Problem 53 - Prealgebra

Question

Complete. $$\frac{2}{3} \text { hour }=\underline{?} \text { minutes }$$

Step-by-Step Solution

Answer

There are 40 minutes in \(\frac{2}{3}\) of an hour.

Step 1: Understand the Conversion Rate

To convert hours into minutes, you need to know the conversion rate between the two units. There are 60 minutes in 1 hour.

Step 2: Setup the Equation

To find the number of minutes in a fraction of an hour, you can set up the equation using the known conversion rate: \[ x = \frac{2}{3} \times 60 \] where \( x \) is the number of minutes.

Step 3: Calculate the Minutes

Carry out the multiplication using the fraction and the conversion rate: \[ x = \frac{2}{3} \times 60 = 40 \] This means that there are 40 minutes in \( \frac{2}{3} \) of an hour.

Key Concepts

Time Conversion

Time conversion is essential when working with different time units, such as hours, minutes, and seconds. Understanding this concept can simplify many everyday tasks and math problems. The basic idea is to know the equivalence between time units.

• 1 hour = 60 minutes
• 1 minute = 60 seconds

This knowledge allows you to easily convert from one unit to another. For example, if you have a fraction of an hour, like \(\frac{2}{3}\), and you want to find out how many minutes that is, you'll multiply the fraction by 60 (since there are 60 minutes in an hour).

By using the formula \( x = \frac{2}{3} \times 60 \), you can calculate that \(\frac{2}{3}\) of an hour is equivalent to 40 minutes. This skill is invaluable for making sense of durations and scheduling in everyday life.

Unit Conversion

Unit conversion is an important mathematical technique used to change a value from one measurement unit to another. It's especially handy in fields like science and engineering, but it’s also used in daily life. The key is to understand the relationship between different units.

• Identify the units you are converting between.
• Find the conversion factor (the number you multiply by to change units).
• Perform the multiplication to convert the value.

Consider the example of converting \(\frac{2}{3}\) of an hour to minutes. Here, the unit conversion factor is 60 (since 1 hour = 60 minutes). You apply the factor by multiplying: \(\frac{2}{3} \times 60 = 40\).

Unit conversion streamlines calculations and ensures consistency in understanding and communication across different systems of measurement. Whether dealing with time, length, mass, or temperature, mastering unit conversions is crucial.

Arithmetic Operations

Arithmetic operations form the foundation of mathematics. They include addition, subtraction, multiplication, and division. Each operation has specific rules and applications, but together they enable complex problem-solving.

When converting time units with fractions, multiplication is key. Using fractions in multiplication is straightforward:

• Multiply the numerators (top parts) of the fractions.
• Multiply the denominators (bottom parts) of the fractions.
• Simplify the result if needed.

For example, when you multiply \(\frac{2}{3} \times 60\), think of 60 as \(\frac{60}{1}\). Multiply the numerator 2 by 60 and the denominator 3 by 1. Simplify by dividing 120 by 3, resulting in 40.

Understanding these operations helps in a variety of mathematical problems beyond just fractions and is fundamental in mastering mathematics and problem-solving skills.