Evaluate 1/4+13/120+13/120+13/240+1/24+1/20+1/20+1/20+13/480+13/480+13/480+13/480+1/32+1/72+1/72+1/72+1/144+1/144+1/144+1/144+1/144+1/192+1/192+1/432+1/432+1/432+13/240

Math
14+13120+13120+13240+124+120+120+120+13480+13480+13480+13480+132+172+172+172+1144+1144+1144+1144+1144+1192+1192+1432+1432+1432+13240
Simplify terms.
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Combine fractions with similar denominators.
14+13+13120+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Add 13 and 13.
14+26120+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor of 26 and 120.
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Factor 2 out of 26.
14+2(13)120+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factors.
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Factor 2 out of 120.
14+2⋅132⋅60+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor.
14+2⋅132⋅60+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Rewrite the expression.
14+1360+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13+13240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Add 13 and 13.
14+1360+26240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor of 26 and 240.
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Factor 2 out of 26.
14+1360+2(13)240+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factors.
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Factor 2 out of 240.
14+1360+2⋅132⋅120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor.
14+1360+2⋅132⋅120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Rewrite the expression.
14+1360+13120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+1+1+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Simplify the numerator.
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Add 1 and 1.
14+1360+13120+124+2+120+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Add 2 and 1.
14+1360+13120+124+320+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13+13+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Simplify the numerator.
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Add 13 and 13.
14+1360+13120+124+320+26+13+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Add 26 and 13.
14+1360+13120+124+320+39+13480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Add 39 and 13.
14+1360+13120+124+320+52480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+52480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor of 52 and 480.
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Factor 4 out of 52.
14+1360+13120+124+320+4(13)480+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factors.
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Factor 4 out of 480.
14+1360+13120+124+320+4⋅134⋅120+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor.
14+1360+13120+124+320+4⋅134⋅120+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Rewrite the expression.
14+1360+13120+124+320+13120+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+1+1+172+1+1+1+1+1144+1+1192+1+1+1432
Simplify the numerator.
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Add 1 and 1.
14+1360+13120+124+320+13120+132+2+172+1+1+1+1+1144+1+1192+1+1+1432
Add 2 and 1.
14+1360+13120+124+320+13120+132+372+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+372+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor of 3 and 72.
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Factor 3 out of 3.
14+1360+13120+124+320+13120+132+3(1)72+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factors.
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Factor 3 out of 72.
14+1360+13120+124+320+13120+132+3⋅13⋅24+1+1+1+1+1144+1+1192+1+1+1432
Cancel the common factor.
14+1360+13120+124+320+13120+132+3⋅13⋅24+1+1+1+1+1144+1+1192+1+1+1432
Rewrite the expression.
14+1360+13120+124+320+13120+132+124+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+124+1+1+1+1+1144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+124+1+1+1+1+1144+1+1192+1+1+1432
Simplify the numerator.
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Add 1 and 1.
14+1360+13120+124+320+13120+132+124+2+1+1+1144+1+1192+1+1+1432
Add 2 and 1.
14+1360+13120+124+320+13120+132+124+3+1+1144+1+1192+1+1+1432
Add 3 and 1.
14+1360+13120+124+320+13120+132+124+4+1144+1+1192+1+1+1432
Add 4 and 1.
14+1360+13120+124+320+13120+132+124+5144+1+1192+1+1+1432
14+1360+13120+124+320+13120+132+124+5144+1+1192+1+1+1432
Reduce the expression by cancelling the common factors.
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Add 1 and 1.
14+1360+13120+124+320+13120+132+124+5144+2192+1+1+1432
Cancel the common factor of 2 and 192.
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Factor 2 out of 2.
14+1360+13120+124+320+13120+132+124+5144+2(1)192+1+1+1432
Cancel the common factors.
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Factor 2 out of 192.
14+1360+13120+124+320+13120+132+124+5144+2⋅12⋅96+1+1+1432
Cancel the common factor.
14+1360+13120+124+320+13120+132+124+5144+2⋅12⋅96+1+1+1432
Rewrite the expression.
14+1360+13120+124+320+13120+132+124+5144+196+1+1+1432
14+1360+13120+124+320+13120+132+124+5144+196+1+1+1432
14+1360+13120+124+320+13120+132+124+5144+196+1+1+1432
14+1360+13120+124+320+13120+132+124+5144+196+1+1+1432
Simplify the numerator.
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Add 1 and 1.
14+1360+13120+124+320+13120+132+124+5144+196+2+1432
Add 2 and 1.
14+1360+13120+124+320+13120+132+124+5144+196+3432
14+1360+13120+124+320+13120+132+124+5144+196+3432
Simplify terms.
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Cancel the common factor of 3 and 432.
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Factor 3 out of 3.
14+1360+13120+124+320+13120+132+124+5144+196+3(1)432
Cancel the common factors.
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Factor 3 out of 432.
14+1360+13120+124+320+13120+132+124+5144+196+3⋅13⋅144
Cancel the common factor.
14+1360+13120+124+320+13120+132+124+5144+196+3⋅13⋅144
Rewrite the expression.
14+1360+13120+124+320+13120+132+124+5144+196+1144
14+1360+13120+124+320+13120+132+124+5144+196+1144
14+1360+13120+124+320+13120+132+124+5144+196+1144
Combine fractions with similar denominators.
14+1360+13+13120+1+124+320+132+5+1144+196
Add 13 and 13.
14+1360+26120+1+124+320+132+5+1144+196
Cancel the common factor of 26 and 120.
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Factor 2 out of 26.
14+1360+2(13)120+1+124+320+132+5+1144+196
Cancel the common factors.
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Factor 2 out of 120.
14+1360+2⋅132⋅60+1+124+320+132+5+1144+196
Cancel the common factor.
