Basic Math Examples

Find the Mean 90 , 90 , 95 , 100 , 80 , 75 , 80 , 70 , 60 , 95 , 100 , 100 , 100 , 75 , 80 , 90 , 90 , 90 , 70 , 70 , 80 , 85 , 90 , 90 , 85
9090 , 90 , 95 , 100 , 80 , 75 , 80 , 70 , 60 , 95 , 100 , 100 , 100 , 75 , 80 , 90 , 90 , 90 , 70 , 70 , 80 , 85 , 90 , 90 , 85
Step 1
The mean of a set of numbers is the sum divided by the number of terms.
90+90+95+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2
Cancel the common factor of 90+90+95+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+85 and 25.
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Step 2.1
Factor 5 out of 90.
5(18)+90+95+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.2
Factor 5 out of 90.
518+518+95+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.3
Factor 5 out of 518+518.
5(18+18)+95+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.4
Factor 5 out of 95.
5(18+18)+5(19)+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.5
Factor 5 out of 5(18+18)+5(19).
5(18+18+19)+100+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.6
Factor 5 out of 100.
5(18+18+19)+5(20)+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.7
Factor 5 out of 5(18+18+19)+5(20).
5(18+18+19+20)+80+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.8
Factor 5 out of 80.
5(18+18+19+20)+5(16)+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.9
Factor 5 out of 5(18+18+19+20)+5(16).
5(18+18+19+20+16)+75+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.10
Factor 5 out of 75.
5(18+18+19+20+16)+5(15)+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.11
Factor 5 out of 5(18+18+19+20+16)+5(15).
5(18+18+19+20+16+15)+80+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.12
Factor 5 out of 80.
5(18+18+19+20+16+15)+5(16)+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.13
Factor 5 out of 5(18+18+19+20+16+15)+5(16).
5(18+18+19+20+16+15+16)+70+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.14
Factor 5 out of 70.
5(18+18+19+20+16+15+16)+5(14)+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.15
Factor 5 out of 5(18+18+19+20+16+15+16)+5(14).
5(18+18+19+20+16+15+16+14)+60+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.16
Factor 5 out of 60.
5(18+18+19+20+16+15+16+14)+5(12)+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.17
Factor 5 out of 5(18+18+19+20+16+15+16+14)+5(12).
5(18+18+19+20+16+15+16+14+12)+95+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.18
Factor 5 out of 95.
5(18+18+19+20+16+15+16+14+12)+5(19)+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.19
Factor 5 out of 5(18+18+19+20+16+15+16+14+12)+5(19).
5(18+18+19+20+16+15+16+14+12+19)+100+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.20
Factor 5 out of 100.
5(18+18+19+20+16+15+16+14+12+19)+5(20)+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.21
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19)+5(20).
5(18+18+19+20+16+15+16+14+12+19+20)+100+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.22
Factor 5 out of 100.
5(18+18+19+20+16+15+16+14+12+19+20)+5(20)+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.23
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20)+5(20).
5(18+18+19+20+16+15+16+14+12+19+20+20)+100+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.24
Factor 5 out of 100.
5(18+18+19+20+16+15+16+14+12+19+20+20)+5(20)+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.25
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20)+5(20).
5(18+18+19+20+16+15+16+14+12+19+20+20+20)+75+80+90+90+90+70+70+80+85+90+90+8525
Step 2.26
Factor 5 out of 75.
5(18+18+19+20+16+15+16+14+12+19+20+20+20)+5(15)+80+90+90+90+70+70+80+85+90+90+8525
Step 2.27
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20)+5(15).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15)+80+90+90+90+70+70+80+85+90+90+8525
Step 2.28
Factor 5 out of 80.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15)+5(16)+90+90+90+70+70+80+85+90+90+8525
Step 2.29
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15)+5(16).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16)+90+90+90+70+70+80+85+90+90+8525
Step 2.30
Factor 5 out of 90.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16)+5(18)+90+90+70+70+80+85+90+90+8525
Step 2.31
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16)+5(18).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18)+90+90+70+70+80+85+90+90+8525
Step 2.32
Factor 5 out of 90.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18)+5(18)+90+70+70+80+85+90+90+8525
Step 2.33
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18)+5(18).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18)+90+70+70+80+85+90+90+8525
Step 2.34
Factor 5 out of 90.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18)+5(18)+70+70+80+85+90+90+8525
Step 2.35
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18)+5(18).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18)+70+70+80+85+90+90+8525
Step 2.36
Factor 5 out of 70.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18)+5(14)+70+80+85+90+90+8525
Step 2.37
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18)+5(14).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14)+70+80+85+90+90+8525
Step 2.38
Factor 5 out of 70.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14)+5(14)+80+85+90+90+8525
Step 2.39
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14)+5(14).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14)+80+85+90+90+8525
Step 2.40
Factor 5 out of 80.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14)+5(16)+85+90+90+8525
Step 2.41
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14)+5(16).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16)+85+90+90+8525
Step 2.42
Factor 5 out of 85.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16)+5(17)+90+90+8525
Step 2.43
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16)+5(17).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17)+90+90+8525
Step 2.44
Factor 5 out of 90.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17)+5(18)+90+8525
Step 2.45
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17)+5(18).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18)+90+8525
Step 2.46
Factor 5 out of 90.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18)+5(18)+8525
Step 2.47
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18)+5(18).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18)+8525
Step 2.48
Factor 5 out of 85.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18)+5(17)25
Step 2.49
Factor 5 out of 5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18)+5(17).
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+17)25
Step 2.50
Cancel the common factors.
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Step 2.50.1
Factor 5 out of 25.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+17)5(5)
Step 2.50.2
Cancel the common factor.
5(18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+17)55
Step 2.50.3
Rewrite the expression.
18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
18+18+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3
Simplify the numerator.
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Step 3.1
Add 18 and 18.
36+19+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.2
Add 36 and 19.
55+20+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.3
Add 55 and 20.
75+16+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.4
Add 75 and 16.
91+15+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.5
Add 91 and 15.
106+16+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.6
Add 106 and 16.
122+14+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.7
Add 122 and 14.
136+12+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.8
Add 136 and 12.
148+19+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.9
Add 148 and 19.
167+20+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.10
Add 167 and 20.
187+20+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.11
Add 187 and 20.
207+20+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.12
Add 207 and 20.
227+15+16+18+18+18+14+14+16+17+18+18+175
Step 3.13
Add 227 and 15.
242+16+18+18+18+14+14+16+17+18+18+175
Step 3.14
Add 242 and 16.
258+18+18+18+14+14+16+17+18+18+175
Step 3.15
Add 258 and 18.
276+18+18+14+14+16+17+18+18+175
Step 3.16
Add 276 and 18.
294+18+14+14+16+17+18+18+175
Step 3.17
Add 294 and 18.
312+14+14+16+17+18+18+175
Step 3.18
Add 312 and 14.
326+14+16+17+18+18+175
Step 3.19
Add 326 and 14.
340+16+17+18+18+175
Step 3.20
Add 340 and 16.
356+17+18+18+175
Step 3.21
Add 356 and 17.
373+18+18+175
Step 3.22
Add 373 and 18.
391+18+175
Step 3.23
Add 391 and 18.
409+175
Step 3.24
Add 409 and 17.
4265
4265
Step 4
Divide.
85.2
 [x2  12  π  xdx ]