why would i times this by three

Discussion in 'Algebra' started by kiallabrahams, Mar 8, 2024.

1. kiallabrahams

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In the equation 6 3/4=r/3 . You times both sides by three. why?

kiallabrahams, Mar 8, 2024
2. HallsofIvy

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To "solve for r" MEANS to get r by itself on one side of the equation: "r= something" or "something= r".
In 5 3/4= r/3" r is NOT by itself because it is divided by 3. To get rid of that 3, we need to do the opposite- and the opposite of "divide by 3" is "multiply by 3". And, of course, to keep things balanced we need to do the same thing to both sides of the equation.=

Multiplying r/3 by 3 gives r(3/3)= r(1)= r.
On the other side, either 3*5= 15 and 3*3/4= 9/4= 2 1/4 so 17 1/4
or 5 3/4= 20/4+ 3/4= 23/4 multiplying by 3, 69/4= 17 1/4.

HallsofIvy, Mar 8, 2024
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3. kiallabrahams

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yho bruh i wish u were my math teacher

kiallabrahams, Mar 9, 2024
4. RobertSmart

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"Solving for r" entails isolating the variable r on one side of the equation, typically in the form of "r = something" or "something = r". In the equation "5 3/4 = r/3", r is not isolated because it's divided by 3. To isolate r, we perform the opposite operation of division, which is multiplication. Maintaining balance, we apply the same operation to both sides of the equation.

Multiplying r/3 by 3 yields r(3/3) = r(1) = r. On the other side, we can calculate 3 * 5 = 15 and 3 * 3/4 = 9/4 = 2 1/4, thus 17 1/4. Alternatively, 5 3/4 can be expressed as 20/4 + 3/4 = 23/4, and multiplying by 3 gives 69/4 = 17 1/4.

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RobertSmart, Apr 22, 2024
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