Which of the equations would be completely cleared of decimals if both sides were multiplied by 100?

Understand the Problem

The question is asking which of the provided equations would have all decimals removed if both sides are multiplied by 100. This involves identifying the equation where multiplying by 100 results in all whole numbers.

Answer

The equation that would be completely cleared of decimals is: $$ 18.25 - 3.4x = 2.4x $$

Steps to Solve

Analyze Equation A: $0.2x + 0.521 = 0.32$

Multiply each term by 100: $$ 100(0.2x) + 100(0.521) = 100(0.32) $$ This simplifies to: $$ 20x + 52.1 = 32 $$ The term $52.1$ still has a decimal, so this equation does not work.

Analyze Equation B: $2.672 - 1.52x = 4.8$

Multiply each term by 100: $$ 100(2.672) - 100(1.52x) = 100(4.8) $$ This simplifies to: $$ 267.2 - 152x = 480 $$ The term $267.2$ still has a decimal, so this equation does not work.

Analyze Equation C: $6.95x - 2.71 = 5.934$

Multiply each term by 100: $$ 100(6.95x) - 100(2.71) = 100(5.934) $$ This simplifies to: $$ 695x - 271 = 593.4 $$ The term $271$ still has a decimal, so this equation does not work.

Analyze Equation D: $18.25 - 3.4x = 2.4x$

Multiply each term by 100: $$ 100(18.25) - 100(3.4x) = 100(2.4x) $$ This simplifies to: $$ 1825 - 340x = 240x $$ All terms are now whole numbers.

Conclusion

The only equation that is completely cleared of decimals is Equation D.

The equation that would be completely cleared of decimals when both sides are multiplied by 100 is:

$$ 18.25 - 3.4x = 2.4x $$

More Information

Multiplying by 100 is a method to eliminate decimals by scaling each term. This is particularly useful for equations involving monetary amounts or measurements where decimals are common.

Tips

Failing to multiply every term by 100, leading to oversight of decimals.
Incorrect simplification of terms when multiplying, leading to the wrong conclusion about whether decimals remain.

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