62
33. Which of the following is the largest number?
0.034, 0.403, 0.043, 0.304
34. Which of the following is the smallest number?
1.014, 1.011, 1.104, 1.041
For Problems 35 to 42, round the numbers to one decimal place (nearest tenth).
35. 415.1654
36. 7.8725
37. 264.1545
38. 25.5742
39. 24.1575
40. 112.1255
41. 10.3756
42. 0.9753
Fo Problems 43 to 50, round the numbers to two decimal places (nearest hundredth, or nearest cent).
43. 14.3585
44. 0.0645
45. 181.1267
46. 19.6916
47. $16.775
48. $10.954
49. $9.987
50. $24.995
2.4 Arithmetic Operations with Decimal Numbers
Addition of Decimal Numbers
Addition of decimal numbers (finding the total or sum) refers to combining numbers. It is similar
to adding whole numbers.
Follow these steps to add one decimal number to another decimal number:
Step 1:
Write the numbers one under the other by aligning the decimal points of these numbers.
Step 2:
Add zeros to the right to have the same number of decimal places, if necessary, and draw
a horizontal line.
Step 3:
Starting from the right, add all the numbers in that column and continue towards the left.
■■ If the total is less than 10, write the total under the horizontal line.
■■ If the total is 10 or more, write the ‘ones’ digit of the total under the horizontal line and
write the tens digit above the tens column.
Step 4:
Example 2.4-a
Follow this procedure for each column going from right to left. Write the decimal point
in the answer.
Adding Decimal Numbers
Perform the following additions:
Solution
(i)
25.125 + 7.14
(ii)
741.87 + 135.456
(iii)
127 + 68.8 + 669.95
(i)
25.125 + 7.14
1
25.125
7.140
32.265
Add a zero to match the number of decimal places.
Therefore, adding 25.125 and 7.14 results in 32.265.
(ii)
hapter 2 | FractionsChapter
and Decimals
2 | Fractions and Decimals
741.87 + 135.456
1
1
741.870
135.456
877.326
Add a zero to match the number of decimal places.
Therefore, adding 741.87 and 135.456 results in 877.326.
63
(iii) 127 + 68.8 + 669.95
1 2 1
127.00
68.80
669.95
865.75
Add two zeros to match the number of decimal places.
Add a zero to match the number of decimal places.
Therefore, adding 127, 68.8 and 669.95 results in 865.75.
Subtraction of Decimal Numbers
Subtraction of decimal numbers refers to finding the difference between decimal numbers. It is
similar to subtracting whole numbers.
Follow these steps to subtract one decimal number from another decimal number:
Step 1:
Write the numbers one under the other by aligning the decimal points of these numbers.
Step 2:
Add zeros to the right to have the same number of decimal places, if necessary, and draw
a horizontal line.
Step 3:
Ensure that the number from which subtraction is indicated is written above the number
that is being subtracted.
Step 4:
Starting from the right, subtract the bottom number from the top number.
■■ If the top digit is greater than the bottom digit, subtract and write the difference under
the line.
■■ If the top digit is smaller than the bottom digit, borrow from the digit to the left of
this top digit, and add one to the digit on the top, then find the difference and write it
under the horizontal line.
Step 5:
Example 2.4-b
Follow this procedure for each column going from right to left. Write the decimal point
in the answer.
Subtracting Decimal Numbers
Perform the following subtractions:
Solution
(i)
Subtract 29.02 from 135.145
(ii)
Subtract 38.7 from 457
(i)
Subtract 29.02 from 135.145
(ii)
Subtract 38.7 from 457
2 15
135.145
– 29.020
106.125
Therefore, subtracting 29.02 from
135.145 results in 106.125.
16
4 6 10
457.0
– 38.7
418.3
Therefore, subtracting 38.7 from 457 results
in 418.3
Multiplication of Decimal Numbers
Multiplication of decimal numbers refers to finding the product of two decimal numbers.
Follow these steps to multiply one decimal number with another decimal number:
Step 1:
Line up the numbers on the right without aligning the decimal points.
