To calculate quickly:

TAKE the biggest number: 10.

Take the next higher number: 11.

One is EVEN, which is it? 10.

Divide the even number by 2. 10/2=5.

Multiply those two numbers: 5*11=55 (MEMORIZED)

Another example: Calculate 1+2+3+4+…+55+56 quickly.

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Take the biggest number: 56.

Take the next higher number: 57.

One of those is even, which is it? 56.

Divide the even number by 2. 56/2=28.

Multiply those two numbers: 28*57=(30–2)*(60–3)

=30*60–2*60–3*30+2*3

=1800–120–90+6

=1800–210+6

=1596

One last example: Calculate 1+2+3+4+…+1290+1291 quickly.

Take the biggest number: 1291.

Take the next higher number: 1292.

One of those is even, which is it? 1292.

Divide the even number by 2. 1292/2=646.

Multiply those two numbers: 646*1291=(650–4)*(1300–9)

=650*1300–4*1300–9*650+4*9

=(65*13)*1000–5200–(9*65)*10+36

=(60+5)*(10+3)*1000–5200-(10–1)*65*10+36

=(60*10+5*10+3*60+5*3)*1000–5200-(650–65)*10+36

=(600+50+180+15)*1000–5200–5850+36

=845000–11050+36

=833986