Transcript Sports Roller skating

Estimating
Fraction
Sums
Estimating
Fraction
Sums
4-9
4-9 and Differences
and Differences
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
Estimating Fraction Sums
4-9 and Differences
Warm Up
Write each sum or difference in
simplest form.
3
5
__
__
1
1. +
8
8
1
1 __
1
__
__
3. 2 + 1 3
4
4
2
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3 __
3
9
__
__
2.
–
10 5
10
2
2
8
__
__
__
4. 5 –1
4
9
3
9
Estimating Fraction Sums
4-9 and Differences
Problem of the Day
Students at a school dance formed equal
teams to play a game. When they
formed teams of 3, 4, 5, or 6, there was
always one person left. What is the
smallest number of people that there
could have been at the dance?
61, the LCM of all the numbers, plus 1
Course 1
Estimating Fraction Sums
4-9 and Differences
Learn to estimate sums and differences of
fractions and mixed numbers.
Course 1
Estimating Fraction Sums
4-9 and Differences
1
__
You can estimate fractions by rounding to 0, 2 , or 1.
1
__
2
0
1
__
8
1
__
4
3
__
8
5
__
8
3
__
4
•
1
7
__
8
3
1
The fraction __ is halfway between __ and 1, but we
4
2
3
usually round up. So the fraction __ rounds to 1.
4
Course 1
Estimating Fraction Sums
4-9 and Differences
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.
Course 1
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.
Estimating Fraction Sums
4-9 and Differences
Additional Example 1A: Estimating Fractions
1
2
Estimate each sum or difference by rounding to 0, __, or 1.
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
Course 1
Estimating Fraction Sums
4-9 and Differences
Additional Example 1B: Estimating Fractions
1
2
Estimate each sum or difference by rounding to 0,__ , or 1.
9
7
__
__
–
10
8
7
9
__
__
–
8
10
9
7
Think: __ rounds to 1 and __ rounds to 1.
10
8
1 – 1 =0
9
7
__
__
–
10
8
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is about 0.
Estimating Fraction Sums
4-9 and Differences
Check It Out: Example 1A
1
2
Estimate each sum or difference by rounding to 0, __, or 1.
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
Course 1
Estimating Fraction Sums
4-9 and Differences
Check It Out: Example 1B
1
Estimate each sum or difference by rounding to 0, __, or 1.
2
13
2
__
__
–
19
11
13
2
__
– __
19
11
13
2
Think: __ rounds to 1 and __ rounds to 0.
19
11
1–0 =1
13
2
__
– __ is about 1.
19
11
Course 1
Estimating Fraction Sums
4-9 and Differences
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 .
Course 1
Estimating Fraction Sums
4-9 and Differences
Additional Example 2A: Sports Application
The table shows the distances Tosha walked.
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.
Course 1
Estimating Fraction Sums
4-9 and Differences
Additional Example 2B: Sports Application
The table shows the distances Tosha walked.
About how much farther did
Tosha walk on Sunday than
Thursday?
7
8
9
8 __
– 4 __
10
9–5=4
She walked about 4 miles farther on Sunday
than on Thursday.
Course 1
Estimating Fraction Sums
4-9 and Differences
Additional Example 2C: Sports Application
The table shows the distances Tosha walked.
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.
Course 1
on Thursday,
Estimating Fraction Sums
4-9 and Differences
Check It Out: Example 2A
The table shows the distances Jerry roller skated.
About how far did Jerry
skate on Tuesday and Sunday?
1
__
3 5
+2
6
__
7
3+3=6
Jerry’s Roller Skating Distances
Day
Distance (mi)
1
__
Tuesday
3 5
Thursday
6 7
Saturday
1
8 __
7
Sunday
2 7
3
__
6
__
He roller skated about 6 miles on Tuesday and
Sunday.
Course 1
Estimating Fraction Sums
4-9 and Differences
Check It Out: Example 2B
The table shows the distances Jerry roller skated.
About how much farther did
Jerry skate on Saturday than
Jerry’s Roller Skating Distances
Day
Tuesday?
1
__
8 7
1
5
– 3 __
8–3=5
1
__
Tuesday
3 5
Thursday
6 7
Saturday
1
8 __
7
Sunday
2 7
He roller skated about 5 miles farther on
Saturday than Thursday.
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Distance (mi)
3
__
6
__
Estimating Fraction Sums
4-9 and Differences
Check It Out: Example 2C
The table shows the distances Jerry roller skated.
Estimate the total distance
Tosha walked on Tuesday,
Thursday, and Sunday.
6
1
3
__
__
__
3
+6
+2
7
5
7
1
2
1
2
3 + 6 __ + 3 = 12 __
He roller skated about 12
Thursday, and Sunday.
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Jerry’s Roller Skating Distances
Day
Distance (mi)
1
__
Tuesday
3 5
Thursday
6 7
Saturday
1
8 __
7
Sunday
2 7
1
__
miles
2
3
__
6
__
on Tuesday,
Estimating Fraction Sums
4-9 and Differences
Lesson Quiz: Part I
Estimate each sum or difference by rounding
to 0,
, or 1.
1.
3.
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2.
0
4.
1
Estimating Fraction Sums
4-9 and Differences
Lesson Quiz: Part II
5. The conservation club picked up trash along the
road for three weeks. The table shows the
number of pounds of trash they collected.
About how many pounds did they collect in
weeks 2 and 3?
about 37 pounds
Course 1