All the multiplying has been done already. Your task is to put the decimal point in the product by doing a whole number estimate of the question.

[latex]\begin{array}{rr}&2.8\\ \times &4.3\\ \hline &84\\+&1120\\\hline&12.04\end{array}[/latex]     Estimate: [latex]\begin{array}{rr}&3\\ \times &4\\ \hline &12\end{array}[/latex]

1. [latex]\begin{array}[t]{rr}&56.9\\ \times&12.3\\ \hline &1707\\ &11380\\&56900\\ \hline &69987 \\ \end{array}[/latex]
2. [latex]\begin{array}[t]{rr}&7.3\\ \times&19.6\\ \hline &14308 \\ \end{array}[/latex]
3. [latex]\begin{array}[t]{rrrr}&28.7\\ \times&64.97\\ \hline &1864639 \\ \end{array}[/latex]
4. [latex]\begin{array}[t]{rrrr}&73.2\\ \times&1.6\\ \hline &11712 \\ \end{array}[/latex]
5. [latex]\begin{array}[t]{rrrr}&1.8\\ \times&1.3\\ \hline &234 \\ \end{array}[/latex]
6. [latex]\begin{array}[t]{rrrr}&48.29\\ \times&55.6\\ \hline&2684924 \\ \end{array}[/latex]
7. [latex]\begin{array}[t]{rrrr}&91.2\\ \times&1.5\\ \hline&13680 \\ \end{array}[/latex]

Exercise 1 Answers

1. 699.87
2. 143.08
3. 1864.639
4. 117.12
5. 2.34
6. 2684.924
7. 136.80

Again, the multiplying has been done. Use the method of multiplying the understood denominators to put the decimal point in the product.

Examples:

• [latex]\begin{array}{lrl}&9.2&\text{1 decimal place}\\ \times&0.3&\text{1 decimal place}\\ \hline &2.76&\text{2 decimal places}\end{array}[/latex]
• [latex]\begin{array}{lrl}&0.27&\text{2 decimal places}\\ \times&1.8&\text{1 decimal place}\\ \hline &0.486&\text{3 decimal places}\end{array}[/latex]

1. [latex]\begin{array}{rr}&6.8\\ \times&0.4\\ \hline &272 \\ \end{array}[/latex]
2. [latex]\begin{array}{rr}&2.4\\ \times &0.13\\ \hline &0312 \\ \end{array}[/latex]
3. [latex]\begin{array}{rr}&240\\ \times &0.05\\ \hline &1200 \\ \end{array}[/latex]
4. [latex]\begin{array}{rr}&0.91\\ \times&6.2\\ \hline &5642 \\ \end{array}[/latex]
5. [latex]\begin{array}{rr}&0.29\\ \times&1.2\\ \hline &0348 \\ \end{array}[/latex]
6. [latex]\begin{array}{rr}&0.87\\ \times&0.19\\ \hline &01653 \\ \end{array}[/latex]
7. [latex]\begin{array}{rr}&7.3\\ \times &3.8\\ \hline & 2744 \\ \end{array}[/latex]
8. [latex]\begin{array}{rr}&4.24\\ \times &0.07\\ \hline &02968 \\ \end{array}[/latex]
9. [latex]\begin{array}{rr}&0.042\\ \times &60\\ \hline &2520 \\ \end{array}[/latex]

Exercise 2 Answers

1. 2.72
2. 0.312
3. 12.00
4. 5.642
5. 0.348
6. 0.1653
7. 27.74
8. 0.2968
9. 2.52

If you had trouble with the first two exercises, then get help from your instructor. Here is extra practice if you want or need it.

