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Reasonableness with Fractions and
Decimals
1. Find what whole numbers the first decimal or fraction would be between.
2. Write the two numbers down.
For Addition
3. Find what whole numbers the second decimal or fraction would be between.
4. Write the two numbers down below the other two.
5. Add the pairs of whole numbers.
6. Work the “real” problem.
7. Make sure your answer is BETWEEN the “answer range” answers.
If it IS NOT BETWEEN, your answer is wrong!
2
+ 3 4
33
2
What whole numbers is 2 between on a number line?3
20 1 2 3 4
2
+ 3 4
33
2
0 1 2 3 42 3
2
+ 3 4
33
2
What whole numbers is 3 between on a number line?4
30 1 2 3 4
2 3
2 32
+ 3 4
33
2
0 1 2 3 43 4
2 32
+ 3 4
33
2
0 1 2 3 4
3 4+ +
5 7
12
2
+ 3 4
33
2
12
129
8
17= 112
5x 3
x 3x 4
x 4
5 6 7
2 32
+ 3 4
33
2
3 4+ +
5 7
0 1 2 3 4 6 8
1125
1125
2 32
+ 3 4
33
2
3 4+ +
5 7
0 1 2 3 4 5 6 7 8
1125
1125
2 32
+ 3 4
33
2
3 4+ +
5 75+ 1 12
5
0 1 2 3 4 5 6 7 8 9
2 32
+ 3 4
33
2
3 4+ +
5 76 12
56 12
5
0 1 2 3 4 5 6 7 8 9
5 6 7
2 32
+ 3 4
33
2
3 4+ +
5 76 12
5
6 12
5
0 1 2 3 4 6 8 9
0 1 2 3 4 5 6 7 8 9
What whole numbers is 4 between on a number line?4
3
4
+ 32
14
3
0 1 2 3 4 5 6 7 8 94 5
4
+ 32
14
3
0 1 2 3 4 5 6 7 8 9
What whole numbers is 3 between on a number line?2
1
4 54
+ 32
14
3
0 1 2 3 4 5 6 7 8 9
4 5
3 4
4
+ 32
14
3
4 54
+ 3 2
14
3
3 4+ +
7 9
0 1 2 3 4 5 6 7 8 9
4
4
+ 3 2
14
3
4
4
3
2
5 = 1 41
4
x 2
x 2
7 9
4 54
+ 3 2
14
3
3 4+ +
7 9141
1 41
0 1 2 3 4 5 6 8
4 54
+ 33 4+ +
7 98
0 1 2 3 4 5 6 7 8 9
2
14
3
8 41
4
1
7 9
4 54
+ 33 4+ +
7 98
0 1 2 3 4 5 6 8
2
14
3
8 41
4
1
0 1 2 3 4 5 6 7 8 9
.075 + 5.2
What whole numbers is .075 between on a number line?
0 1 2 3 4 5 6 7 8 90 1
.075 + 5.2
0 1 2 3 4 5 6 7 8 9
0 1.075 + 5.2
What whole numbers is 5.2 between on a number line?
0 1 2 3 4 5 6 7 8 9
0 1
5 6
.075 + 5.2
0 15 6+ +
5 7
0 1 2 3 4 5 6 7 8 9
.075 + 5.2
.075 + 5.2= .127
5 7
0 15 6+ +
5 7
0 1 2 3 4 6 8 9
.127
0 15 6+ +
5 7
.075 + 5.2=1.27
5 70 1 2 3 4 6 8 9
+ .075
+5.2000 15 6+ +
5 75.275
5 70 1 2 3 4 6 8 9
5.275
0 1 2 3 4 5 6 7 8 9
1.375 + 4
What whole numbers is 1.375 between on a number line?
0 1 2 3 4 5 6 7 8 91 2
1.375 + 4
4 is a whole number. Just use 4 both times.
1 2 1.375 + 4
0 1 2 3 4 5 6 7 8 9
1 2
44
1.375 + 4
1 24 4+ +
5 6
0 1 2 3 4 5 6 7 8 9
1.375 + 4
1.375 + 4=
5 6
1 24 4+ +
5 6
0 1 2 3 4 7 8 9
1.3791.379
1 24 4+ +
5 6
1.375 + 4=1.379
5 60 1 2 3 4 7 8 9
1 24 4+ +
5 6
+1.375
+4.000
5 60 1 2 3 4 7 8 9
5.375 5.375
1. Follow steps 1 – 3 from addition.
2. Switch the 2nd numbers before you write them down.
For Subtraction
3. Subtract.
If you get the If you get the same same answeranswer, instead of an , instead of an “answer range”, you “answer range”, you forgot to SWITCH the forgot to SWITCH the set of numbers.set of numbers.
