Transcript Estimating Fractions

4.9 Estimating Fraction Sums
and Differences
I can estimate sums and differences of
fractions and mixed number
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•You can estimate fractions by rounding to 0, ½, or 1.
•You can round fractions by comparing the numerator and denominator
You can round fractions by comparing the numerator
and denominator.
1
__
2
0
•
closer to 0
1
__
5
2
__
11
2
__
15
Each numerator is
much less than half
the denominator, so
the fractions are
close to 0.
1
__
closer to
2
5 __
9
4 __
__
11 7 20
Each numerator is
about half the
denominator, so
the fractions are
1.
close to __
2
1
•
closer to 1
9
__
10
16
__
19
6
__
7
Each numerator is
about the same as
the denominator, so
the fractions are
close to 1.
Additional Example 1A: Estimating Fractions
Estimate each sum or difference by rounding to 0,
1
__
, or 1.
2
6
3
__
__
7 + 8
6
__
+
7
3
__
8
6
3
1
Think: __ rounds to 1 and __ rounds to __.
7
8
2
1
1
1 + __ = 1 __
2
2
1
6
3
__
__
__
+
is about 1 .
2
7
8
Additional Example 1B: Estimating Fractions
1
__
, or 1.
2
Estimate each sum or difference by rounding to 0,
9
7
__
__
10 – 8
9
7
__
__
–
10
8
9
7
Think: __ rounds to 1 and __ rounds to 1.
10
8
1 – 1 =0
9
7
__
__
–
10
8
is about 0.
Check It Out: Example 1A
Estimate each sum or difference by rounding to 0,
1
__
, or 1.
2
5
3
__
__
6 + 7
5
3
__
__
+
6
7
5
3
1
Think: __ rounds to 1 and __ rounds to __.
6
7
2
1
1
1 + __ = 1 __
2
2
5
3
1
__
__
__
+
is about 1 .
6
7
2
You can also estimate by rounding mixed
numbers. You compare each mixed number to the
1
__
two nearest whole numbers and the nearest 2 .
3
1
__
__
Does 10 10 round to 10, 10 2 , or 11?
3
10
1
2
10 __
10
1
__
2
__
10 10 10 10
•
10 __
4
__
10 10
11
6
__
7
__
8
__
9
__
10 10 10 10 10 10 10 10
1
3
__
__
The mixed number 10 10 rounds to 10 2 .
Additional Example 2A: Sports Application
About how far did Tosha
walk on Tuesday and Thursday?
1
__
5 10
+4
7
__
8
5 + 5 = 10
She walked about 10 miles on Tuesday and
Thursday.
Additional Example 2C: Sports Application
Estimate the total distance
Tosha walked on Thursday,
Saturday, and Sunday.
3
9
7 + 6 __
4 __
+ 8 __
8
7
1
2
10
1
2
5 + 6 __ + 9 = 20 __
1
__
miles
2
She walked about 20
Saturday, and Sunday.
on Thursday,
Lesson Quiz: Part I
Estimate each sum or difference by rounding
to 0,
, or 1.
1.
3.
2.
0
4.
1