Examples:

• [latex]\begin{array}{lrl}&41&\text{0 decimal places}\\ \times&0.061&\text{3 decimal places}\\ \hline &2.501&\text{3 decimal places}\end{array}[/latex]
• [latex]\begin{array}{lrl}&7.8&\text{1 decimal place}\\ \times&0.5&\text{1 decimal place}\\ \hline &3.90&\text{2 decimal places total}\end{array}[/latex]

1. [latex]\begin{array}{rr}&59.275\\ \times&0.08\\ \hline &474200 \\ \end{array}[/latex]
2. [latex]\begin{array}{rr}&7.18\\ \times &23.46\\ \hline &1684428 \\ \end{array}[/latex]
3. [latex]\begin{array}{rr}&0.84\\ \times &2.1\\ \hline &1764 \\ \end{array}[/latex]
4. [latex]\begin{array}{rr}&18.6\\ \times&0.3\\ \hline &558 \\ \end{array}[/latex]
5. [latex]\begin{array}{rr}&100\\ \times&0.35\\ \hline &3500 \\ \end{array}[/latex]
6. [latex]\begin{array}{rr}&0.72\\ \times&3.4\\ \hline &2448 \\ \end{array}[/latex]

Exercise 3 Answers

1. 4.74200
2. 168.4428
3. 1.764
4. 5.58
5. 35.00
6. 2.448

Multiply to find the product. Remember to put the decimal point in the correct place; you know two methods!

Example:     [latex]\begin{array}{lr}&13.8\\ \times&3.9\\ \hline &1242\\&4140\\ \hline &53.82\end{array}[/latex]

1. [latex]\begin{array}{rrr}&0.076\\ \times&24\\ \hline \\ \end{array}[/latex]
2. [latex]\begin{array}{rrr}&2.05\\ \times &1.7\\ \hline \\ \end{array}[/latex]
3. [latex]\begin{array}{rrr}&0.429\\ \times &7.5\\ \hline \\ \end{array}[/latex]
4. [latex]\begin{array}{rrr}&96\\ \times&0.2\\ \hline \\ \end{array}[/latex]
5. [latex]\begin{array}{rrr}&1.79\\ \times&0.33\\ \hline \\ \end{array}[/latex]
6. [latex]\begin{array}{rrr}&40.1\\ \times&0.9\\ \hline \\ \end{array}[/latex]

Exercise 4 Answers

1. 1.824
2. 3.485
3. 3.2175
4. 19.2
5. 0.5907
6. 36.09

Find the products. Be certain to place all decimal points correctly.

Example:     [latex]\begin{array}{rr}&0.35\\ \times&0.13\\ \hline&105\\&350\\ \hline & 0.0455\end{array}[/latex]

1. [latex]\begin{array}{rr}&1.8\\ \times&0.05\\ \hline \\ \end{array}[/latex]
2. [latex]\begin{array}{rr}&300\\ \times&0.04\\ \hline \\ \end{array}[/latex]
3. [latex]\begin{array}{rr}&1.3\\ \times&0.027\\ \hline \\ \end{array}[/latex]
4. [latex]\begin{array}{rr}&500\\ \times&0.073\\ \hline \\ \end{array}[/latex]
5. [latex]\begin{array}{rr}&0.603\\ \times&0.4\\ \hline \\ \end{array}[/latex]
6. [latex]\begin{array}{rr}&38.2\\ \times&1.9\\ \hline \\ \end{array}[/latex]
7. [latex]\begin{array}{rr}&0.025\\ \times&0.25\\ \hline \\ \end{array}[/latex]
8. [latex]\begin{array}{rr}&3.5\\ \times&0.018\\ \hline \\ \end{array}[/latex]
9. [latex]\begin{array}{rr}&0.043\\ \times&3.3\\ \hline \\ \end{array}[/latex]
10. [latex]\begin{array}{rr}&0.013\\ \times&1.4\\ \hline \\ \end{array}[/latex]
11. [latex]\begin{array}{rr}&0.201\\ \times&2.1\\ \hline \\ \end{array}[/latex]

Exercise 5 Answers

1. 0.0455
2. 0.09
3. 12.00
4. 0.0351
5. 36.500
6. 0.2412
7. 72.58
8. 0.00625
9. 0.063
10. 0.1419
11. 0.0182
12. 0.4221

1. [latex]2.2 \times 10 =[/latex]
2. [latex]6.67 \times 10 =[/latex]
3. [latex]2.1 \times 100 =[/latex]

Exercise 6 Answers

1. 22
2. 66.7
3. 210

1. [latex]5.67 \times 100 =[/latex]
2. [latex]92.737 \times 100 =[/latex]
3. [latex]25 \times 100 =[/latex]

Exercise 7 Answers

1. 567
2. 9273.7
3. 2500

1. [latex]6.721 \times 1\,000 =[/latex]
2. [latex]1.56 \times 1\,000 =[/latex]
3. [latex]0.7246 \times 1\,000 =[/latex]
4. [latex]2.1 \times 1\,000 =[/latex]

Exercise 7 Answers

1. 6721
2. 1560
3. 724.6
4. 2100

Write the products using the short method you now know.

