Lesson 9.9 Estimating Sums and Differences
I can estimate sums and differences with mixed numbers
Steps
1) Round each mixed number to the nearest whole number
1
a. Any fraction or greater rounds up to the next whole number
2
1
b. Any fraction less than remains the whole number that is
2
already there.
2) Add or subtract the rounded numbers
Examples
3
1
4
3
A) 2 + 5 ≈
3
1
4
1
2
1
3
2
First, round 2 . Since
Next, round 5 . Since
2
3
4
1.5
4
1
= , therefore
=
3
, therefore
3
6
16
−6
11
20
3
4
1
4
1
2
3
< , & 5 will round to 5
So now the problem becomes 3 + 5 = 8
B) 8
2
> , & 2 will round up to 3
≈
6
1
16
11
2
1
20
2
First, round 8 . Since
Next, round 6 . Since
=
=
8
, therefore
16
10
11
20
20
, thus
6
16
1
1
6
2
16
< ,&8
> ,&6
2
So now the problem becomes 8 – 7 = 1
11
20
will round to 8
will round up to 7
Samples
Estimate each item below. Be sure to show your rounding.
3
5
7
9
1) 5 + 9 ≈
2) 4
4
11
5
−3 ≈
9
1
3
3
4
5
1
8
4
3) 3 + 2 ≈
4) 9 − 2 ≈
2
1
5
2
5
3
8
6
5) 8 + 4 ≈
6) 2 − 1 ≈
7) 9
5
81
8) 35
+7
17
18
7
11
− 24
≈
1
23