4/9=x/27

This faces adding, subtracting and also finding the least typical multiple.




You are watching: 4:9 = x:27

Step by step Solution

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Rearrange:

Rearrange the equation by individually what is come the ideal of the equal sign from both sides of the equation : 4/9-(x/27)=0

Step by action solution :

Step 1 :

x leveling —— 27Equation in ~ the end of action 1 : 4 x — - —— = 0 9 27

Step 2 :

4 simplify — 9Equation at the end of step 2 : 4 x — - —— = 0 9 27

Step 3 :

Calculating the Least typical Multiple :3.1 uncover the Least typical Multiple The left denominator is : 9 The right denominator is : 27

Number that times every prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
3233
Product that allPrime Factors92727

Least usual Multiple: 27

Calculating multiplier :

3.2 calculate multipliers because that the two fractions denote the Least common Multiple through L.C.M represent the Left Multiplier by Left_M represent the ideal Multiplier through Right_M signify the Left Deniminator through L_Deno denote the ideal Multiplier through R_DenoLeft_M=L.C.M/L_Deno=3Right_M=L.C.M/R_Deno=1

Making tantamount Fractions :

3.3 Rewrite the two fractions into identical fractionsTwo fountain are dubbed equivalent if they have the exact same numeric value. For example : 1/2 and also 2/4 room equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are tantamount as well. To calculation equivalent portion , multiply the molecule of every fraction, by its corresponding Multiplier.

L. Mult. • L. Num. 4 • 3 —————————————————— = ————— L.C.M 27 R. Mult. • R.

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Num. X —————————————————— = —— L.C.M 27Adding fountain that have a common denominator :3.4 including up the two identical fractions include the two indistinguishable fractions which now have actually a typical denominatorCombine the molecule together, put the sum or difference over the typical denominator then reduce to lowest state if possible:

4 • 3 - (x) 12 - x ——————————— = —————— 27 27 Equation in ~ the end of step 3 : 12 - x —————— = 0 27

Step 4 :

When a fraction equals zero :4.1 as soon as a portion equals zero ...Where a fraction equals zero, its numerator, the part which is over the portion line, must equal zero.Now,to remove the denominator, Tiger multiplys both sides of the equation through the denominator.Here"s how:

12-x ———— • 27 = 0 • 27 27 Now, ~ above the left hand side, the 27 cancels out the denominator, while, top top the best hand side, zero times anything is quiet zero.The equation now takes the shape:12-x=0

Solving a single Variable Equation:4.2Solve:-x+12 = 0Subtract 12 from both sides of the equation:-x = -12 main point both sides of the equation through (-1) : x = 12