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Practice adding and subtracting whole numbers.
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CHAPTER 4
1 Adding and Subtracting Whole Numbers
Goal Use mental math strategies to calculate sums and differences.
1. Use mental math to calculate each sum. At-Home Help
Describe your strategy. Rounding is a mental math
a) 680  210  890
numbers. When you round, you will
Regroup 600 + 200 + (80 + 10) = 600 + 200 + 90, or 890. need to adjust your answer to get
For example:
23  58 can be rounded to
b) 763  847  289  1899 20  60  80. 23 is 3 more than 20
Round 289 to nearest hundred, then regroup to get and 58 is 2 less than 60. So adjust
750 + (847 + 3) + (300 + 10) = 750 + 850 + 310, or 1910. your answer by adding 1.
289 is 11 less than 300. So subtract 11 from 1910.
76  40 can be rounded to
80  40  40. 76 is 4 less than 80.
2. Use mental math to calculate each sum. subtracting 4. The answer is 36.
a) 545  655  1200 d) 715  903  422  2040 Regrouping is another mental math
b) 874  926  1800 e) 1822  428  650  2900 numbers. Regroup numbers into 5s
or 10s to make calculations easier.
c) 766  704  1470 f ) 2016  624  910  3550
For example:
3. Use mental math to calculate each difference. 43  92 can be regrouped as
(43  2)  90.
80  19 can be regrouped as
a) 680  490  190
(80  10)  9.
If the question was 690 – 490, the answer would be The answer is 70  9  61.
200. 680 is 10 less than 690. So subtract 10 from 200.
b) 1650  95  1555
Round 95 to nearest hundred to get 1650 – 100 = 1550. 95 is 5 less than 100.
4. Use mental math to calculate each difference.
a) 820  450  370 c) 903  237  520 e) 3005  755  2250
b) 625  175  450 d) 1020  500  666 f ) 2103  487  1616
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CHAPTER 4
2 Estimating Sums and Differences
Goal Estimate sums and differences to solve problems.
1. Which sums are greater than 2200? At-Home Help
a) 840  622  713 less than 2200 To solve problems, use estimation
if the problem does not ask for an
b) 372  923  987 greater than 2200 exact answer.
Round to the place value that gives
c) 565  834  879 greater than 2200
you numbers that are easy to add
d) 703  543  824 less than 2200 or subtract. You might adjust your
rounding up or down, depending
2. Which differences are less than 540? on the numbers.
Sometimes you may want to use
a) 1280  640 greater than 540
more than one strategy to solve
b) 6080  5590 less than 540 the problem.
c) 4608  3024 greater than 540
is reasonable.
d) 8146  7870 less than 540 Remember to show all your work.
3. A mountain-climbing contest had teams climb two different mountains. One team
climbed Mount Everest. It has a height of 8848 m. Another team climbed Mount Logan
in the Yukon Territory. It has a height of 5959 m. About how much higher did the
Mount Everest team climb? Describe your strategy.
About 2800 m. Round 8848 and 5959 to nearest hundred to get 8800 – 6000 = 2800.
4. Sam recorded the forms of transportation used by neighbourhood students to get
to school. The neighbourhood will win an award if more than 5000 students use a
physically active form of transportation to get to school.
Form of transportation Number of students
walk 3162
bicycle 1072
bus 2154
car 936
other (skateboard, inline skates, etc.) 636
Will Sam’s neighbourhood win the award? Describe your strategy.
No. Round numbers to nearest thousand or hundred to get 3000 + 1000 + 600 = 4600.
About 4600 students use a physically active form of transportation.
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CHAPTER 4
Goal Solve problems by adding four 3-digit whole numbers.
1. Calculate. At-Home Help
1 2 1 1
a) 2 0 6 b) 3 2 9 c) 4 2 1 To add numbers, add digits with the
same place value.
3 4 9 4 6 2 2 3 0
1 2 7 5 0 3 3 2 9 Check your answer using estimation.
 4 6 7 3 6 8 5 4 7 For example:
1 1
1 1 4 9 1 5 0 0 1 5 2 7 2 1 3 or 2 1 3
1 4 0 3 2 7 3 2 7
2 2 1 6 3 1 6 3
1 6 6 2  2 0 4 2 0 4
9 0 7 8 0 0
9 0
2. During summer camp, Cecilia’s group planted 1 7
trees on five days. The group planted 154 trees on 9 0 7
the first day, 183 trees on the second day, 189 trees Estimate:
200  300  200  200  900
on the third day, and 196 trees on the fifth day.
