# Simplify 9/10*(-2/3)+(1/7-2/3)÷( square root of 343/7)

910⋅(-23)+(17-23)÷3437
To write 17 as a fraction with a common denominator, multiply by 33.
910⋅(-23)+17⋅33-233437
To write -23 as a fraction with a common denominator, multiply by 77.
910⋅(-23)+17⋅33-23⋅773437
Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.
Multiply 17 and 33.
910⋅(-23)+37⋅3-23⋅773437
Multiply 7 by 3.
910⋅(-23)+321-23⋅773437
Multiply 23 and 77.
910⋅(-23)+321-2⋅73⋅73437
Multiply 3 by 7.
910⋅(-23)+321-2⋅7213437
910⋅(-23)+321-2⋅7213437
Combine the numerators over the common denominator.
910⋅(-23)+3-2⋅7213437
Simplify the numerator.
Multiply -2 by 7.
910⋅(-23)+3-14213437
Subtract 14 from 3.
910⋅(-23)+-11213437
910⋅(-23)+-11213437
Simplify each term.
Cancel the common factor of 3.
Move the leading negative in -23 into the numerator.
910⋅-23+-11213437
Factor 3 out of 9.
3(3)10⋅-23+-11213437
Cancel the common factor.
3⋅310⋅-23+-11213437
Rewrite the expression.
310⋅-2+-11213437
310⋅-2+-11213437
Cancel the common factor of 2.
Factor 2 out of 10.
32(5)⋅-2+-11213437
Factor 2 out of -2.
32⋅5⋅(2⋅-1)+-11213437
Cancel the common factor.
32⋅5⋅(2⋅-1)+-11213437
Rewrite the expression.
35⋅-1+-11213437
35⋅-1+-11213437
Combine 35 and -1.
3⋅-15+-11213437
Multiply 3 by -1.
-35+-11213437
Move the negative in front of the fraction.
-35+-11213437
Cancel the common factor of 343 and 7.
Factor 7 out of 343.
-35+-11217⋅497
Cancel the common factors.
Factor 7 out of 7.
-35+-11217⋅497(1)
Cancel the common factor.
-35+-11217⋅497⋅1
Rewrite the expression.
-35+-1121491
Divide 49 by 1.
-35+-112149
-35+-112149
-35+-112149
Multiply the numerator by the reciprocal of the denominator.
-35+-1121⋅149
Move the negative in front of the fraction.
-35-1121⋅149
Simplify the denominator.
Rewrite 49 as 72.
-35-1121⋅172
Pull terms out from under the radical, assuming positive real numbers.
-35-1121⋅17
-35-1121⋅17
Multiply -1121⋅17.
Multiply 17 and 1121.
-35-117⋅21
Multiply 7 by 21.
-35-11147
-35-11147
-35-11147
To write -35 as a fraction with a common denominator, multiply by 147147.
-35⋅147147-11147
To write -11147 as a fraction with a common denominator, multiply by 55.
-35⋅147147-11147⋅55
Write each expression with a common denominator of 735, by multiplying each by an appropriate factor of 1.
Multiply 35 and 147147.
-3⋅1475⋅147-11147⋅55
Multiply 5 by 147.
-3⋅147735-11147⋅55
Multiply 11147 and 55.
-3⋅147735-11⋅5147⋅5
Multiply 147 by 5.
-3⋅147735-11⋅5735
-3⋅147735-11⋅5735
Combine the numerators over the common denominator.
-3⋅147-11⋅5735
Simplify the numerator.
Multiply -3 by 147.
-441-11⋅5735
Multiply -11 by 5.
-441-55735
Subtract 55 from -441.
-496735
-496735
Move the negative in front of the fraction.
-496735
The result can be shown in multiple forms.
Exact Form:
-496735
Decimal Form:
-0.67482993…
Simplify 9/10*(-2/3)+(1/7-2/3)÷( square root of 343/7)

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