1. [latex]0.4 \times 10 =[/latex]
2. [latex]0.27 \times 10 =[/latex]
3. [latex]10 \times 0.926 =[/latex]
4. [latex]10 \times 0.09 =[/latex]
5. [latex]0.62 \times 100 =[/latex]
6. [latex]0.119 \times 100 =[/latex]
7. [latex]100 \times 2.03 =[/latex]
8. [latex]100 \times 0.345 =[/latex]
9. [latex]1.934 \times 1\,000 =[/latex]
10. [latex]28.9 \times 100 =[/latex]

Exercise 8 Answers

1. 4
2. 2.7
3. 9.26
4. 0.9
5. 62
6. 11.9
7. 203
8. 34.5
9. 1934
10. 2890

Find the area of the rectangles described below. The measures of the length (l) and width (w) have been given. You should draw and label a sketch for each.

1. l = 10.5 cm
   w = 6.6 cm
   
   A = l × w
   A = 10.5 × 6.6 cm
   A =
2. l = 100.04 km
   w = 70.2 km
3. l = 15.5 mm
   w = 10.5 mm
4. l = 9.75 cm
   w = 3.5 cm
5. l = 40.43 km
   w = 10.9 km
6. l = 19.6 cm
   w = 2.8 cm

Exercise 9 Answers

1. 69.3 cm²
2. 7022.808 km²
3. 162.75 mm²
4. 34.125 cm²
5. 440.687 km²
6. 54.88 cm²

Find the area of each square described in the questions below. Even though this is a simple square, it is still good practice to draw a picture.

Remember: All four sides of a square are the same length.

1. A _square, if  s = 5 cm
   
2. A _square, if  s = 12.5 km
3. A _square, if  s = 1.4 km
4. A _square, if  s = 25.4 cm

Exercise 10 Answers

1. 25 cm²
2. 156.25 km²
3. 1.96 km²
4. 645.16 cm²

Solve the following word problems. Estimate first.

1. One crate of juice costs $11.73. How much will five crates cost?
   • Estimation: $[latex]11.73  \approx  $12[/latex], [latex]12 \times 5 = 60[/latex]
   • Actual Solution:
   • Answer:
2. It takes Maria 0.75 hours to install a bathroom sink. The owner of the Ramada Hotel wants her to install 35 new sinks. How many hours of labour will Maria charge the hotel for this job?
   • Estimation:
   • Actual Solution:
   • Answer:
3. Find the longest hallway in your learning centre. Stand at one end and count how many steps you take until you reach the other end. Write that number here.
   1. How many steps would you take if you walked down your hallway 4.5 times?
   2. How many steps would you take if you walked down your hallway 33.68 times?
4. Jessica’s 4×4 truck averages 15.75 kilometres per litre of gas (km/L). How far could her truck travel with 52 L of gas?
   • Estimation:
   • Actual Solution:
   • Answer:
5. The distance between Jackie’s workplace and her home is 4.3 kilometres. She walks to work in the morning and then walks back to her home at the end of the workday, five days a week. How far does she walk each week?
   • Estimation:
   • Actual Solution:
   • Answer:
6. A new subdivision is being built outside of Terrace. There are 21 new houses. Each house needs 25.2 metric tonnes of crushed rock for the driveway. How much crushed rock will be used to build all the driveways?
   • Estimation:
   • Actual Solution:
   • Answer:
7. Union workers who work on statutory holidays are paid double time and a half. This is 2.5 times their regular pay.
   1. The employees at the coal terminal earn $17.37 per hour. How much are they paid per hour if they work on a statutory holiday?
   2. Jesse worked a 7.5-hour shift at the coal terminal on Labour Day last year. What were his earnings for that day?
8. Lucy’s aunt in Hartley Bay has a large 50.5 m square vegetable garden. Lucy is going to help her aunt build a barbed wire fence to keep the deer out. The fence will be made with four strands of barbed wire. How much barbed wire should Lucy buy for her aunt? The fence will look like Figure 4.10.2 below.
   

