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Chapter 5: Problem 29

Find the ratio of the first number to the second and simplify. $$ 2.8 \text { to } 3.6 $$

Short Answer

Expert verified
The simplified ratio is 7:9.

Step by step solution

01

Write the Ratio

Express the given values as a ratio. So, you have 2.8 to 3.6, which can be written as a fraction: \( \frac{2.8}{3.6} \)
02

Simplify the Fraction

To simplify the fraction, divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). Here, the GCD of 2.8 and 3.6 is 0.4: \( \frac{2.8 \div 0.4}{3.6 \div 0.4} = \frac{7}{9} \)
03

Write the Simplified Ratio

Now that you have simplified the fraction, express it back as a ratio. So, the ratio of 2.8 to 3.6 simplifies to 7 to 9. Therefore, the simplified ratio is 7:9.

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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 way to compare two quantities. It tells us how much of one thing there is compared to another. For example, if you have 2 apples and 3 oranges, the ratio of apples to oranges is 2 to 3. This can also be written as 2:3 or as a fraction \(\frac{2}{3}\).

Ratios can be used to compare any kinds of quantities, like lengths, weights, or even costs. They help us understand the relationship between different amounts.

In our exercise, we are comparing the numbers 2.8 and 3.6. First, we write it as a ratio: 2.8 to 3.6. Then, we simplify it.
greatest common divisor
The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. It helps in simplifying fractions.

To find the GCD of 2.8 and 3.6, we typically convert them into whole numbers first. Multiplying both numbers by 10 results in 28 and 36.

Next, we find the GCD of 28 and 36. The divisors of 28 are 1, 2, 4, 7, 14, 28, and for 36 they are 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest common divisor between them is 4. Dividing both by 10 again, we get the GCD of 2.8 and 3.6, which is 0.4.
fraction simplification
Fraction simplification is the process of reducing a fraction to its simplest form. A fraction is in its simplest form when the numerator and denominator are as small as possible, but still whole numbers.

To simplify, divide both the numerator and the denominator by their GCD.

For our fraction \(\frac{2.8}{3.6}\), we divide both the numerator (2.8) and the denominator (3.6) by the GCD of 0.4: \[\frac{2.8 \div 0.4}{3.6 \div 0.4} = \frac{7}{9} \] So, \(\frac{2.8}{3.6}\) simplifies to \(\frac{7}{9}\).

This means the original ratio simplifies to 7 to 9.
basic mathematics
Basic mathematics involves fundamental concepts like addition, subtraction, multiplication, and division. It also includes understanding and working with fractions, ratios, and decimals.

In this exercise, we used division for finding the GCD and simplifying our fraction. Knowing how to convert between numbers and fractions is key in many math problems.

These skills are foundational and are used in everyday tasks, like cooking recipes or handling finances. It helps to practice and understand these concepts thoroughly to solve more complex math problems efficiently.

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Most popular questions from this chapter

Solve. $$ \frac{1}{2}=\frac{7}{x} $$

Solve. $$ \frac{x}{11}=\frac{7.1}{2} $$

A black racer snake can travel \(4.6 \mathrm{~km}\) in \(2 \mathrm{hr}\). What is its rate, or speed, in kilometers per hour?

Solve. $$ \frac{3}{y}=\frac{5}{4.5} $$

Solve. $$ \frac{y}{\frac{3}{5}}=\frac{\frac{7}{12}}{\frac{14}{15}} $$
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