Vocabulary (types of estimation) Estimating with Fractions ...

Estimating with Fractions, Pi and Square Roots

Vocabulary (types of estimation)

Benchmark Numbers - used with fractions, decide if fraction is closest to 0, ? or 1.

Estimating Fractions

Benchmark Numbers

? Use with fractions!

? Decide if fraction is closest to 0, ? or 1.

Examples:

4 + 2 + 5 + 3 + ? 8?

12 - 2 13 - 2 11

1

Sometimes, when solving problems, you may

not need an exact answer. To estimate sums

and differences of fractions and mixed numbers, round each fraction to 0, 1 , or 1. you can use a number line to help. 2

0

21

1

52

You can also round fractions by comparing numerators with denominators.

Guidelines for Rounding Fractions

Round to 0 if the numerator is much smaller than the denominator.

Round

to

1 2

if

the

numerator is about

half the denominator.

Round to 1 if the numerator is nearly

equal to the denominator.

Examples: 1,3 ,2 9 20 11

Examples: 2 ,5 ,7 5 12 13

Examples: 8 ,23, 97 9 25 100

Additional Example 2A & 2B: Estimating Sums and Differences

Estimate each sum or difference.

A.

7? 1 95

7 9

1

1 5

0

1?0=1

B. 4 5 + 3 1

9

8

45

4 1 31

9

28

41+ 2

3=

7

1 2

Round each fraction. Subtract.

3 Round each mixed fraction. Add.

Additional Example 2C: Estimating Sums and Differences

Estimate the sum.

C.

?2

1 8

+

7 12

?2 1 8

?2

7 12

?2 +

1 2

= ?112

1 2

Round each number.

Add.

2

Try This: Example 2A & 2B

Estimate each sum or difference.

A.

7? 1 86

7 8

1

1 6

0

1?0=1

B. 5 3 + 2 2

5

9

53

5 1 22

5

29

51+ 2

2=

7

1 2

Round each fraction. Subtract.

2 Round each mixed fraction. Add.

Try This: Example 2C

Estimate the sum.

C.

?4 2 + 9

8 15

?4 2 9

?4

8 15

?4 +

1 2

= ?312

1 2

Round each number.

Add.

Insert Lesson Title Here

Additional Example 1: Measurement Application

A

blue

whale

can

grow

to

33

3 5

the great white shark may be

m as

long, long

while

as

4

1 2

m.

About how much longer is the blue whale?

33 3 5

?

4

1 2

33 3 5

33 1 2

4

1 2

4 1 Round each mixed 2 number.

33

1 2

?

4

1 2

=

29

Subtract.

The blue whale is about 29 m longer.

Insert Lesson Title Here

Try This: Example 1

A Cocker Spaniel may grow to weigh about

1w1e12ighkim loogrreamthsawn h2il7e

the Chihuahua will not kilograms. About how

8

much more can a Cocker Spaniel weigh?

11 1 2

?

2

7 8

11 1 2

11 1 2

2

7 8

3

Round each mixed number.

11

1 2

?

3

=

81 2

Subtract.

The Cocker Spaniel weighs about 8 1 kg more. 2

3

When exact answers are not needed for a problem, you can use estimation. When exact answers are needed, an estimate can help you decide if your answer is reasonable.

Helpful Hint Words like about and around signal that an exact answer is not necessary.

Insert Lesson Title Here

Additional Example 3A: Deciding If an Estimate is Enough

Decide if you need an exact answer or if an estimate is enough.

A. Michael knows there will be 18 people at his party. He plans to give each person a 12 cup

3

serving of popcorn. If he can buy popcorn in 10cup bags, how many bags should he buy?

Since he will be buying the popcorn in 10 cup bags, an estimate of the amount will give him enough information to decide how many bags of popcorn to buy.

Additional Example 3B: Deciding If an Estimate is Enough

Decide if you need an exact answer or if an estimate is enough.

B. For a soccer celebration, Ellis buys rolls for

$5.29

and

3

1 4

pounds

of

barbequed

ham

for

$9 per pound. How much does she spend for

the food?

Since the problem is asking for the exact amount of money she spends, an estimate would not be appropriate.

Insert Lesson Title Here

Try This: Example 3A

Decide if you need an exact answer or if an estimate is enough. Cynthia has two dogs. Each dog is fed 1 3

4

cups of dog food each day. If she buys a 30 lb bag of dog food, is that enough to last for three weeks?

Since she is only trying to get an idea of how long a 30 lb bag of dog food will last, an estimate should give her enough information to decide .

4

Insert Lesson Title Here

Try This: Example 3B

Decide if you need an exact answer or if an estimate is enough.

William's uncle was going on a 14-day

camping trip. He is required of a certain medication each

tdoatya.kHeo1w12

pills

many pills should he take with him on this

trip?

Since his uncle must take a certain amount of pills each day for a medical condition, an estimate would not be appropriate.

Square Roots

Additional Example 1A: Estimating Square Roots of Numbers

Each square root is between two integers. Name the integers.

A. 55 72 = 49

Think: What are perfect squares close to 55?

49 < 55

82 = 64

64 > 55

55 is between 7 and 8. 7 < 55 < 8

Additional Example 1B: Estimating Square Roots of Numbers Continued

Each square root is between two integers. Name the integers.

B. ? 90

Think: What are perfect squares close to 90?

?92 = 81 81 < 90

?102 = 100 100 > 90

? 90 is between ?9 and ?10. ?9 < ? 90 < ?10

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