The group planted a total of 934 trees.
a) How many trees were planted on the fourth day? Show your work.
212 trees 3 2
154 934
183 –722
189 212
+196
722
Round 154 down and the other numbers up.
100 + 200 + 200 + 200 = 700 900 – 700 = 200
My estimate of 200 is close to 212. So my answer is reasonable.
3. Balvinder sells chocolate bars to raise money \$130 \$117 \$676
for his school. From Monday to Friday, \$130 –\$546
Balvinder sold \$676 worth of chocolate bars. \$143 \$130
On Monday he sold \$117, on Tuesday he sold +\$156
\$130, on Wednesday he sold \$143, and on 400
Friday he sold \$156. Calculate how much 130
he sold on Thursday. Show your work. 16
\$546
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CHAPTER 4
4 Subtracting Whole Numbers
Goal Subtract whole numbers to solve problems.
1. Estimate and then subtract. Show your work. At-Home Help
a) 8702  6914 c) 64 902  5964 To subtract numbers, start subtracting
from the smallest place value.
Estimate: more or Estimate: more or
Regroup if you need to.
less than 2000? less than 60 000?
For example:
less less
10
7 0 12
5 8 1 2
16 9 13 18 9
7 6 10 12 5 3 8 10 12 2 6 4 9
8 7 0 2 6 4 9 0 2 3 1 6 3
–6 9 1 4 –5 9 6 4 You can also add a number to both
1 7 8 8 5 8 9 3 8 numbers to get numbers that are
easier to subtract.
For example, add 51 to both
b) 10 550  9845 d) 56 003  7894 numbers. 5812  51  5863
Estimate: more or Estimate: more or 2649  51  2700
less than 1000? less than 46 000? 5 8 6 3
less more 2 7 0 0
3 1 6 3
10 550 + 155 = 10 705 4 5 10 10 13 or addition.
9845 + 155 = 10 000 5 6 0 0 3
Estimate: 5800  2600  3200
– 7 8 9 4
1 0 7 0 5 4 8 1 0 9
–1 0 0 0 0
7 0 5
2. Rico’s home town had a population of 75 692 people in 1990. In 2000,
the population was 83 020 people. By how much did the population increase?
7328 people
Add 8 to both numbers. 83 020 + 8 = 83 028
75 692 + 8 = 75 700
8 3 0 2 8
–7 5 7 0 0
7 3 2 8
Estimate: 85 000 – 75 000 = 10 000
My estimate of 10 000 is close to 7328. So my answer is reasonable.
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CHAPTER 4
Decimal Numbers
Goal Use mental math strategies to calculate sums and differences.
Samantha, Matthew, and Akira went to buy some At-Home Help
clothes from a charity fundraiser. To add or subtract money amounts
mentally, regroup the numbers to
\$9.95
\$8.75 make the calculations easier.
Remember to check if your
\$7.90
\$0.80 \$6.95  \$3.25  \$7.75, regroup.
\$8.75
\$2.80 7.00  0.05  3.00  0.25  7.00
 0.75  7.00  3.00  7.00  0.05
\$7.90  0.25  0.75
 17.00  0.05  1.00
1. a) Samantha has \$22.00. Choose three items she  18.00  0.05
Suggested answer: 1 jacket, 1 hat, and 1 sweater
b) Use mental math to calculate the total cost. What bills and coins can she use to
pay for the items?
(using answer above) \$21.50 one \$20 bill, one loonie, and two quarters
c) Use mental math to calculate Samantha’s change.
\$0.50
2. Akira has \$18.75 and Matthew has \$24.50. How much more money does Matthew
\$5.75
3. a) Choose three items that Akira can buy. Use mental math to calculate the
total cost.
Suggested answer: 1 pair of gloves, 1 sweater, and 1 shirt (total cost) \$17.45
b) Use mental math to calculate Akira’s change.
\$1.30
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CHAPTER 4
Goal Add decimals using base ten blocks and pencil and paper.
a) 0.56  0.98 d) 3.498  2.635  0.384 Decimal tenths, hundredths, and
Estimate: 0.5 + 1 = 1.5 Estimate: 3 + 3 + 0.3 = 6.3 same rules as whole numbers.
