This document provides guidance on estimating sums and differences of fractions by rounding fractions to benchmarks of 0, 1/2, or 1. It explains that benchmarks are easy reference numbers to use when estimating. Examples are provided that show how to change each fraction in a sum or difference to the nearest benchmark, then calculate the sum or difference. For mixed numbers, the fraction part should be rounded up to 1 if it is greater than 1/2, or rounded down to 0 if it is less than 1/2 before calculating. This allows for quick estimation of fraction calculations.

1. Estimating Sums and Differences
Lesson 6-5

2. Benchmark Numbers
A benchmark is a number that is easy to use when you estimate.
When estimating the sums and differences of fractions, we use the
benchmarks 0, ½, and 1.

3. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
+

4. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
+

5. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
½ +

6. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
½ +

7. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
½ + 0

8. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
½ + 0 =

9. • Change each fraction to 0, ½, or 1.
• Add or subtract.
5 + 3
11 25
½ + 0 = ½

10. Example 2
7 + 4
15 9
+

11. Example 2
7 + 4
15 9
+

12. Example 2
7 + 4
15 9
½ +

13. Example 2
7 + 4
15 9
½ +

14. Example 2
7 + 4
15 9
½ + ½

15. Example 2
7 + 4
15 9
½ + ½ =

16. Example 2
7 + 4
15 9
½ + ½ = 1

17. Estimating Mixed Numbers
• If you have mixed numbers, then round the
fraction part up to 1 or down to 0.
• If the fraction is greater than ½, then round
up to 1.
• If it is less than ½, then round down to 0.

18. Example
15 3
4 10 1
8

19. Example
15 3
4 10 1
8

20. Example
15 3
4 10 1
8
16

21. Example
15 3
4 10 1
8
16

22. Example
15 3
4 10 1
8
16 10

23. Example
15 3
4 10 1
8
16 10 =

24. Example
15 3
4 10 1
8
16 10 =6

25. Homework Time