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Chapter 2: Problem 36

Determine whether each proportion is true or false. $$ \frac{\frac{1}{3}}{6}=\frac{1}{18} $$

Short Answer

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Step by step solution

01

- Simplify the left side of the equation

Simplify the expression \(\frac{\frac{1}{3}}{6}\). This can be rewritten as \(\frac{1}{3} \times \frac{1}{6}\).
02

- Multiply the fractions

Multiply \(\frac{1}{3} \times \frac{1}{6}\) to get \(\frac{1}{18}\).
03

- Compare both sides of the equation

Now, compare \(\frac{1}{18} \) on the left side and \(\frac{1}{18}\) on the right side. Both sides are equal.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction Multiplication
Multiplying fractions is a straightforward process. To multiply two fractions, follow these steps:
  • Multiply the numerators (the top numbers) together.
  • Multiply the denominators (the bottom numbers) together.
For example, if we have \(\frac{1}{3} \times \frac{1}{6}\), we multiply the numerators: 1 脳 1 = 1, and we multiply the denominators: 3 脳 6 = 18. Thus, the multiplication result is \(\frac{1}{18}\). This is exactly what we did in Step 2 of our solution above. Notice that we converted the complex fraction \(\frac{\frac{1}{3}}{6}\) into a simple multiplication of fractions before comparing the results.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. This often involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
For example, if you have the fraction \(\frac{6}{18}\), the GCD of 6 and 18 is 6. Simplifying \(\frac{6}{18}\), we divide both the numerator and the denominator by 6, resulting in \(\frac{1}{3}\).
In our exercise, we simplified \(\frac{\frac{1}{3}}{6}\) by converting it first into \(\frac{1}{3} \times \frac{1}{6}\). This step made it easier to understand and to handle the fractions involved.
Comparing Fractions
When comparing fractions, you need to ensure both fractions have the same denominator or convert them into the same form.
Once they have the same denominator, it becomes easier to tell if the fractions are equal or which one is larger.
In our example, we compared \(\frac{1}{18}\) to \(\frac{1}{18}\). Clearly, both are the same, making the given proportion true.
For more complex comparisons, you might need to find a common denominator or convert to decimal form to compare fractions accurately. This helps in determining whether one fraction is larger than, smaller than, or equal to another fraction.

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Most popular questions from this chapter

Solve each formula for the specified variable. \(S=\frac{1}{2}(a+b+c)\) for \(b\)

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The sum of a number and 9 is \(-26 .\) What is the number?

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