Step 2:
Multiply the number assuming that there are no decimal points; i.e., multiply each digit on
the top number by each digit in the bottom number and add the products, similar to the
process of multiplying whole numbers.
Step 3:
Count the total number of decimal places in the numbers that are being multiplied.
Step 4:
Place the decimal point in the answer starting at the right and moving towards the left by
the total number of decimal places counted.
2.4 Arithmetic Operations with Decimal Numbers
64
Example 2.4-c
Multiplying Decimal Numbers
Multiply 12.56 and 1.8.
Solution
{
12.56 (2 Decimal places) Total of 3 Decimals places
1.8 (1 Decimal places)
10048
12560
22.608 (3 Decimal places)
Therefore, multiplying 12.56 and 1.8 results in 22.608.
Division of Decimal Numbers
Division of decimal numbers is the process of determining how many times one decimal number is
contained in another decimal number.
Follow these steps to divide a decimal number:
Step 1:
If the divisor is not a whole number, convert it to a whole number by moving the decimal
point to the right. Move the decimal point in the dividend by the same number of places.
Step 2:
Divide by following a similar process to the process of dividing whole numbers.
■■ Add zeros to the right of the last digit of the dividend and keep dividing until no
remainder or a repeating pattern shows up in the quotient.
Example 2.4-d
Dividing Decimal Numbers
Perform the following divisions:
(i) Divide 8.25 by 0.6
Solution
(i)
Step 1:
8.25÷
0.6
8.25
8.25
÷÷0.6
0.6
8.25
8.25
8.25
== 0.6
=
0.6
0.6
8 2 .5
== 88 22 .55
=
666
Step 2:
13.75
6 82.50
–6
22
–18
45
–42
30
–30
0
(ii) Divide: 0.166 by 0.03
Since the denominator contains one decimal place, move the
decimal point by one decimal place to the right for both the
numerator and the denominator,
This is the same as multiplying both the numerator and
denominator by 10.
= 8. 2 5 × 10 = 82.5
0.6 × 10
6
Position the decimal point within the quotient directly above
the decimal point within the dividend.
Add a Zero
Therefore, when 8.25 is divided by 0.6, the quotient is 13.75 and the remainder is 0.
Chapter 2 | Fractions and Decimals
65
Solution
continued
(ii)
Step 1:
0.166 ÷ 0.03 =
0.166
0.03
= 16.6
3
Since the denominator contains two decimal places,
move the decimal point by two decimal places to the
right for both the numerator and the denominator.
This is the same as multiplying both the numerator and
denominator by 100.
= 0.166 × 100 = 16.6
0.03 × 100
3
Step 2:
Repeating decimals are usually
represented by a horizontal bar on
top of the repeating decimal; i.e.,
5.533333... is written as 5.53.
5.533
3 16.600
–15
16
–15
10
–9
10
–9
1
Position the decimal point within the quotient directly
above the decimal point within the dividend.
Add a Zero
Add a Zero
Therefore, when 0.166 is divided by 0.03, the quoitent is 5.53 and the remainder is 1.
2.4 Exercises
Answers to odd-numbered problems are available at the end of the textbook.
For Problems 1 to 8, perform the additions.
1. 927.896 + 659.50 + 128.649
2. 619.985 + 52.82 + 3.187
3. 74 + 129.258 + 0.32 + 666.015
4. 17 + 3.48 + 0.278 + 78.24
5. 292.454 + 121.69 + 65.3
6. 396.716 + 191.68 + 90.6
7. 948.684 + 15.17 + 0.717
8. 625.365 + 27.97 + 0.613
9. Find the sum of the following numbers:
Twenty and ninety-five hundredths, Two hundred and seventy-two thousandths , and Nineteen and nine tenths.
10. Find the sum of the following numbers:
Six and thirty-nine thousandths, Eighty and fourteen hundredths , and Sixteen and eight tenths.
For Problems 11 to 18, perform the subtractions.