4. Work the “real” problem.
5. Make sure your answer is BETWEEN the “answer range” answers.
If it IS NOT BETWEEN, your answer is wrong!
0 1 2 3 4 5 6 7 8
3
- 1
10
7
5
2
What whole numbers is 3 between on a number line?10
7
0 1 2 3 4 6 83 43
- 1
10
7
5
2
What whole numbers is 1 between on a number line?5
2
3 43
- 1
0 1 2 3 4 5 6 7 8
10
7
5
2
0 1 2 3 4 5 6 7 8
3 4
1 23
- 1
10
7
5
2
3 41 2- -
2 2
3
- 1
0 1 2 3 4 5 6 7 8
10
7
5
2
If you get the same If you get the same answer, instead of an answer, instead of an “answer range”, you “answer range”, you forgot to SWITCH the forgot to SWITCH the set of numbers.set of numbers.
3 41 2- -
1 3
3
- 1
0 1 2 3 4 5 6 7 8
10
7
5
2
10
10
10
3
- 14
7
3
10
7
5
2
x 2
x 2
10
7
5
23 42 1-
1 3
3
- 1
10
3
10
3
-
0 2 4 5 6 7 8 91 3
3 42 1- -
1 3
3
- 1
10
310
410
7
2
10
7
5
2
0 2 4 5 6 7 8 91 3
10
32
3 42 1- -
10
321 3
0 2 4 5 6 7 8 91 3
3
- 1
10
7
5
2
0 1 2 3 4 5 6 7 8 9
What whole numbers is 7 between on a number line?
7
- 24
32
1
2
1
0 1 2 3 4 5 6 7 8 97 8
7
- 24
32
1
0 1 2 3 4 5 6 7 8 9
What whole numbers is 2 between on a number line?4
3
7 87
- 2 4
32
1
0 1 2 3 4 5 6 7 8 9
7 8
2 3
7
- 2 4
32
1
7 82 3- -
5 5
0 1 2 3 4 5 6 7 8 9
7
- 24
32
1
7 82 3- -
4 6
0 1 2 3 4 5 6 7 8 9
7
- 24
32
1
4
47
- 2
x 2
x 2 226
-3
+
4
32
1
4 4
6
3
4
3
4 6
7 83 2- -
4 6
0 1 2 3 5 7 8 9
4
32
1
4
3
7
- 2
4
3
7 83 2- -
4 64 4
3
7
- 2
4
266
4
3
4 60 1 2 3 5 7 8 9
7 83 2- -
4 64 4
3
7
- 2
4
266
4
3
4 60 1 2 3 5 7 8 9
4 43
0 1 2 3 4 5 6 7 8 9
5.3 - .086
What whole numbers is 5.3 between on a number line?
0 1 2 3 4 5 6 7 8 95 6
5.3 - .086
5.3 - .086
0 1 2 3 4 5 6 7 8 9
5 6
What whole numbers is .086 between on a number line?
5 6
0 1 2 3 4 5 6 7 8 90 1
5.3 - .086- -
5 5
5 6
0 1 2 3 4 5 6 7 8 9
0 15.3 - .086
- -
4 6
.033
5 601
5.3 - .086=- -
4 6
4 60 1 2 3 5 7 8 9
.033
5 601
5.3 - .086=.033- -4 6
4 60 1 2 3 5 7 8 9
5 601
5.300
- .086- -4 6
2 9 10
4125.
4 60 1 2 3 5 7 8 9
5.214
0 1 2 3 4 5 6 7 8 9
6 is a whole number. Just use 6 both times.
6 - 1.375
0 1 2 3 4 5 6 7 8 966
6 - 1.375
6 - 1.375
0 1 2 3 4 5 6 7 8 9
What whole numbers is 1.375 between on a number line?6 6
6
0 1 2 3 4 5 6 7 8 91 2
66 - 1.375
6 61 2- -
5 4
0 1 2 3 4 5 6 7 8 9
6 - 1.375
0 1 2 3 6 7 8 9
61-
5
62-4
4 5
1.3696 - 1.375 = 1.369
6 61 2- -
5 4
6 – 1.375=1.369
0 1 2 3 6 7 8 94 5
+6.000
- 1.3756 61 2- -
5 4
5 9 9 10
5264.
0 1 2 3 6 7 8 94 5
+6.000
- 1.3754.625
6 61 2- -
5 4
5 9 9 10
4.625
0 1 2 3 6 7 8 94 5
