Mental math: .25 + .45 + .65 + .85 +....+1.45=___The answer is 5.95. What is the best way to derive this mentally?

1 Answer

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lfryerda | High School Teacher | (Level 2) Educator

Posted on

Since each term in the sum is 0.2 higher than the term before it, we have the total sum:

`0.25+0.45+0.65+0.85+1.05+1.25+1.45`

for a total of 7 terms.  I find the 0.05 for each part to be annoying, so that's a total of 0.35, with the rest of the sum as 

`0.2+0.4+0.6+0.8+1.0+1.2+1.4`

Now, I add in groups of 1.0, so think in pairs:

`0.2+0.8=1.0`

`0.4+0.6=1.0`

`1.0=1.0`

with the last one getting its own group

`1.2+1.4=2.6`

This means when we add this up, we end up with

`3+2.6=5.6`

`5.6+0.35=5.95`

The total sum is 5.95