds digit as it is.

Step 4: If the digit in the tens place is 5 or more,

• write a zero in the tens place and the ones place.
• add one more hundred to the hundreds place.

Note: If you are rounding to the nearest hundred, one and two-digit numerals round like this:

• the numbers from 0 to 49 round to 0
• the numbers from 50 to 99 round to 100.

Rounding to the Nearest Thousand

A number rounded to the nearest thousand will have zeros in the ones, tens, and hundreds places. The number will end with 0 000, 1 000, 2 000, 3 000, 4 000, 5 000, 6 000, 7 000,

8000, or 9000.

When rounding to the nearest thousand, do this:

Step 1: Underline the thousands place.

4398

Step 2: Look at the digit following in the hundreds place.

Step 3: If the digit in the hundreds place is less than 5,

• write a zero in the hundreds place, the tens place, and the ones place.
• leave the thousands digit as it is.

Step 4: If the digit in the hundreds place is 5 or more,

• write a zero in the hundreds, tens, and ones places.
• add one more thousand to the thousands place.

Note: If you are rounding to the nearest thousand, one, two, and three-digit numerals round like this:

• numerals from 0 to 499 round to 0
• numerals from 500 to 999 round to 1000.

Rounding to the Nearest Ten Thousand

A number rounded to the nearest ten thousand will have zeros in the ones, tens, hundreds and thousands places. The number will end with 0 000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, or 90000.

When rounding to the nearest ten thousand, do this:

Step 1: Underline the ten thousands place.

42398

Step 2: Look at the digit following in the thousands place.

Step 3: If the digit in the thousands place is less than 5,

• write a zero in the thousands place, the hundreds place, the tens place, and the ones place.
• leave the ten thousands digit as it is.

Similarly:

Step 4: If the digit in the thousands place is 5 or more,

• write a zero in the thousands, hundreds, tens, and ones places.
• add one more ten thousand to the ten thousands place (or in other words, add 1 to the ten thousands digit)

Note: If you are rounding to the nearest ten thousand, one, two, three and four- digit numerals round like this:

• numerals from 0 to 4 999 round to 0
• numerals from 5000 to 9999 round to 10000.

Rounding to the Nearest Hundred Thousand

A number rounded to the nearest hundred thousand will have zeros in the ones, tens, hundreds, thousands and ten thousands places. The number will end with 000 000, 100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, or 900000.

When rounding to the nearest hundred thousand, do this:

Step 1: Underline the hundred thousands place.

414 398

Step 2: Look at the digit following in the ten thousands place.

Step 3: If the digit in the ten thousands place is less than 5,

• write a zero in the ten thousands place, the thousands place, the hundreds place, the tens place, and the ones place.
• leave the hundred thousands digit as it is.

Step 4: If the digit in the thousands place is 5 or more,

• write a zero in the ten thousands place, thousands place, hundreds place, tens place, and ones place.
• add one more hundred thousand to the hundred thousands place (or add 1 to the hundred thousands digit).

Note: If you are rounding to the nearest hundred thousand, one, two, three, four and five-digit numerals round like this:

• numerals from 0 to 49 999 round to 0
• numerals from 50 000 to 99 999 round to 100 000.

Rounding to the Nearest Million

A number rounded to the nearest million will have zeros in the ones, tens, hundreds, thousands, ten thousands and hundred thousands places. The number will end with0 000 000, 1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000, or 9000000.

When rounding to the nearest million, do this:

Step 1: Underline the millions place.

4214398

Step 2: Look at the digit following in the hundred thousands place.

Step 3: If the digit in the hundred thousands place is less than 5,

• write a zero in the hundred thousands place, the ten thousands place, the thousands, the hundreds place, the tens place, and the ones place.
• leave the millions digit as it is.

4214398 rounds to 4000000 (4214398 is nearer to 4000000 than to 500000)

5367263 rounds to 5000000

Step 4: If the digit in the hundred thousands place is 5 or more,

• write a zero in the hundred thousands place, the ten thousands place, the thousands place, the hundreds place, tens place, and ones place.
• Add one more million to the millions place.