1 1 2 1 • It is easier to add vertically if
0 .5 6 3 .4 9 8 the decimal points are aligned.
+0 .9 8 2 .6 3 5 • Add place values that are
1 .4 0 +0 .3 8 4 the same.
0 .1 4 6 .5 1 7 • If the sum of a place value is
1 .5 4 10 or more, regroup using
the next greater place value.
estimation.
b) 2.804  0.426 e) 4.675  3.899  0.269 For example:
Estimate: 3 + 0.5 = 3.5 Estimate: 5 + 4 = 9 2 1 1
0 . 7 6 2 0 . 7 6 2
1 1 4 .6 7 5 0 . 4 5 0 . 4 5
2.8 0 4 3 .8 9 9 0 . 8 0 3 0 . 8 0 3
+0 .4 2 6 +0 .2 6 9 0 . 1 0 7 0 . 1 0 7
3.2 3 0 7 .0 0 0 2 . 1 2 2 2 . 0 0 0
1 .6 0 0 0 . 1 1 0
0 .2 2 0 0 . 0 1 2
0 .0 2 3 2 . 1 2 2
8 .8 4 3 Estimate:
0.8  0.4  0.8  0.1  2.1
To add a decimal number that has
only tenth and hundredth place
c) 0.897  5.824 f ) 4.8  3.152  0.59 values and a decimal number that
has a thousandth place value, add
Estimate: 1 + 6 = 7 Estimate: 5 + 3 + 1 = 9 a zero for the thousandth place value.
0 .8 9 7 1 1
For example, calculating
+5 .8 2 4 4 .8 0 0
1.34  0.379 is the same as
5 .0 0 0 3 .1 5 2
1.340  0.379. Answer is 1.719.
1 .6 0 0 +0 .5 9 0
0 .1 1 0 8 .5 4 2
0 .0 1 1
6 .7 2 1
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CHAPTER 4
7 Subtracting Decimals
Goal Subtract decimals using base ten blocks and pencil and paper.
1. Estimate and then subtract. Show your work. At-Home Help
a) 5.0  2.3 d) 6.411  2.58 Decimal tenths, hundredths, and
thousandths are subtracted using
Estimate: 5 – 2 = 3 Estimate: 6.5 – 2.5 = 4 the same rules as whole numbers.
4 10 Add 0.42 to both numbers. • It is easier to subtract vertically if
5.0 6.411 + 0.42 = 6.831 the decimal points are aligned.
–2 .3 2.58 + 0.42 = 3.00 • Subtract place values that are the
2.7 same, starting from the smallest
6.8 3 1 place value.
–3 .0 0 0 • If you can’t find the difference for
3.8 3 1 a particular place value, regroup
using the next greater place value.
b) 8.21  3.63 e) 9.05  6.208 For example:
Estimate: 8 – 3 = 5 Estimate: 9 – 6 = 3
9 9
Add 0.37 to both numbers. 8 10 4 10 2 10 10 10
8.21 + 0.37 = 8.58 9.0 5 0 3.0 0 0
3.63 + 0.37 = 4.00 –6 .2 0 8 –0.7 5 7
2.8 4 2 2.2 4 3
8.5 8
–4 .0 0 You can also add a number to both
4.5 8 numbers to get numbers that are
easier to subtract.
both numbers.
3.000  0.243  3.243
c) 4.020  1.989 f ) 3.8  0.058 0.757  0.243  1.000
Estimate: 4 – 2 = 2 Estimate: 4 – 0 = 4
3.2 4 3
9 11 Add 0.942 to both numbers.  1 . 0 0 0
3 10 1 10 3.8 + 0.942 = 4.742 2.2 4 3
4.0 2 0 0.058 + 0.942 = 1.000
To subtract a decimal number that
–1 .9 8 9 4.7 4 2 has only tenth and hundredth place
2.0 3 1 –1 .0 0 0 values from a decimal number that
3.7 4 2 has a thousandth place value, add
a zero for the thousandth place value.
For example, calculating 3.25  1.722
is the same as 3.250  1.722.
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CHAPTER 4
a Multi-Step Problem
Goal Explain a solution to a problem.
