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Chapter 3: Problem 2

Write the ratio as a fraction in simplest form. 45 to 15

Short Answer

Expert verified
The ratio 45 to 15 in simplest form is 3 to 1.

Step by step solution

01

Write the Ratio as a Fraction

The first step is to write the given ratio as a fraction. Hence, 45 to 15 can be written as \(\frac{45}{15}\).
02

Find the Greatest Common Divisor (GCD)

We need to find the GCD of 45 and 15. The GCD of 45 and 15 is 15.
03

Simplify the fraction

Now, divide both the numerator and the denominator of the fraction by the GCD. Thus, \(\frac{45}{15} = \frac{45 梅 15}{15 梅 15} = \frac{3}{1}\).

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Key Concepts

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

Ratios
A ratio is a comparison between two numbers, showing how many times one value contains or is contained within the other. It can be expressed in several formats such as "\( a:b \)" or as a fraction "\( \frac{a}{b} \)."
For instance, the ratio "45 to 15" can be written as \( \frac{45}{15} \).
This is handy, as fractions can be further simplified, helping us understand the relationship between the numbers in their most basic form. Practically, ratios help us solve problems related to proportions, sharing or scaling quantities.
To summarize:
  • Ratios compare two quantities.
  • They can be written using a colon or as a fraction.
  • Useful in understanding proportions and scaling.
Greatest Common Divisor
The Greatest Common Divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
Finding the GCD is crucial in simplifying fractions since it helps us reduce them to their simplest form.
For example, in the ratio 45 to 15, the numbers are divided by their GCD, which is 15. This helps transform the fraction \( \frac{45}{15} \) into its simplest form. Determining the GCD involves looking for factors that two numbers share.Here are steps to find the GCD:
  • List the factors of each number.
  • Select the largest common factor.
This method is useful for classroom problems and everyday calculations to make numbers simpler to work with.
Fractions in Simplest Form
Fractions in simplest form are fractions that have been reduced as much as possible.
This means that the numerator and the denominator have no common factors other than 1.
By presenting a fraction in its simplest form, you're providing the clearest expression of the ratio between two numbers. For example, the fraction \( \frac{45}{15} \) simplifies to \( \frac{3}{1} \) when divided by their GCD, 15.
Simplifying fractions is important because it makes them easier to understand and work with. It also makes calculations simpler, especially when adding, subtracting, or comparing fractions. Key takeaways include:
  • Simplifying involves dividing by the GCD.
  • The simplest form has no common factors except 1.
  • Easier to interpret and compute with.

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Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. The statement that \(u\) is at least 10 is equivalent to the inequality \(u \geq 10\).

Solution Sets How many real numbers are in the solution set of a linear inequality? Give an example.

Error Analysis A student solves the equation \(S=2 l w+2 l h+2 w h\) for \(w\) and his answer is \(w=\frac{S-2 l w-2 l h}{2 h}\). Describe and correct the student's error.

Determine whether each value of \(x\) is a solution of the inequality. \(5 x+3 \leq x-5\) (a) \(x=1\) (b) \(x=-2\) (c) \(x=-1\) (d) \(x=2\)

Match the statement with the property it represents. (a) Addition Property of Inequality (b) Subtraction Property of Inequality (c) Multiplication Property of Inequality (d) Division Property of Inequality \(-8>-9\), so \(-8+4>-9+4\).
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