14+1360+2⋅132⋅60+1+124+320+132+5+1144+196
Rewrite the expression.
14+1360+1360+1+124+320+132+5+1144+196
14+1360+1360+1+124+320+132+5+1144+196
14+1360+1360+1+124+320+132+5+1144+196
Add 1 and 1.
14+1360+1360+224+320+132+5+1144+196
Cancel the common factor of 2 and 24.
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Factor 2 out of 2.
14+1360+1360+2(1)24+320+132+5+1144+196
Cancel the common factors.
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Factor 2 out of 24.
14+1360+1360+2⋅12⋅12+320+132+5+1144+196
Cancel the common factor.
14+1360+1360+2⋅12⋅12+320+132+5+1144+196
Rewrite the expression.
14+1360+1360+112+320+132+5+1144+196
14+1360+1360+112+320+132+5+1144+196
14+1360+1360+112+320+132+5+1144+196
Add 5 and 1.
14+1360+1360+112+320+132+6144+196
Cancel the common factor of 6 and 144.
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Factor 6 out of 6.
14+1360+1360+112+320+132+6(1)144+196
Cancel the common factors.
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Factor 6 out of 144.
14+1360+1360+112+320+132+6⋅16⋅24+196
Cancel the common factor.
14+1360+1360+112+320+132+6⋅16⋅24+196
Rewrite the expression.
14+1360+1360+112+320+132+124+196
14+1360+1360+112+320+132+124+196
14+1360+1360+112+320+132+124+196
Combine fractions with similar denominators.
14+13+1360+112+320+132+124+196
Add 13 and 13.
14+2660+112+320+132+124+196
Cancel the common factor of 26 and 60.
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Factor 2 out of 26.
14+2(13)60+112+320+132+124+196
Cancel the common factors.
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Factor 2 out of 60.
14+2⋅132⋅30+112+320+132+124+196
Cancel the common factor.
14+2⋅132⋅30+112+320+132+124+196
Rewrite the expression.
14+1330+112+320+132+124+196
14+1330+112+320+132+124+196
14+1330+112+320+132+124+196
14+1330+112+320+132+124+196
Find the common denominator.
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Multiply 14 by 120120.
14⋅120120+1330+112+320+132+124+196
Combine.
1⋅1204⋅120+1330+112+320+132+124+196
Multiply 1330 by 1616.
1⋅1204⋅120+1330⋅1616+112+320+132+124+196
Combine.
1⋅1204⋅120+13⋅1630⋅16+112+320+132+124+196
Multiply 112 by 4040.
1⋅1204⋅120+13⋅1630⋅16+112⋅4040+320+132+124+196
Combine.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+320+132+124+196
Multiply 320 by 2424.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+320⋅2424+132+124+196
Combine.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+132+124+196
Multiply 132 by 1515.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+132⋅1515+124+196
Combine.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+124+196
Multiply 124 by 2020.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+124⋅2020+196
Combine.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+196
Multiply 196 by 55.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+196⋅55
Combine.
1⋅1204⋅120+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Multiply 4 by 120.
1⋅120480+13⋅1630⋅16+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Reorder the factors of 30⋅16.
1⋅120480+13⋅1616⋅30+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Multiply 16 by 30.
1⋅120480+13⋅16480+1⋅4012⋅40+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Multiply 12 by 40.
1⋅120480+13⋅16480+1⋅40480+3⋅2420⋅24+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Multiply 20 by 24.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅1532⋅15+1⋅2024⋅20+1⋅596⋅5
Reorder the factors of 32⋅15.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅1515⋅32+1⋅2024⋅20+1⋅596⋅5
Multiply 15 by 32.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅2024⋅20+1⋅596⋅5
Reorder the factors of 24⋅20.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅2020⋅24+1⋅596⋅5
Multiply 20 by 24.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅20480+1⋅596⋅5
Reorder the factors of 96⋅5.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅20480+1⋅55⋅96
Multiply 5 by 96.
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅20480+1⋅5480
1⋅120480+13⋅16480+1⋅40480+3⋅24480+1⋅15480+1⋅20480+1⋅5480
Combine fractions.
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Combine fractions with similar denominators.
1⋅120+13⋅16+1⋅40+3⋅24+1⋅15+1⋅20+1⋅5480
Multiply.
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Multiply 120 by 1.
120+13⋅16+1⋅40+3⋅24+1⋅15+1⋅20+1⋅5480
Multiply 13 by 16.
120+208+1⋅40+3⋅24+1⋅15+1⋅20+1⋅5480
Multiply 40 by 1.
120+208+40+3⋅24+1⋅15+1⋅20+1⋅5480
Multiply 3 by 24.
120+208+40+72+1⋅15+1⋅20+1⋅5480
Simplify.
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Multiply 15 by 1.
120+208+40+72+15+1⋅20+1⋅5480
Multiply 20 by 1.
120+208+40+72+15+20+1⋅5480
Multiply 5 by 1.
120+208+40+72+15+20+5480
120+208+40+72+15+20+5480
120+208+40+72+15+20+5480
120+208+40+72+15+20+5480
Simplify the numerator.
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Add 120 and 208.
328+40+72+15+20+5480
Add 328 and 40.
368+72+15+20+5480
Add 368 and 72.
440+15+20+5480
Add 440 and 15.
455+20+5480
Add 455 and 20.
475+5480
Add 475 and 5.
480480
480480
Divide 480 by 480.
1
Evaluate 1/4+13/120+13/120+13/240+1/24+1/20+1/20+1/20+13/480+13/480+13/480+13/480+1/32+1/72+1/72+1/72+1/144+1/144+1/144+1/144+1/144+1/192+1/192+1/432+1/432+1/432+13/240

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