2818884 rounds to 3000000 (2818884 is nearer to 3000000 than to 2000000)

6729583 rounds to 7000000

9991965 rounds to 10000000

Topic D: Self-Test

Mark /36    Aim 30/36

1. Round your answer to the nearest hundred. (4 marks)
   1. 329
   2. 2481
   3. 8065
   4. 3916
2. Round your answer to the nearest thousand. (4 marks)
   1. 5521
   2. 21813
   3. 46499
   4. 34860
3. Round your answer to the nearest ten thousand. (4 marks_
   1. 15521
   2. 26318
   3. 176994
   4. 86486
4. Round your answer to the nearest hundred thousand. (4 marks)
   1. 523521
   2. 821932
   3. 761949
   4. 464051
5. Round your answer to the nearest million. (4 marks)
   1. 7312908
   2. 6009280
   3. 9152801
   4. 576679
6. For each problem, round to the number asked. 16 Marks
   1. The longest river in North America is the Mississippi River which is 6275 kilometers long. The longest river in Canada is the Mackenize River which is 4 242 kilometers long. The Yukon River is 3701 kilometers long. The St. Lawrence River is 3058 kilometers long. Round each number to the nearest hundred.
      

      River	Number	Rounded Number
      Mississippi River
      Mackenzie River
      Yukon River
      St. Lawrence River

   2. In 2009, the population of Shanghai, China was 13831900. The population of Moscow, Russia was 10 508 971. The population of New York City, United States of America was 8363710. The population of Vancouver, Canada was 578041. Round each of these numbers to the nearest hundred thousand.
      

      City	Number	Rounded Number
      Shanghai, China
      Moscow, Russia
      New York City, USA
      Vancouver, Canada

Answers to Topic D Self-Test

1. 1. 300
   2. 2500
   3. 8100
   4. 4000
2. 1. 6000
   2. 22000
   3. 46000
   4. 35000
3. 1. 20000
   2. 30000
   3. 180000
   4. 860000
4. 1. 500000
   2. 800000
   3. 800000
   4. 500000
5. 1. 7000000
   2. 6000000
   3. 9000000
   4. 1000000

6. 1. River	Number	Rounded Number
      Mississippi River	6275 kilometers	6300 kilometers
      Mackenzie River	4242 kilometers	4200 kilometers
      Yukon River	3701 kilometers	3700 kilometers
      St. Lawrence River	3058 kilometers	3100 kilometers

   2. City	Number	Rounded Number
      Shanghai, China	13831900 people	13800000 people
      Moscow, Russia	10508971 people	10500000 people
      New York City, USA	8363710 people	8400000 people
      Vancouver, Canada	578041 people	600000 people

You will now practice all the skills you learned in Unit 1. Check your work using the answer key at the end of the review.

1. Write the place value names (ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions) for each bolded digit.
   1. 4392
   2. 765
   3. 18293
   4. 56428
   5. 3641758
   6. 426153
   7. 8429576
   8. 4258
2. Using the number 349285106, write the digit that is in each of the following place values.
   1. millions
   2. ones
   3. ten thousands
   4. thousands
   5. hundreds
   6. hundreds thousands
   7. tens
3. Underline the digit for the place value named.
   1. hundreds,    5321
   2. tens,    8703
   3. ten thousands,    34891
   4. hundred thousands,    891402
   5. thousands,    72491
   6. millions,    4201856
4. Write the word names for the numbers.
   1. 818
   2. 1678
   3. 29764
   4. 1984152
   5. 42803
   6. 226917
5. Write the numerals for these word names.
   1. twenty-five thousand one hundred thirty-two
   2. one thousand two hundred seven
   3. two hundred fifteen thousand twenty-four
   4. one million six hundred ninety-five thousand four hundred twenty
   5. seven hundred twenty-six
   6. nine thousand four
6. Write each number in expanded form.
   1. 184
   2. 3908
   3. 61281
   4. 1539587
   5. 366524
7. Write each number from expanded form.
   1. 50000  +  6000  + 600  +  90  + 8
   2. 200000  +  70000  +  8000  +  200  +  60  + 1
   3. 3000  +  800  +  80  + 5
   4. 1000000 + 400000 + 70000 + 6000 + 100 + 50 + 3
   5. 700  +  1
8. Arrange these numbers in order from smallest to largest.
   1. 18; 34937; 727; 1487; 147832
   2. 769; 6790; 697; 76976; 76796
9. Write <, >, or = in each blank as needed.
   1. 9698          6899
   2. 7542         7452
   3. 34682         39421
   4. 124693         124693
   5. 738423         783423
   6. 45832         54123
10. Round each number to the nearest hundred.
    1. 774
    2. 2581
    3. 21204
    4. 692
    5. 572098
    6. 7652931
11. Round each number to the nearest thousand.
    1. 948
    2. 75767
    3. 288869
    4. 479
    5. 3976
    6. 5012
12. Round each number to the nearest ten thousand.
    1. 4028
    2. 226917
    3. 126804
    4. 9794487
    5. 87805
    6. 5912
13. Round each number to the nearest hundred thousand.
    1. 687029
    2. 1326876
    3. 523715
    4. 4766883
    5. 8182390
    6. 792013
14. Round each number to the nearest million.
    1. 1009627
    2. 28101052
    3. 894063
    4. 9778656
    5. 80379591
    6. 3102975
15. Word Problems.
    1. The three heaviest sharks are the whale shark weighing 30500 kilograms. The basking shark weighing 9258 kilograms. The great white shark weighing 3507 kilograms. Round each number to the nearest thousand.
       

