Simplify 2/3 pq (- ( 9)/10 p^2 q^2)
Answers
Answer:
STEP
1
:
1
Simplify —
3
Equation at the end of step
1
:
1 1 1
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-((—•(p2))•(q2)))+((—•p)•(q2)))-((—•p)•q))+5
2 3 3
STEP
2
:
1
Simplify —
3
Equation at the end of step
2
:
1 1 pq
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-((—•(p2))•(q2)))+((—•p)•q2))-——)+5
2 3 3
STEP
3
:
Equation at the end of step 3
1 pq2 pq
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-((—•(p2))•(q2)))+———)-——)+5
2 3 3
STEP
4
:
1
Simplify —
2
Equation at the end of step
4
:
1 pq2 pq
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-((—•p2)•q2))+———)-——)+5
2 3 3
STEP
5
:
Equation at the end of step 5
p2 pq2 pq
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-(——•q2))+———)-——)+5
2 3 3
STEP
6
:
Equation at the end of step 6
p2q2 pq2 pq
((((((((2•(p2))•(q2))-(3p•(q2)))+3pq)-10)-————)+———)-——)+5
2 3 3
STEP
7
:
Equation at the end of step
7
:
p2q2 pq2 pq
((((((((2•(p2))•(q2))-3pq2)+3pq)-10)-————)+———)-——)+5
2 3 3
STEP
8
:
Equation at the end of step
8
:
p2q2 pq2 pq
(((((((2p2•q2)-3pq2)+3pq)-10)-————)+———)-——)+5
2 3 3
STEP
9
:
Rewriting the whole as an Equivalent Fraction
9.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
2p2q2 - 3pq2 + 3pq - 10 (2p2q2 - 3pq2 + 3pq - 10) • 2
2p2q2 - 3pq2 + 3pq - 10 = ——————————————————————— = —————————————————————————————
1 2
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 :
9.2 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:
(2p2q2-3pq2+3pq-10) • 2 - (p2q2) 3p2q2 - 6pq2 + 6pq - 20
———————————————————————————————— = ———————————————————————
2 2
Equation at the end of step
9
:
(3p2q2 - 6pq2 + 6pq - 20) pq2 pq
((————————————————————————— + ———) - ——) + 5
2 3 3
STEP
10
:
Calculating the Least Common Multiple :
10.1 Find the Least Common Multiple
The left denominator is : 2
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}
2 1 0 1
3 0 1 1
Product of all
Prime Factors 2 3 6
Least Common Multiple:
6
Calculating Multipliers :
10.2 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 = 3
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
10.3 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. (3p2q2-6pq2+6pq-20) • 3
—————————————————— = ———————————————————————
L.C.M 6
R. Mult. • R. Num. pq2 • 2
—————————————————— = ———————
L.C.M 6
Adding fractions that have a common denominator :
10.4 Adding up the two equivalent fractions
(3p2q2-6pq2+6pq-20) • 3 + pq2 • 2 9p2q2 - 16pq2 + 18pq - 60
————————————————————————————————— = —————————————————————————
6 6
Equation at the end of step
10
:
(9p2q2 - 16pq2 + 18pq - 60) pq
(——————————————————————————— - ——) + 5
6 3
STEP
11
:
Calculating the Least Common Multiple :
11.1 Find the Least Common Multiple
The left denominator is : 6
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}
2 1 0 1
3 1 1 1
Product of all
Prime Factors 6 3 6
Least Common Multiple:
6
Calculating Multipliers :
11.2 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 = 2
Making Equivalent Fractions :
11.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (9p2q2-16pq2+18pq-60)
—————————————————— = —————————————————————
L.C.M 6
R. Mult. • R. Num. pq • 2
—————————————————— = ——————
L.C.M 6
Adding fractions that have a common denominator :
11.4 Adding up the two equivalent fractions
(9p2q2-16pq2+18pq-60) - (pq • 2) 9p2q2 - 16pq2 + 16pq - 60
———————————————————————————————— = —————————————————————————
6 6
Equation at the end of step
11
:
(9p2q2 - 16pq2 + 16pq - 60)
——————————————————————————— + 5
6
STEP
12
:
Rewriting the whole as an Equivalent Fraction :
12.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 6 as the de
Explanation:
Answer:
HOPE IT WILLL HELP U...
PLSSS MARK AS BRAINLIEST...
Explanation:
