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}&&20\,000 \\-&6\,148&\text{rounds to}&-&6\,000 \\ \hline &&&&14\,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 &&&&3\,000 \end{array}[/latex]
- [latex]\begin{array}[t]{rrrrr}&70\,534&\approx&&70\,000 \\-&7\,689&\approx&-&8\,000 \\ \hline &&&&62\,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
- 70000 − 8000 = 62000
- 700 − 400 = 300
- 800 − 200 = 600
- 8000 − 2000 = 6000
- 6000 − 2000 = 4000
- 5000 − 4000 = 1000
- 7000 − 6000 = 1000
- 6000 − 3000 = 3000
- 40000 − 5000 = 35000
- 40000 − 9000 = 31000
- 50000 − 10000 = 40000
- 50000 − 8000 = 42000
- 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: Self-Test
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 Self-Test
-
- 40
- 50
- 500
- 300
- 1000
- 2000
- 51000
- 18000
- 20000
- 20000
- 60000
- 200000
-
- 20000 readers
- 500000 marriages
- 160000 Martins