Factor (5 1/3)m-30-1 1/9m-18

Math
(513)m-30-119m-18
Regroup terms.
(513)m-30-119m-18
Convert 513 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
(5+13)m-30-119m-18
Add 5 and 13.
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To write 5 as a fraction with a common denominator, multiply by 33.
(5⋅33+13)m-30-119m-18
Combine 5 and 33.
(5⋅33+13)m-30-119m-18
Combine the numerators over the common denominator.
5⋅3+13m-30-119m-18
Simplify the numerator.
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Multiply 5 by 3.
15+13m-30-119m-18
Add 15 and 1.
163m-30-119m-18
163m-30-119m-18
163m-30-119m-18
163m-30-119m-18
Combine 163 and m.
16m3-30-119m-18
Factor 2 out of 16m3-30.
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Factor 2 out of 16m3.
28m3-30-119m-18
Factor 2 out of -30.
28m3+2(-15)-119m-18
Factor 2 out of 28m3+2(-15).
2(8m3-15)-119m-18
2(8m3-15)-119m-18
Convert 119 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
2(8m3-15)-(1+19)m-18
Add 1 and 19.
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Write 1 as a fraction with a common denominator.
2(8m3-15)-(99+19)m-18
Combine the numerators over the common denominator.
2(8m3-15)-9+19m-18
Add 9 and 1.
2(8m3-15)-109m-18
2(8m3-15)-109m-18
2(8m3-15)-109m-18
Combine m and 109.
2(8m3-15)-m⋅109-18
Move 10 to the left of m.
2(8m3-15)-10⋅m9-18
Multiply 10 by m.
2(8m3-15)-10m9-18
Rewrite -10m9-18 in a factored form.
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Factor -1 out of -10m9-18.
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Factor -1 out of -10m9.
2(8m3-15)-(10m9)-18
Rewrite -18 as -1(18).
2(8m3-15)-(10m9)-1(18)
Factor -1 out of -(10m9)-1(18).
2(8m3-15)-(10m9+18)
2(8m3-15)-(10m9+18)
Factor.
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Factor 2 out of 10m9+18.
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Factor 2 out of 10m9.
2(8m3-15)-(25m9+18)
Factor 2 out of 18.
2(8m3-15)-(25m9+2(9))
Factor 2 out of 25m9+2(9).
2(8m3-15)-(2(5m9+9))
2(8m3-15)-(2(5m9+9))
Remove unnecessary parentheses.
2(8m3-15)-1⋅2(5m9+9)
2(8m3-15)-1⋅2(5m9+9)
Multiply -1 by 2.
2(8m3-15)-2(5m9+9)
2(8m3-15)-2(5m9+9)
Factor 2 out of 2(8m3-15)-2(5m9+9).
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Factor 2 out of -2(5m9+9).
2(8m3-15)+2(-(5m9+9))
Factor 2 out of 2(8m3-15)+2(-(5m9+9)).
2(8m3-15-(5m9+9))
2(8m3-15-(5m9+9))
Apply the distributive property.
2(8m3-15-5m9-1⋅9)
Multiply -1 by 9.
2(8m3-15-5m9-9)
To write 8m3 as a fraction with a common denominator, multiply by 33.
2(8m3⋅33-5m9-15-9)
Write each expression with a common denominator of 9, by multiplying each by an appropriate factor of 1.
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Multiply 8m3 and 33.
2(8m⋅33⋅3-5m9-15-9)
Multiply 3 by 3.
2(8m⋅39-5m9-15-9)
2(8m⋅39-5m9-15-9)
Combine the numerators over the common denominator.
2(8m⋅3-5m9-15-9)
To write -15 as a fraction with a common denominator, multiply by 99.
2(8m⋅3-5m9-15⋅99-9)
Combine -15 and 99.
2(8m⋅3-5m9+-15⋅99-9)
Combine the numerators over the common denominator.
2(8m⋅3-5m-15⋅99-9)
To write -9 as a fraction with a common denominator, multiply by 99.
2(8m⋅3-5m-15⋅99-9⋅99)
Combine -9 and 99.
2(8m⋅3-5m-15⋅99+-9⋅99)
Combine the numerators over the common denominator.
28m⋅3-5m-15⋅9-9⋅99
Reorder terms.
23⋅8m-5m-9⋅9-15⋅99
Rewrite 3⋅8m-5m-9⋅9-15⋅99 in a factored form.
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Multiply 3 by 8.
224m-5m-9⋅9-15⋅99
Multiply -9 by 9.
224m-5m-81-15⋅99
Multiply -15 by 9.
224m-5m-81-1359
Subtract 5m from 24m.
219m-81-1359
Subtract 135 from -81.
219m-2169
219m-2169
Factor (5 1/3)m-30-1 1/9m-18

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