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Course 1
4-9 Estimating Fraction Sums and Differences
Learn to estimate sums and differences of fractions and mixed numbers.
Course 1
4-9 Estimating Fraction Sums and Differences
You can estimate fractions by rounding to 0, , or 1.12__
1
5311
3
7
12__
8__
8__
4__
8__
4__
8__
0•
The fraction is halfway between and 1, but we
usually round up. So the fraction rounds to 1.
34__
34__
12__
Course 1
4-9 Estimating Fraction Sums and Differences
closer to 0
Each numerator is much less than half the denominator, so the fractions are close to 0.
closer to 1
Each numerator is about the same as the denominator, so the fractions are close to 1.
• •
1
2__
0 1
15__ 2
11__ 2
15__ 4
7__5
11__ 6
7__9
10__ 16
19__9
20__
1
2__
You can round fractions by comparing the numerator and denominator.
closer to
Each numerator is about half the denominator, so the fractions are close to .
1
2__
Course 1
4-9 Estimating Fraction Sums and Differences
Additional Example 1A: Estimating Fractions
Estimate each sum or difference by rounding to 0, , or 1.
+
1
2__
6
7__ 3
8__
+6
7__ 3
8__
1 + = 11
2__
6
7__ 3
8__ + is about 1 .
1
2__
Think: rounds to 1 and rounds to .
67__ 3
8__ 1
2__
1
2__
Course 1
4-9 Estimating Fraction Sums and Differences
Additional Example 1B: Estimating Fractions
Estimate each sum or difference by rounding to 0, , or 1.
–
1
2__
9
10__ 7
8__
–9
10__ 7
8__
1 – 1 = 0
9
10__ 7
8__ – is about 0.
Think: rounds to 1 and rounds to 1. 910__ 7
8__
Course 1
4-9 Estimating Fraction Sums and Differences
Check It Out: Example 1A
Estimate each sum or difference by rounding to 0, , or 1.
+
1
2__
5
6__ 3
7__
+5
6__ 3
7__
1 + = 11
2__
5
6__ 3
7__ + is about 1 .
1
2__
Think: rounds to 1 and rounds to .
56__ 3
7__ 1
2__
1
2__
Course 1
4-9 Estimating Fraction Sums and Differences
Check It Out: Example 1B
Estimate each sum or difference by rounding to 0, , or 1.
–
1
2__
13
19__ 2
11__
1 – 0 = 1
13
19__ 2
11__ – is about 1.
Think: rounds to 1 and rounds to 0. 1319__ 2
11__– 2
11__13
19__
Course 1
4-9 Estimating Fraction Sums and Differences
You can also estimate by rounding mixed numbers. You compare each mixed number to the
two nearest whole numbers and the nearest .
Does 10 round to 10, 10 , or 11?
12__
310__ 1
2__
10 10 10 10 10 10 10610__2
10__1
10__ 4
10__ 7
10__ 9
10__8
10__
10 10 10 11 310__ 1
2__
•
The mixed number 10 rounds to 10 .310__ 1
2__
Course 1
4-9 Estimating Fraction Sums 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
10__ 7
8__5 + 4
5 + 5 = 10
She walked about 10 miles on Tuesday and Thursday.
Course 1
4-9 Estimating Fraction Sums 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?
9
10__ 7
8__8 – 4
9 – 5 = 4
She walked about 4 miles farther on Sunday than on Thursday.
Course 1
4-9 Estimating Fraction Sums 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.
1
2__
7
8__4 + 6 + 8
She walked about 20 miles on Thursday, Saturday, and Sunday.
9
10__3
7__
1
2__5 + 6 + 9 = 20
1
2__
Course 1
4-9 Estimating Fraction Sums 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
5__ 6
7__3 + 2
3 + 3 = 6
He roller skated about 6 miles on Tuesday and Sunday.
Jerry’s Roller Skating Distances
Distance (mi)
3
6
2
8
15__
37__
17__
67__
Day
Tuesday
Thursday
Saturday
Sunday
Course 1
4-9 Estimating Fraction Sums 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
Tuesday?
1
7__ 1
5__8 – 3
8 – 3 = 5
He roller skated about 5 miles farther on Saturday than Thursday.
Jerry’s Roller Skating Distances
Distance (mi)
3
6
2
8
15__
37__
17__
67__
Day
Tuesday
Thursday
Saturday
Sunday
Course 1
4-9 Estimating Fraction Sums 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.
1
2__
He roller skated about 12 miles on Tuesday, Thursday, and Sunday.
1
5__3 + 6 + 2
6
7__3
7__
1
2__3 + 6 + 3 = 12
1
2__
Jerry’s Roller Skating Distances
Distance (mi)
3
6
2
8
15__
37__
17__
67__
Day
Tuesday
Thursday
Saturday
Sunday
Course 1
4-9 Estimating Fraction Sums and Differences
Lesson Quiz: Part I
1. 2.
3. 4. 0 1
Estimate each sum or difference by rounding
to 0, , or 1.
Course 1
4-9 Estimating Fraction Sums 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
