Unit 3: Subtraction
Topic E: Estimating Answers in Subtraction
You have learned how to round numbers. Now you can use that skill in rounding numbers to find an approximate difference.
By estimating your answer first, you can tell if your answer is sensible.
In these examples, estimate the answer. Round each number BEFORE you subtract.
Example A: [latex]\begin{array}[t]{rrrrr} &47&\text{rounds to}&&50 \\&26&\text{rounds to}&&30 \\ \hline &&&&20 \end{array}[/latex]
Example B: [latex]\begin{array}[t]{rrrrr} &870&\text{rounds to}&&900 \\&342&\text{rounds to}&&300 \\ \hline &&&&600 \end{array}[/latex]
Example C: [latex]\begin{array}[t]{rrrrr} &24\,397&\text{rounds to}&&24\,000 \\&6\,148&\text{rounds to}&&6\,000 \\ \hline &&&&18\,000 \end{array}[/latex]
Usually you estimate to the largest place value that you can.
Exercise One
Estimate the differences. Round the numbers before you subtract. Check your work using the answer key at the end of the exercise.
 [latex]\begin{array}[t]{rrrrr}&9\,963&\approx&&10\,000 \\&7\,099&\approx&&7\,000 \\ \hline &&&&2\,000 \end{array}[/latex]
 [latex]\begin{array}[t]{rrrrr}&70\,534&\approx&&71\,000 \\&7\,689&\approx&&8\,000 \\ \hline &&&&63\,000 \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&687\\&438\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&754\\&236\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&8\,442\\& 1\, 876\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&5 \,630\\& 1 \,752\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&5 \,342\\& 3 \,647\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&7 \,111\\& 5 \,982\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&6 \,031 \\& 2\, 899\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&41 \,573\\& 4\, 846\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&36 \,154\\& 9 \,038\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&46 \,124 \\& 9 \,762\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&54 \,751 \\& 7 \,896\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&72 \,450 \\& 31\, 924\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&81 \,692 \\& 53\, 908\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&92 \,163 \\& 45\, 517\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&171 \,234\\& 82\, 169\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&102 \,085 \\& 36 \,526\\ \hline \\ \end{array}[/latex]
Answers to Exercise One
 10000 − 7000 = 3000
 71000 − 8000 = 63000
 700 − 400 = 300
 800 − 200 = 600
 8000 − 2000 = 6000
 6000 − 2000 = 4000
 5000 − 4000 = 1000
 7000 − 6000 = 1000
 6000 − 3000 = 3000
 42000 − 5000 = 37000
 36000 − 9000 = 27000
 46000 − 10000 = 36000
 55000 − 8000 = 47000
 70000 − 30000 = 40000
 80000 − 50000 = 30000
 90000 − 50000 = 40000
 170000 − 80000 = 90000
 100000 − 40000 = 60000
Estimating Answers in Subtraction Word Problems
When you are solving word problems, an estimate tells you if your answer makes sense. 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 subtract your numbers again.
Exercise Two
Estimate the following answers. Be sure to round to the largest place value possible before adding or subtracting. Remember to circle the information and underline what is being asked. Check your work using the answer key at the end of the exercise.
Example:
On a recent petition about sales tax, Mulan had 2865 people sign. Arnav had 1564 people sign the petition. Estimate how many more people Mulan had sign than Arnav.
On a recent petition about sales tax, Mulan had 2865 people sign. Arnav had 1564 people sign the petition. Estimate how many more people Mulan had sign than Arnav.
[latex]\begin{array}[t]{rrrrr}&2\,865&\text{Estimate: }&&3\,000\\ − &1\,564&&&2\,000\\ \hline &&&&1\,000\end{array}[/latex]
Mulan had 1 000 more people sign the petition.
 On Tuesday, a coffee shop had sales of $8523. On Wednesday, the same coffee shop had sales of $6914. Estimate the difference between Tuesday’s sales and Wednesday’s sales.
 Last week, 4931 passengers used the ABE Taxi Company. This week, there were 3491 passengers. Estimate how many more passengers used ABE Taxi Company last week.
 In Japan, people chew 52700 tons of gum. In Russia, people chew 25700 tons of gum. Estimate the how many more tons of gum the Japanese chew.
 In Colombia there are 1897 bird species. In China, there are 1319 bird species. Estimate how many more bird species there are in Colombia.
 The whale shark weighs 30500 kilograms. The basking shark weighs 9258 kilograms. Estimate how much more the whale shark weighs.
 In India there were 155204 post offices in 2007. In China there were 59886 post offices. Estimate the difference.
 By 2008, the Montreal Canadiens had played the most games 5792. The Buffalo Sabres had played 2952. Estimate how many more games the Montreal Canadiens had played.
 In 2006, the population of Kelowna was 162276. The population of Prince George was 83225. Estimate how many more people live in Kelowna in 2006.
Answers to Exercise Two
 $9000 − $7000 = $2000
 5000 − 3000 = 2000 passengers
 50000 − 30000 = 20000 tons
 2000 − 1000 = 1000 species
 31000 − 9000 = 22000 kilograms
 160000 − 60000 = 100000 post offices
 6000 − 3000 = 3000 games
 160000 − 80000 = 80000 people
Topic E: SelfTest
Mark /18 Aim 14/18
 Estimate the differences. Show your work. (12 marks)
 [latex]\begin{array}[t]{rr}&73\\&34\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&67\\&18\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&896\\&385\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&467\\&214\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&4\,071\\& 2\, 986\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&5 \,946 \\& 4 \,281\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&57\, 201\\& 5 \,892\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&23 \,006\\& 4 \,999\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&49 \,053\\& 28 \,954\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&36 \,174\\& 16\,925\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&86 \,502 \\& 26 \,590\\ \hline \\ \end{array}[/latex]
 [latex]\begin{array}[t]{rr}&943 \,982 \\& 721\, 354\\ \hline \\ \end{array}[/latex]
 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.
 A magazine has 54823 readers. Last year the magazine had 26876 readers. By how much did number of readers increase?
 In 2009, the number of marriages per year in Japan was 964702. The number of marriages per year in Egypt was 525412. How many more marriages were there in Japan than Egypt?
 In 2010, in France there were 235846 people with the last name Martin. There were 78177 people with the last name Moreau. How many more Martins were there?
Answers to Topic E SelfTest

 40
 50
 500
 300
 1000
 2000
 51000
 18000
 20000
 20000
 60000
 200000

 20000 readers
 500000 marriages
 160000 Martins