Evaluate 4 1/2-3 1/4+(6 1/5-5 1/6)

Math
412-314+(615-516)
Remove parentheses.
412-314+615-516
Convert 412 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
4+12-314+615-516
Add 4 and 12.
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To write 4 as a fraction with a common denominator, multiply by 22.
4⋅22+12-314+615-516
Combine 4 and 22.
4⋅22+12-314+615-516
Combine the numerators over the common denominator.
4⋅2+12-314+615-516
Simplify the numerator.
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Multiply 4 by 2.
8+12-314+615-516
Add 8 and 1.
92-314+615-516
92-314+615-516
92-314+615-516
92-314+615-516
Convert 314 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
92-(3+14)+615-516
Add 3 and 14.
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To write 3 as a fraction with a common denominator, multiply by 44.
92-(3⋅44+14)+615-516
Combine 3 and 44.
92-(3⋅44+14)+615-516
Combine the numerators over the common denominator.
92-3⋅4+14+615-516
Simplify the numerator.
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Multiply 3 by 4.
92-12+14+615-516
Add 12 and 1.
92-134+615-516
92-134+615-516
92-134+615-516
92-134+615-516
Convert 615 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
92-134+6+15-516
Add 6 and 15.
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To write 6 as a fraction with a common denominator, multiply by 55.
92-134+6⋅55+15-516
Combine 6 and 55.
92-134+6⋅55+15-516
Combine the numerators over the common denominator.
92-134+6⋅5+15-516
Simplify the numerator.
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Multiply 6 by 5.
92-134+30+15-516
Add 30 and 1.
92-134+315-516
92-134+315-516
92-134+315-516
92-134+315-516
Convert 516 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
92-134+315-(5+16)
Add 5 and 16.
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To write 5 as a fraction with a common denominator, multiply by 66.
92-134+315-(5⋅66+16)
Combine 5 and 66.
92-134+315-(5⋅66+16)
Combine the numerators over the common denominator.
92-134+315-5⋅6+16
Simplify the numerator.
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Multiply 5 by 6.
92-134+315-30+16
Add 30 and 1.
92-134+315-316
92-134+315-316
92-134+315-316
92-134+315-316
To write 92 as a fraction with a common denominator, multiply by 22.
92⋅22-134+315-316
Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.
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Multiply 92 and 22.
9⋅22⋅2-134+315-316
Multiply 2 by 2.
9⋅24-134+315-316
9⋅24-134+315-316
Combine the numerators over the common denominator.
9⋅2-134+315-316
Simplify the numerator.
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Multiply 9 by 2.
18-134+315-316
Subtract 13 from 18.
54+315-316
54+315-316
To write 54 as a fraction with a common denominator, multiply by 55.
54⋅55+315-316
To write 315 as a fraction with a common denominator, multiply by 44.
54⋅55+315⋅44-316
Write each expression with a common denominator of 20, by multiplying each by an appropriate factor of 1.
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Multiply 54 and 55.
5⋅54⋅5+315⋅44-316
Multiply 4 by 5.
5⋅520+315⋅44-316
Multiply 315 and 44.
5⋅520+31⋅45⋅4-316
Multiply 5 by 4.
5⋅520+31⋅420-316
5⋅520+31⋅420-316
Combine the numerators over the common denominator.
5⋅5+31⋅420-316
Simplify the numerator.
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Multiply 5 by 5.
25+31⋅420-316
Multiply 31 by 4.
25+12420-316
Add 25 and 124.
14920-316
14920-316
To write 14920 as a fraction with a common denominator, multiply by 33.
14920⋅33-316
To write -316 as a fraction with a common denominator, multiply by 1010.
14920⋅33-316⋅1010
Write each expression with a common denominator of 60, by multiplying each by an appropriate factor of 1.
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Multiply 14920 and 33.
149⋅320⋅3-316⋅1010
Multiply 20 by 3.
149⋅360-316⋅1010
Multiply 316 and 1010.
149⋅360-31⋅106⋅10
Multiply 6 by 10.
149⋅360-31⋅1060
149⋅360-31⋅1060
Combine the numerators over the common denominator.
149⋅3-31⋅1060
Simplify the numerator.
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Multiply 149 by 3.
447-31⋅1060
Multiply -31 by 10.
447-31060
Subtract 310 from 447.
13760
13760
The result can be shown in multiple forms.
Exact Form:
13760
Decimal Form:
2.283‾
Mixed Number Form:
21760
Evaluate 4 1/2-3 1/4+(6 1/5-5 1/6)

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