Simplify ( 3 -7÷ -9 ) × -4 .
Answers
104
——— = 1.65079
63
Step-by-step explanation:
Step by step solution :
Step 1 :
2
Simplify —
3
Equation at the end of step 1 :
3 5 2
(— + —) - (0 - —)
7 9 3
Step 2 :
5
Simplify —
9
Equation at the end of step 2 :
3 5 -2
(— + —) - ——
7 9 3
Step 3 :
3
Simplify —
7
Equation at the end of step 3 :
3 5 -2
(— + —) - ——
7 9 3
Step 4 :
Calculating the Least Common Multiple :
4.1 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}
7 1 0 1
3 0 2 2
Product of all
Prime Factors 7 9 63
Least Common Multiple:
63
Calculating Multipliers :
4.2 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 :
4.3 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. 3 • 9
—————————————————— = —————
L.C.M 63
R. Mult. • R. Num. 5 • 7
—————————————————— = —————
L.C.M 63
Adding fractions that have a common denominator :
4.4 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:
3 • 9 + 5 • 7 62
————————————— = ——
63 63
Equation at the end of step 4 :
62 -2
—— - ——
63 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 63
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 2 1 2
7 1 0 1
Product of all
Prime Factors 63 3 63
Least Common Multiple:
63
Calculating Multipliers :
5.2 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 = 1
Right_M = L.C.M / R_Deno = 21
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 62
—————————————————— = ——
L.C.M 63
R. Mult. • R. Num. -2 • 21
—————————————————— = ———————
L.C.M 63
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
62 - (-2 • 21) 104
—————————————— = ———
63 63
Final result :
104
——— = 1.65079
63
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