       Shark	Number	Rounded Number
       Whale shark
       Basking shark
       Great White Shark

    2. Three of the largest islands in the world are New Guinea covering 785753 square kilometers, Baffin Island covering 503944 square kilometers and Honshu Island covering 227413 square kilometers. Round each number to the nearest ten thousand.
       

       Island	Number	Rounded Number
       New Guinea
       Baffin Island
       Honshu Island

Answers to Unit 1 Review – Number Sense

1. 1.  tens
   2. ones
   3. thousands
   4. hundreds
   5. hundred thousands
   6. ten thousands
   7. millions
   8. thousands
2. 1. 9
   2. 6
   3. 8
   4. 5
   5. 1
   6. 2
   7. 0
3. 1. 5321
   2. 8703
   3. 34891
   4. 891402
   5. 72491
   6. 4201856
4. 1. eight hundred eighteen
   2. one thousand six hundred seventy-eight
   3. twenty-nine thousand seven hundred sixty-four
   4. one million nine hundred eighty-four thousand one hundred fifty-two
   5. forty-two thousand eight hundred three
   6. two hundred twenty-six thousand nine hundred seventeen
5. 1. 25132
   2. 1207
   3. 215024
   4. 1695420
   5. 726
   6. 9004
6. 1. 100 + 80 + 4
   2. 3000 + 900 + 8
   3. 60000 + 1000 + 200 + 80 + 1
   4. 1000000 + 500000 + 30000 +
      9000 + 500 + 80 + 7
   5. 300 000 + 60 000 + 6 000 + 500 + 20 + 4
7. 1. 56698
   2. 278261
   3. 3885
   4. 1476153
   5. 701
8. 1. 18,  727,  1487,  34937,  147832
   2. 697,  769,  6790,  76796,  76976
9. 1. >
   2. >
   3. <
   4. =
   5. <
   6. <
10. 1. 800
    2. 2600
    3. 21200
    4. 700
    5. 572100
    6. 7652900
11. 1. 1000
    2. 76000
    3. 289000
    4. 0
    5. 4000
    6. 5000
12. 1. 0
    2. 230000
    3. 130000
    4. 9790000
    5. 90000
    6. 10000
13. 1. 700000
    2. 1300000
    3. 500000
    4. 4800000
    5. 8200000
    6. 800000
14. 1. 1000000
    2. 28000000
    3. 1000000
    4. 10000000
    5. 80000000
    6. 3000000

15. 1. Shark	Number	Rounded Number
       Whale shark	30500	31000
       Basking shark	9258	9000
       Great White Shark	3507	4000

    2. Kilometers	Number	Rounded Number
       New Guinea	785753	790000
       Baffin Island	503944	500000
       Honshu Island	227413	230000

Addition puts amounts together. The answer of addition is called the sum or the total.

The plus sign + means to add.

3 + 2 = 5 says three plus two equals five or three and two is five.

The sum is 5.

Addition of Larger Numbers

Use these steps to complete each addition question.

• Step 1: Add the ones to the ones.
• Step 2: Add the tens to the tens.
• Step 3: Add the hundreds to the hundreds.
• Step 4: Add the thousands to the thousands.
• Step 5: Add the ten thousands to the ten thousands.

If an addition question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on.

Topic A: Self-Test

Mark /22 Aim 17/22

1. Find the sums. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
2. Find the sums. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
3. Find the sums. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
4. Add these numbers. (4 marks)
   1. 
   2. 
   3. 
   4. 

Answers to Topic A Self-Test

1. 1. 88
   2. 87
   3. 97
   4. 89
   5. 108
   6. 139
2. 1. 775
   2. 994
   3. 1686
   4. 1199
   5. 1077
   6. 1288
3. 1. 8965
   2. 10695
   3. 11897
   4. 87796
   5. 68649
   6. 112497
4. 1. 98
   2. 679
   3. 14689
   4. 47789

When the digits of one column add up to a two digit number (10 or more), you must carry the digit to the next column.