   

   • Draw a picture:
   • Estimation:
   • Actual Solution:
   • Answer:
9. The directions on a bottle of carpet shampoo say one bottle will clean 50 m² of carpet. Joyce wants to clean the wall-to-wall carpet in three rooms. The living room is 6 m by 4.5 m, the bedroom is 3 m by 4 m, and the hall is 1.2 m by 5 m. How many bottles of carpet shampoo should she buy? (This is a two-part question: Calculate the area of each of the rooms and then find the total area to be cleaned. Remember, Joyce cannot buy a partial bottle!)
   • Draw a picture:
   • Estimation:
   • Actual Solution:
   • Answer:

Exercise 11 Answers

1. Estimation: [latex]$12 \times 5 \approx $60[/latex]
   Actual Solution: [latex]$11.73 \times 5 =  $58.65[/latex]
   Five packages of juice will cost $58.65
2. Estimation: [latex]1 \times 35 \approx 35 \text{ hours}[/latex]
   Actual Solution: 0[latex].75 \times 35 = 26.25 \text{ hours}[/latex]
   It will take Maria 26.25 hours to install the sinks.
3. Answers will vary. Please ask your instructor to check your work.
4. Estimation: [latex]16 \text{ km } \times 50 \text{ L } \approx 800 \text{ km}[/latex]
   Actual Solution: [latex]15.75 \text{ km } \times 52 \text{ L } = 819 \text{ km}[/latex]
   The truck could travel 819 km.
5. Estimation: [latex]4 \times 10 \text{ km (5 trips there and 5 trips home) } \approx 44 \text{ seconds}[/latex]
   Actual Solution: [latex]4.3 \text{ km } \times 10 = 43 \text{ km}[/latex]
   Jackie walks 43 km each week.
6. Estimation: [latex]25 \text{ m } \times 20 \text{ m } \approx 500 \text{ m}[/latex]
   Actual Solution: [latex]25.2 \text{ m } \times 21 = 529.2 \text{ m}[/latex]
   There will be 529.2 metric tonnes of crushed rock used for the driveways.
7. Union workers:
   1. [latex]$17.37 \times 2.5 = $43.425 \text{ per hour}[/latex]
   2. [latex]$43.425 \times 7.5 \text{ hours } = $325.69[/latex]
      Jesse earned $325.69 on Labour Day.
8. Estimation: [latex]50 + 50 + 50 + 50 \approx 200 \text{ m }, 200 \text{ m} \times 4 \approx 800 \text{ m}[/latex]
   Actual Solution: [latex]50.5 \text{ m } \times 4 = 202 \text{ m }, 202 \text{ m } \times 4 = 808 \text{ m }[/latex]
   Lucy should buy 808 m of barbed wire.
9. Estimation:
   [latex]6 \text{ m } \times 5 \text{ m } \approx 30 \text{m}^2[/latex]
   [latex]3 \text{ m } \times 4 \text{ m } \approx 12 \text{m}^2[/latex]
   [latex]1 \text{ m } \times 5 \text{ m } \approx 5 \text{m}^2[/latex]
   [latex]30 \text{ m}^2 + 12 \text{ m}^2 + 5 \text{ m}^2 ≈ 47 \text{m}^2[/latex]
   Actual Solution:
   [latex]6 \text{ m } \times 4.5 \text{ m } = 27 \text{ m}^2[/latex]
   [latex]3 \text{ m } \times 4 \text{ m } = 12 \text{ m}^2[/latex]
   [latex]1.2 \text{ m } \times 5 \text{ m } = 6 \text{ m}^2[/latex]
   [latex]27 \text{ m}^2 + 12 \text{ m}^2 + 6 \text{ m}^2 = 45 \text{ m}^2[/latex]
   Joyce should buy just one bottle of carpet cleaner.