Simplify using disterbutive property of mutiplication (3/8 × -4/5) + (7/9 × 3/8) - (3/8 × -8/10)PLEASE HELP ME FAST
Accepted Solution
A:
Answer: 7 —— = 0.29167 24 Step-by-step explanation:Step 1 :
-4
Simplify ——
5 Equation at the end of step 1 :
3 -4 7 3 3 -4
((—•——)+(—•—))-(—•——)
8 5 9 8 8 5 Step 2 :
3
Simplify —
8
Equation at the end of step 2 :
3 -4 7 3 3 -4
((—•——)+(—•—))-(—•——)
8 5 9 8 8 5 Step 3 :
3
Simplify —
8
Equation at the end of step 3 :
3 -4 7 3 -3
((—•——)+(—•—))-——
8 5 9 8 10
Step 4 :
7
Simplify —
9
Equation at the end of step 4 :
3 -4 7 3 -3
((—•——)+(—•—))-——
8 5 9 8 10
Step 5 :
-4
Simplify ——
5 Equation at the end of step 5 :
3 -4 7 -3
((— • ——) + ——) - ——
8 5 24 10
Step 6 :
3
Simplify —
8
Equation at the end of step 6 :
3 -4 7 -3
((— • ——) + ——) - ——
8 5 24 10Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 10
The right denominator is : 24
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 3 3
5 1 0 1
3 0 1 1
Product of all Prime Factors 10 24 120
Least Common Multiple:
120
Calculating Multipliers :
7.2 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 = 12
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
7.3 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 • 12
—————————————————— = ———————
L.C.M 120
R. Mult. • R. Num. 7 • 5
—————————————————— = —————
L.C.M 120 Adding fractions that have a common denominator :
7.4 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 • 12 + 7 • 5 -1
——————————————— = ———
120 120
Equation at the end of step 7 :
-1 -3
——— - ——
120 10
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : 120
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} 2 3 1 3
3 1 0 1
5 1 1 1
Product of all Prime Factors 120 10 120
Least Common Multiple:
120
Calculating Multipliers :
8.2 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 = 12
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. -1
—————————————————— = ———
L.C.M 120
R. Mult. • R. Num. -3 • 12
—————————————————— = ———————
L.C.M 120
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
-1 - (-3 • 12) 7
—————————————— = ——
120 24