Question

In a 30 -minute television program, there were 12 one-minute commercials. How many minutes of actual programming were there? A. 42 minutes B. 18 minutes C. 260 minutes D. 28 minutes

Short answer

The actual programming time is 18 minutes.

Step-by-step solution

Identify Total Time of Program

The total duration of the television program is given as 30 minutes.

Determine Time Used by Commercials

There are 12 commercials, each lasting 1 minute. Therefore, commercials take up 12 minutes in total.

Calculate Actual Programming Time

Subtract the time taken by commercials from the total program time: \(30 - 12 = 18\) minutes.

Confirm the Correct Answer

The actual programming time is 18 minutes. Hence, the correct answer is option B: 18 minutes.

Key concepts

Understanding Word Problems

Word problems can often seem tricky because they tell a story using words rather than just numbers and symbols. The key to solving them is to break down what the problem is asking.

• First, identify what you are looking to find out. In this problem, we want to know the actual programming time.
• Next, identify the pieces of information provided. Here, we know the total program time and the time taken by commercials.
• Translate these into equations or simple arithmetic to find the solution.

Word problems connect math to real life, so focusing on the information you need can make solving them easier.

Basic Arithmetic in Problem Solving

Basic arithmetic involves the foundational operations in math: addition, subtraction, multiplication, and division. In our exercise, subtraction is the key operation used.

• Addition is about combining amounts. It wasn't central to this problem but is crucial in math.
• Subtraction helps find out what remains after part of something is taken away.
• Multiplication and division are useful for more complex word problems when you deal with groups or parts of a whole.

Mastering these basic operations forms the building blocks for understanding more complex math concepts.

Simplifying Subtraction in Math

Subtraction is taking away one number from another. It helps in finding the difference between two quantities. In the exercise, you subtract the commercial time from the total program time.

• Place the larger number first in the subtraction equation: The total program time is 30 minutes, so it comes first.
• Subtract the smaller number, which is the total commercials time, from the larger number: 30 - 12 = 18.
• Check your work by adding the result to the subtracted number (12 commercials minutes) to ensure the total matches: 18 + 12 should equal 30.

Understanding subtraction is an essential math skill, especially in real-life situations like time management.

Solving Equations Step by Step

Solving equations step by step is like following a recipe to bake a cake. It's important to proceed systematically to avoid errors.

• Start by identifying what you know and what you need to find out.
• Break the process into clear, manageable steps. Here, you start with the total time and subtract the commercials time.
• Perform each arithmetic operation carefully and in order, just like following precise steps to mix ingredients.
• Finally, verify your result to make sure it's correct by reversing the calculation.

Using a methodical approach to solving equations ensures accuracy and builds confidence in problem-solving.