Use the same method for carrying when you add the columns of tens, hundreds, thousands, ten thousands, and so on. Look at these examples:

If you are having any problems with this work, ask your instructor to check your method of addition with carrying before you go any further.

If you feel that you need more practice, your instructor will give you more addition questions to do.

Adding Across

If an addition question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on.

Topic B: Self-Test

Mark   /15    Aim 12/15

1. Find the sums. Be sure to check your answers. (12 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
   10. 
   11. 
   12. 
2. Add these numbers. (3 marks)
   1. 74 + 32 + 67 + 85 =
   2. 721 + 8462 + 968 + 99 =
   3. 389 + 2517 + 2 =

Answers to Topic B Self-Test

1. 1. 142
   2. 142
   3. 1725
   4. 1132
   5. 10003
   6. 8057
   7. 133442
   8. 81000
   9. 15186
   10. 53223
   11. 1505236
   12. 82383
2. 1. 258
   2. 10250
   3. 2908

Sometimes, an exact answer is not needed — especially when you just want a quick idea of what something will cost or total. This is called estimating. When you estimate, you round numbers and then add them. It helps you check if your final answer makes sense.

Why Estimate?

Imagine you are going away for the weekend:

• Hotel: about $60
• Meals: about $80
• Gas: about $40
• Entertainment: about $100

Instead of calculating exactly, you might say:

60 + 80 + 40 + 100 = 280

You estimated the total weekend cost: $280.

Steps to Estimate a Sum

Step 1: Identify the Place to Round To

Round each number to the highest place value they share.

• If both numbers are two-digit numbers, round to the tens.
• Once again, always round to the highest place value that both numbers share. For example, if one number has thousands and the other has only hundreds, round both to the hundreds place. If one number has hundreds and the other has only tens, round both to the tens place.
• If both have thousands, round to the thousands.

This makes the numbers easier to add mentally.

Step 2: Round Each Number

Use the digit to the right of the one you are rounding to.

• If it is 5 or more, round up.
• If it is less than 5, round down.

Step 3: Add the Rounded Numbers

This gives your estimated sum.

In these examples, estimate the answer. Round each number BEFORE you add.

Tip: Round both numbers to the same place — the highest one they both have.

Estimating Answers in Addition Word Problems

When you are solving word problems, an estimate tells you if your answer is sensible. You can use your estimate to help you check your answers. If your answer and the estimate are not close, then you know that you should add your numbers again.

Key Ideas to Remember

• Round to the same place value in both numbers.
• Round up if the next digit is 5 or more.
• Round down (i.e., the digit stays the same) if it is less than 5.
• Add the rounded numbers for your estimate.
• Estimating is not exact — it gives you a ballpark answer.

Topic C: Self-Test

Mark     /15    Aim 11/15

1. Estimate the sums. Show your work. (9 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
2. Estimate each of the following word problems. (6 marks) Be sure to include the unit of measure in your answer. (2 marks each)
   Be sure to circle information and underline what is being asked.
   1. Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.
   2. A magazine has 34783 subscribers. Last year the magazine had 26876 subscribers. Estimate how many subscribers in total.
   3. The area of Canada is 9984670 square kilometres. The area of the United States is 9629091 square kilometres. The area of Mexico is 1964375 square kilometres. Estimate the total area of the three countries.

Answers to Topic C Self-Test

1. 1. 18000
   2. 28000
   3. 13000
   4. 956000
   5. 619000
   6. 453000
   7. 2300000
   8. 13000000
   9. 3800000
2. 1. 1400 books
   2. 60000 subscribers
   3. 22000000 square kilometres

You will now practice all the skills you learned in Unit 2. Check your work using the answer key at the end of the review

1. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
2. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
3. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
4. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
5. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
6. Find the sums.
   1. 45 + 104
   2. 523 + 364
   3. 5231 + 346
   4. 4661 + 2138
   5. 42  +  707  + 350
   6. 63613 + 45165
   7. 22514  +  43262  +  21102
   8. 72510 + 4127 + 13041
7. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
8. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
9. Find the sums.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
   10. 
   11. 
   12. 
10. Find the sums.
    1. 234 + 357 + 526 =
    2. 435 + 16 + 127 =
    3. 4118 + 2671 + 1590 =
    4. 67543 + 17069 =
    5. 4235 + 6815 + 42916 =
    6. 231262 + 64221 + 7143 =
11. Estimate the sums.
    1. 
    2. 
    3. 
    4. 
    5. 
    6. 
12. Estimate the following answers. Be sure to round to the largest place value possible before adding. Remember to circle the information and underline what is being asked.
    1. The Plumbers’ Union has 456 members. The Carpenters’ Union has 875 members. The Electricians’ Union has 1 394 members. Estimate how many members these three unions have.
    2. Last year Seung shipped 42169 orders from his warehouse. So far this year, Seung has shipped 5837 orders. Estimate the total number of orders sent.
    3. Avani has driven 42576 kilometres, 38342 kilometres and 14208 kilometres in the last three years. Estimate how many kilometres Avani has driven in the last three years.

