Sometimes, an exact answer is not needed — especially when you just want a quick idea of what something will cost or total. This is called estimating. When you estimate, you round numbers and then add them. It helps you check if your final answer makes sense.

Why Estimate?

Imagine you are going away for the weekend:

• Hotel: about $60

• Meals: about $80

• Gas: about $40

• Entertainment: about $100

Instead of calculating exactly, you might say:
60 + 80 + 40 + 100 = 280
You estimated the total weekend cost: $280.

Steps to Estimate a Sum

Step 1: Identify the Place to Round To

Round each number to the highest place value they share.

• If both numbers are two-digit numbers, round to the tens.

• Once again, always round to the highest place value that both numbers share. For example, if one number has thousands and the other has only hundreds, round both to the hundreds place. If one number has hundreds and the other has only tens, round both to the tens place.

• If both have thousands, round to the thousands.

This makes the numbers easier to add mentally.

Step 2: Round Each Number

Use the digit to the right of the one you are rounding to.

• If it is 5 or more, round up.

• If it is less than 5, round down.

Step 3: Add the Rounded Numbers

This gives your estimated sum.

In these examples, estimate the answer. Round each number BEFORE you add.

Tip:

Round both numbers to the same place — the highest one they both have.

Estimating Answers in Addition Word Problems

When you are solving word problems, an estimate tells you if your answer is sensible. 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 add your numbers again.

Key Ideas to Remember

• Round to the same place value in both numbers.

• Round up if the next digit is 5 or more.

• Round down (i.e., the digit stays the same) if it is less than 5.

• Add the rounded numbers for your estimate.

• Estimating is not exact — it gives you a ballpark answer.

Topic C: Self-Test

Mark     /15    Aim 11/15

1. Estimate the sums. Show your work. (9 marks)
   1. [latex]\begin{array}[t]{rr}&7\, 964 \\ &971 \\ &6 \,888 \\+& 2\, 021 \\ \hline \\ \end{array}[/latex]
   2. [latex]\begin{array}[t]{rr}&5 \,365 \\ &5 \,100 \\ &9\, 982\\+& 7\, 752 \\ \hline \\ \end{array}[/latex]
   3. [latex]\begin{array}[t]{rr}&5 \,211 \\ &1 \,982 \\ &3\, 371 \\+& 2 \,801 \\ \hline \\ \end{array}[/latex]
   4. [latex]\begin{array}[t]{rr}&3 \,395 \\ &2 \,709 \\ &18\, 060\\+& 932 \,335 \\ \hline \\ \end{array}[/latex]
   5. [latex]\begin{array}[t]{rr}&2 \,364 \\ &62 \,182 \\ &549\, 272 \\+& 6 \,395 \\ \hline \\ \end{array}[/latex]
   6. [latex]\begin{array}[t]{rr}&75\, 536 \\&31 \,807 \\&337 \,427 \\+& 7 \,912 \\ \hline \\ \end{array}[/latex]
   7. [latex]\begin{array}[t]{rr}&898\, 402 \\&465 \,766 \\&558\, 485\\+& 324 \,715 \\ \hline \\ \end{array}[/latex]
   8. [latex]\begin{array}[t]{rr}&6 \,182 \,390\\&2 \,763 \,393 \\&1 \,326 \,879 \\+& 2\, 743 \,912 \\ \hline \\ \end{array}[/latex]
   9. [latex]\begin{array}[t]{rr}&1 \,226 \,590 \\&687 \,029 \\&533 \,905 \\+& 1\, 359 \,254 \\ \hline \\ \end{array}[/latex]
2. 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.
   1. Yuan counted 854 old books and 519 new books. Estimate how many books there were altogether.
   2. A magazine has 34783 subscribers. Last year the magazine had 26876 subscribers. Estimate how many subscribers in total.
   3. The area of Canada is 9984670 square kilometres. The area of the United States is 9629091 square kilometres. The area of Mexico is 1964375 square kilometres. Estimate the total area of the three countries.

Answers to Topic C Self-Test

1. 1. 18000
   2. 28000
   3. 13000
   4. 956000
   5. 619000
   6. 453000
   7. 2300000
   8. 13000000
   9. 3800000
2. 1. 1400 books
   2. 60000 subscribers
   3. 22000000 square kilometres