Twyla wants to add 1 kg of compost to two vegetable At-Home Help
gardens. One garden measures 6.00 m by 3.60 m. To solve problems, follow these steps.
The other garden measures 7.60 m by 5.30 m.
Understand the Problem
One kilogram of compost is needed for 43 m2. • What are you asked to find out?
Does Twyla have enough compost for both gardens? • What information is given?
Write a solution. Determine if your answer is • What information is necessary
reasonable. Use the Communication Checklist. to solve the problem?
• Is there more than one step
Understand the Problem needed to solve the problem?
I need to determine if Twyla has enough compost for • What calculations can be used?
both gardens. Make a Plan: This problem will take more than Carry Out the Plan
one step andmore than one operation to solve. First I need to • Show all your work.
multiply to find the area of each garden. Then I need to add Look Back
to find the total area. I can compare the total area with the • Check whether your answer
area that 1 kg will cover, or 43 m2. is reasonable.
Use the Communication Checklist.
Carry Out the Plan:
Area of one garden: 6.00 m x 3.60 m = 21.60 m2 2 1 . 6 0 m2
2 Communication Checklist
Area of other garden: 7.60 m x 5.30 m = 40.28 m2 + 4 0 . 2 8 m ✓ Did you explain your thinking?
Total area: 61.88 m2 > 43 m2 6 1 . 8 8 m2 ✓ Did you show how you
So Twyla does not have enough compost for both gardens. calculated each step?
✓ Did you explain how you
Look Back: Check whether calculations are reasonable. checked each answer?
Round all numbers in the problem to the nearest whole number. ✓ Did you show the right amount
Area of one garden: 6 m x 4 m = 24 m2 of detail?
Area of other garden: 8 m x 5 m = 40 m2
Total estimated area: 64 m2 > 43 m2
My estimated answer for the problem shows that Twyla does not have enough compost
for both gardens. So my calculated answer is reasonable.
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CHAPTER 4
Test Yourself Page 1
1. Using estimation, which question has an answer greater than 1600?
A. 569  872  236 C. 379  406  765
B. 264  504  429 D. 596  604  366
Use the survey results to answer Questions 2 and 3.
Favourite food Number of students
chili 214
pizza 307
curried chicken 234
sushi 209
2. About how many students were surveyed?
3. How many more students chose pizza than sushi?
A. 86 students B. 89 students C. 98 students D. 96 students
4. Which calculation is not reasonable?
A. 604  392  850  723  2569 C. 356  147  520  801  1824
B. 824  368  456 D. 18 011  9234  7777
5. What are the missing numbers from top to bottom?
6 2 5 2
 7 3
3 2 8
A. 1, 8, 9, 5, 6 B. 1, 8, 9, 5, 7 C. 1, 8, 0, 5, 8 D. 1, 9, 9, 5, 7
Use the chart to answer Questions 6 and 7. Juice Volume (L)
orange 2.615
6. What is the total volume of juice?
apple 2.365
A. 10.300 L C. 10.090 L cranberry 2.130
mango 3.090
B. 10.200 L D. 9.090 L
7. How much more mango juice is there than orange juice?
A. 1.475 L C. 0.685 L
B. 1.685 L D. 0.475 L
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CHAPTER 4
Test Yourself Page 2
Use the picture below to answer Questions 8 and 9.
\$3.35
\$1.75 5
\$0.7
.85
\$2
\$1.
95
8. What is the total cost of the items shown?
A. \$10.65 B. \$7.45 C. \$10.50 D. \$11.05
9. Kittie bought a can of nuts, a package of dried fruit, and a muffin with a \$10 bill.
How much change should she receive?
A. \$1.75 B. \$0.85 C. \$1.85 D. \$0.75
10. Jasmine is making a fruit cake. The recipe has a combination of fruits and nuts.
What is the total mass of fruit and nuts in the fruit cake?
Ingredient Mass (kg)
currants 0.450
raisins 0.525
almonds 0.175
candied peel 0.175
A. 1.200 kg B. 1.325 kg C. 1.550 kg D. 1.860 kg
11. Asgar hiked on two different trails during summer camp. One trail measures 2.863 km.
Asgar hiked a total of 5.501 km. How long is the other trail?
A. 3.738 km B. 3.648 km C. 2.748 km D. 2.638 km