Question

I am working percentages increases and decreases with problems like From 24 pencils to 30 pencils (increase  question) or From 20 miles to 11 miles ( decrease question) How can I check my answers of percentages to make sure they work? Please help!

Answer 1

24 pencils = 100%
30 pencils = ___%
30 - 24 = 6, so:

24 / 6 = 4 (it means that there are 4 sixes in 100%)
100% / 4 = 25%

Check: 25% * 24 = 25/100 * 24 = 1/4 * 24 = 6
30 - 6 = 24 (correct)
Answer: There was an increase by 25%

20 miles = 100%
11 miles = ___%
1 mile = 100% / 20 = 5%, so:

5 * 11 = 55 [percent]
100% - 55% = 45%

Check: 45% * 20 = 45/100 * 20 = 45/10 * 2 = 9/2 * 2 = 9
20 - 9 = 11 (correct)
Abswer: There was a decrease by 45%