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Estimation of Whole Number Addition and Subtraction

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What other kinds of animals are there at a zoo?

Sarah is also a volunteer like Jonah. She spends her time working with the penguins. When Jonah comes to visit her, she tells him all about the penguin population. Sarah explains to Jonah that there will be new penguins born very soon. She tells him that there are 57 penguins, but that 17 new ones are due to be born in the spring. Jonah listens and tries to add the two values together. He takes out paper and pencil. Sarah stops him. She knows a quicker way. She tells Jonah that they can use estimation.

Have you ever estimated a sum? In this Concept, you will learn how to use estimation to figure out the new penguin population.

Guidance

In the real world problem, you saw how puzzled Jonah was when Sarah was able to use estimation to help her solve the penguin problem. Estimation definitely seemed to save Sarah some time.

What do we mean by estimation? When can we use it and when shouldn’t we use it? To estimate means to find an answer that is close to the exact answer. The key with estimation is that you can only use it in instances where you don’t need an exact answer. When we estimate, we want to find an answer that makes sense and works with our problem, but is not necessarily exact.

We can estimate sums and differences. Remember back in the first Concept, we used the word sum and the word difference . Let’s take a minute to review what those two words mean. A sum is the answer to an addition problem . A difference is the answer to a subtraction problem . To estimate a sum or a difference, we can round the numbers that we are working with to find our estimation.

What does it mean to round a number? When we round, we change the number to the nearest power of ten (times a whole number), such as ten or hundred or thousand, etc. Here is a problem we can work with.

69

Let’s say that we want to round this number to the nearest ten. Well, we can look at whether 69 is closer to 60 or to 70. These are the two numbers in the tens surrounding 69. It is closer to 70, so we would change the number to 70. Here is another one.

53

If we want to round this to the nearest ten, then we can look at the numbers surrounding 53 which are multiples of ten. Is 53 closer to 50 or 60? It is closer to 50, so we would “round down” to 50. When rounding, we can follow the rounding rules. If the number being rounded is less than 5, round down. If the number being rounded is greater than 5, round up. In the examples, we were rounding to the tens, so we use the number in the ones place to round. Using 69, since 9 is greater than 5, we round up. In the case of 53, 3 is less than 5, so we round down.

Let’s apply this.

128 Round to the nearest ten.

Look at the number. We are rounding to the tens, so we look at the ones place. 8, is greater than 5, so we round up to 130. What does this have to do with estimating sums and differences? Well, when we estimate a sum or a difference, if we round first, it is easier to add.

58 + 22 = \underline{\;\;\;\;\;\;\;}

We want to estimate this answer. If we round each number first, we can use mental math to find our estimation.

58 rounds to 60

22 rounds to 20

Our estimate is 80.

Here is one with larger numbers.

387 + 293 =\underline{\;\;\;\;\;\;\;}

We want to estimate our answer by rounding to the nearest hundred.

387 rounds to 400

293 rounds to 300

Our estimate is 700.

This worked for addition.

We can estimate differences by rounding too.

Here is one with larger numbers.

990 - 211 = \underline{\;\;\;\;\;\;\;}

We want to estimate our difference by rounding to the nearest hundred.

990 rounds to 1000

211 rounds to 200

Our estimate is 800.

Now let's practice with a few examples.

Example A

17 + 27 =\underline{\;\;\;\;\;\;\;}

Solution: 50

Example B

290 + 510 = \underline{\;\;\;\;\;\;\;}

Solution: 800

Example C

592 - 411 = \underline{\;\;\;\;\;\;\;}

Solution: 200

Now back to Sarah and Jonah and the penguin population.

Here is the original problem once again.

Sarah is also a volunteer like Jonah. She spends her time working with the penguins. When Jonah comes to visit her, she tells him all about the penguin population. Sarah explains to Jonah that there will be new penguins born very soon. She tells him that there are 57 penguins, but that 17 new ones are due to be born in the spring. Jonah listens and tries to add the two values together. He takes out paper and pencil. Sarah stops him. She knows a quicker way. She tells Jonah that they can use estimation.

To solve this problem, Jonah and Sarah can use estimation.

First, we can round both values.

57 rounds up to 60

17 rounds up to 20

Now we add 60 + 20

The new penguin population will be 80 penguins.

Vocabulary

Estimation
to find an approximate answer to a problem
Sum
the answer to an addition problem
Difference
the answer to a subtraction problem

Guided Practice

Here is one for you to try on your own.

56 - 18 = \underline{\;\;\;\;\;\;\;}

Answer

We want to estimate this difference by rounding to the nearest ten.

56 rounds to 60

18 rounds to 20

Our estimate is 40.

Video Review

These videos will help you to estimate sums and differences.

Khan Academy Rounding to Estimate Sums

James Sousa on Estimating Sums and Differences

Practice

Estimate the following sums and differences.

1. 45 + 62 = \underline{\;\;\;\;\;\;\;}

2. 32 + 45 = \underline{\;\;\;\;\;\;\;}

3. 21 + 54 = \underline{\;\;\;\;\;\;\;}

4. 103 + 87 = \underline{\;\;\;\;\;\;\;}

5. 101 + 92 = \underline{\;\;\;\;\;\;\;}

6. 342 + 509 = \underline{\;\;\;\;\;\;\;}

7. 502 + 307 = \underline{\;\;\;\;\;\;\;}

8. 672 + 430 = \underline{\;\;\;\;\;\;\;}

9. 201 + 303 = \underline{\;\;\;\;\;\;\;}

10. 678 + 407 = \underline{\;\;\;\;\;\;\;}

11. 23 - 9 = \underline{\;\;\;\;\;\;\;}

12. 46 - 8 =\underline{\;\;\;\;\;\;\;}

13. 58 - 12 = \underline{\;\;\;\;\;\;\;}

14. 76 - 9 = \underline{\;\;\;\;\;\;\;}

15. 204 - 112 = \underline{\;\;\;\;\;\;\;}

16. 87 - 65 = \underline{\;\;\;\;\;\;\;}

17. 98 - 33 = \underline{\;\;\;\;\;\;\;}

18. 354 - 102 = \underline{\;\;\;\;\;\;\;}

19. 562 - 112 = \underline{\;\;\;\;\;\;\;}

20. 789 - 99 = \underline{\;\;\;\;\;\;\;}

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