Answers to Unit 2 Review

1. 1. 58
   2. 99
   3. 98
   4. 75
   5. 78
   6. 85
2. 1. 99
   2. 147
   3. 119
   4. 164
   5. 99
   6. 168
3. 1. 988
   2. 726
   3. 969
   4. 866
   5. 763
   6. 849
4. 1. 989
   2. 969
   3. 1388
   4. 1299
   5. 1498
   6. 1189
5. 1. 6388
   2. 7999
   3. 10688
   4. 124998
   5. 108998
   6. 96695
6. 1. 149
   2. 887
   3. 5577
   4. 6799
   5. 1099
   6. 108778
   7. 86878
   8. 89678
7. 1. 154
   2. 144
   3. 124
   4. 111
   5. 152
   6. 102
8. 1. 80
   2. 147
   3. 124
   4. 127
   5. 177
   6. 111
9. 1. 846
   2. 858
   3. 8343
   4. 11356
   5. 97121
   6. 81608
   7. 1153
   8. 1865
   9. 12521
   10. 100313
   11. 1056974
   12. 62152
10. 1. 1117
    2. 578
    3. 8379
    4. 84612
    5. 53966
    6. 302626
11. 1. 200 +  300 +  100 =  600
    2. 3000 + 2000 + 1000 = 6000
    3. 20000  +  10000  +  50000 =  80000
    4. 32000 + 12000 + 3000 = 47000
    5. 42000 + 2000 + 33000 + 15000 = 92000
    6. 2000000 + 4000000 + 1000000 = 7000000
12. 1. 500 + 900 + 1400 = 2800 members
    2. 42000 + 6000 = 48000 orders
    3. 40000 + 40000 + 10000 = 90000 kilometres

Subtraction takes an amount away from another amount. The result of subtraction is called the difference.

The minus sign − means to subtract.

This says nine minus three equals six or nine take away three is six. The difference between 9 and 3 is 6.

Subtraction is the opposite of addition. Look at the examples:

Addition	Subtraction
5 + 4 = 9	9 – 4 = 5
4 + 5 = 9	9 – 5 = 4

Subtraction facts are a tool that you use to do subtraction questions.

Note: There is no self-test for this topic.

You can find the difference between two large numbers using the subtraction facts you have been practicing. Always take away or subtract the number after the minus sign.

Use these steps to complete each subtraction question.

• Step 1: Subtract the ones from the ones.
• Step 2: Subtract the tens from the tens.
• Step 3: Subtract the hundreds from the hundreds.
• Step 4: Subtract the thousands from the thousands.
• Step 5: Subtract the ten thousands from the ten thousands and so on.

Checking Subtraction

You can check your subtraction. Add the answer (the difference) to the number you took away (the second number). If your subtracting was correct, the result of the adding will be the number you started with (the top number) in the subtraction question.

Use these steps to complete each subtraction question:

If a subtraction question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on. The first number is always the top number and the second number is always written below the first number.

Topic B: Self-Test

Mark      /24    Aim 19/24

1. Find the differences.  Be sure to check your answers. (6 marks.)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
2. Find the differences. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
3. Find the differences. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
4. Subtract these numbers. (6 marks)
   1. 85 − 61 =
   2. 724 − 13 =
   3. 879  − 152 =
   4. 4957 − 821 =
   5. 94658 − 12307 =
   6. 89653 − 27450 =

Answers to Topic B Self-Test

1. 1. 24
   2. 34
   3. 12
   4. 26
   5. 54
   6. 14
2. 1. 511
   2. 237
   3. 197
   4. 343
   5. 521
   6. 156
3. 1. 8304
   2. 624
   3. 2411
   4. 33523
   5. 25158
   6. 45320
4. 1. 24
   2. 711
   3. 727
   4. 4136
   5. 82351
   6. 62203

When you subtract, you may need to rename. Renaming means changing from one place value to another.

For example:

• 1 ten can be renamed as 10 ones
• 1 hundred can be renamed as 10 tens
• 1 thousand can be renamed as 10 hundreds.

Renaming is an important part of subtracting. Sometimes the digit on top is smaller than the digit you are subtracting. This means that you will have to rename before you can subtract. This is also called borrowing.