Transcript 4.1 Estimating with Fractions

4-1 Estimating with Fractions
California
Standards
Prep for NS2.1 Solve problems
involving addition, subtraction,
multiplication, and division of positive
fractions and explain why a particular
operation was used for a given situation.
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4-1 Estimating with Fractions
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
3
10
1
2
1
3
is closer to than to 0.
2
10
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1
4-1 Estimating with Fractions
You can also round fractions by comparing its
numerators with its denominators.
Holt CA Course 1
4-1 Estimating with Fractions
Teacher Example 1: Measurement Application
3
A blue whale can grow to 33 5 m long, while
1
the great white shark may be as long as 4 2 m.
Estimate how much longer the blue whale is
than the great white shark.
33 3 – 4 1
2
5
1
1
1
Round each mixed
33 3
4
4
33
2
2
5
2
number.
1 – 1 = 29
Subtract.
33
4
2
2
The blue whale is about 29 m longer.
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4-1 Estimating with Fractions
Student Practice 1:
A Cocker Spaniel may grow to weigh about
1
11 2 kilograms while the Chihuahua may
7
weigh about 2 8 kilograms. Estimate how
much more the Cocker Spaniel weighs than
the Chihuahua.
11 1 – 2 7
8
2
7
Round each mixed
11 1
3
2
11 1
8
2
2
number.
1
11 – 3 = 8 1
Subtract.
2
2
The Cocker Spaniel weighs about 8 1 kg more.
2
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4-1 Estimating with Fractions
Teacher Example 2A & 2B: Estimating Sums and
Differences
Estimate each sum or difference.
A. 7 – 2
9
B.
5
2
7
1
5
9
1– 1=1
2 2
45+ 31
8
9
45
41
9
2
1
41+ 3 = 7
2
2
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1
2
Round each fraction.
Subtract.
31
8
3 Round each mixed fraction.
Add.
4-1 Estimating with Fractions
Teacher Example 2C: Estimating Sums and
Differences
Estimate the difference.
C.
1
21 –
12
8
21
8
2
1
12
2–0=2
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0
Round each number.
Subtract.
4-1 Estimating with Fractions
Student Practice 2A & 2B:
Estimate each sum or difference.
A. 7 – 1
8
6
7
8
1
1
6
0
Round each fraction.
Subtract.
1–0=1
B. 5 3 + 2 2
5
53
5
9
51
2
1
51+ 2 = 7
2
2
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22
9
2 Round each mixed fraction.
Add.
4-1 Estimating with Fractions
Student Practice 2C:
Estimate the difference.
C.
8
42 –
15
9
42
9
4
1
1
=
–
3
4
2
2
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8
15
1
2
Round each number.
Subtract.
4-1 Estimating with Fractions
You can estimate products and quotients
of mixed numbers by rounding to the
nearest whole number. If the fraction in
a mixed number is greater than or equal
1
to 2 , round the mixed number
up to the next whole number. If the
fraction is less than 12 , round down to a
whole number by dropping the fraction.
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4-1 Estimating with Fractions
Teacher Example 3A: Estimating Products and
Quotients
Estimate each product or quotient.
32 • 65
6
9
32
3
9
65
6
7
3 • 7 = 21
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Round each mixed number to
the nearest whole number.
Multiply.
4-1 Estimating with Fractions
Teacher Example 3B: Estimating Products and
Quotients
Estimate each product or quotient.
13 4 ÷ 2 1
4
5
13 4
14
5
21
4
2
14 ÷ 2 = 7
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Round each mixed number to
the nearest whole number.
Divide.
4-1 Estimating with Fractions
Student Practice 3A:
Estimate each product or quotient.
72 • 23
4
3
72
8
3
23
4
3
8 • 3 = 24
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Round each mixed number to
the nearest whole number.
Multiply.
4-1 Estimating with Fractions
Student Practice 3B:
Estimate each product or quotient.
11 7 ÷ 3 1
3
8
11 7
12
8
31
3
3
12 ÷ 3 = 4
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Round each mixed number to
the nearest whole number.
Divide.