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raniacakes
05.05.2020 •
Mathematics
Simplify and solve (show work please)
5/7b+2/3(b+4/3)-9
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Ответ:
87b - 511
—————————
63
Step-by-step explanation:
Step by step solution :
Step 1 :
4
Simplify —
3
Equation at the end of step 1 :
5 2 4
((—•b)+(—•(b+—)))-9
7 3 3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
b b • 3
b = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
b • 3 + 4 3b + 4
————————— = ——————
3 3
Equation at the end of step 2 :
5 2 (3b+4)
((—•b)+(—•——————))-9
7 3 3
Step 3 :
2
Simplify —
3
Equation at the end of step 3 :
5 2 (3b + 4)
((— • b) + (— • ————————)) - 9
7 3 3
Step 4 :
Equation at the end of step 4 :
5 2 • (3b + 4)
((— • b) + ————————————) - 9
7 9
Step 5 :
5
Simplify —
7
Equation at the end of step 5 :
5 2 • (3b + 4)
((— • b) + ————————————) - 9
7 9
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : 9
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7101
3022
Product of all
Prime Factors 7963
Least Common Multiple:
63
Calculating Multipliers :
6.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 9
Right_M = L.C.M / R_Deno = 7
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 5b • 9
—————————————————— = ——————
L.C.M 63
R. Mult. • R. Num. 2 • (3b+4) • 7
—————————————————— = ——————————————
L.C.M 63
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
5b • 9 + 2 • (3b+4) • 7 87b + 56
——————————————————————— = ————————
63 63
Equation at the end of step 6 :
(87b + 56)
—————————— - 9
63
Step 7 :
Rewriting the whole as an Equivalent Fraction :
7.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 63 as the denominator :
9 9 • 63
9 = — = ——————
1 63
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
(87b+56) - (9 • 63) 87b - 511
——————————————————— = —————————
63 63
Final result :
87b - 511
—————————
63
Ответ:
ok
Step-by-step explanation:
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