11. 423.92 − 185.728
12. 9.555 – 7.18
13. 29.28 – 13.4
14. 15.7 − 7.92
15. 539.64 – 258.357
16. 848.62 – 495.476
17. 409.5 – 179.832
18. 475.3 – 281.375
19. Subtract three hundred five and thirty-nine hundredths from seven hundred twenty and four tenths.
20. Subtract eight hundred twenty and four hundredths from one thousand, one hundred one and six tenths.
For Problems 21 to 28, perform the multiplications.
21. 137.89 and 5.4
22. 189.945 and 6.3
23. 62.095 and 4.18
24. 92.74 and 3.25
25. 0.43 and 0.8
26. 0.59 and 0.9
27. 109.78 and 2.91
28. 145.75 and 3.74
For Problems 29 to 36, perform the divisions.
29. 67.78 by 9
30. 261.31 by 7
31. 732.6 by 8
32. 413.9 by 6
33. 14.6 by 0.6
34. 9.155 by 0.7
35. 3.1 by 0.25
36. 2.7 by 0.15
2.4 Arithmetic Operations with Decimal Numbers
66
For Problems 37 to 44, formulate arithmetic expressions and evaluate.
37. Find the amount that is $248.76 less than $627.40.
38. Find the amount that is $45.27 less than $90.75.
39. Find the difference in the amounts $30.75 and $15.89.
40. Find the difference in the amounts $235.62 and $115.75.
41. Find the sum of $52.43 and $23.95.
42. Find the sum of $252.34 and $297.90.
43. Find the amount that is $38.89 more than $25.67.
44. Find the amount that is $412.78 more than $634.25.
45. The cost of an item is $88.46. If you gave $90.00 to the cashier, how much change would you receive?
46. The cost of an item is $125.69. If Arun gave $150.00 to the cashier, how much change would Arun receive?
47. Bill saved $578.50 this week. He saved $124.85 more last week than this week. How much did Bill save during the 2-week period?
48. Last week Carol spent $96.75 more on food than on transportation. She spent $223.15 on transport. How much did
Carol spend on both food and transportation last week?
49. The normal selling price of an item is $237.75. When this item was on sale Dave paid $49.89 less for it. How much
did Dave pay for that item?
50. A car driver filled gas when the odometer reading was 35,894.9 km. The odometer reading now is 39,894.4 km. How
many kilometres did the driver travel, rounded to the nearest kilometre?
51. After spending $38.96 on toys and $1.75 on wrapping paper, Ann still had $45.75. How much money did Ann have initially?
52. After paying $515.09 for a car lease and $379.92 for property tax, my bank balance was $675.45. How much money
did I have initially?
53. Simon bought a camera that was on sale for $799.99. He agreed to pay $70.35 every month for 12 months. How much
more money than the sale price did Simon pay for the camera?
54. Andy bought a TV that was on sale for $2,249.95. He agreed to pay $130.45 every month for 18 months. How much
more money than the sale price did Andy pay for the TV?
55. A salesperson earns a salary of $725.35 every week. During the past 3 weeks, he also received commissions of $375.68,
$578.79, and $338.57. Calculate his total income for the past 3 weeks.
56. I leased a car on a 4-year term at $694.38 per month. At the end of the lease period, I paid an additional $18,458.74
to purchase the car. Find the total amount I paid for the car.
57. John bought 2 shirts at $20.95 each and 3 pairs of pants at $34.55 each. He gave $200 to the cashier. Calculate the
balance he should receive from the cashier.
58. I bought 3 kg of walnuts at $8.69 per kg and 4 kg of almonds at $7.72 per kg. I gave the cashier a $100 bill. How much
change should I receive from the cashier?
59. A string that measured 0.875 m was cut into pieces of 0.0625 m each. How many pieces did this result in?
60. A cake that weighed 0.82 kg was cut into slices that weighed 0.1025 kg each. How many slices did this result in?
61. Marion bought 3 dresses at $22.49 per dress and 2 pairs of shoes at $14.99 per pair. She gave a $100 bill to the cashier.
What change should she expect to receive from the cashier?
62. Gilbert bought 2 kg of grapes at $3.29 per kg and 1.5 kg of strawberries at $5.99 per kg. He gave a $20 bill to the
cashier. How much should he expect to receive in change from the cashier?
Chapter 2 | Fractions and Decimals