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Chapter 2: Problem 352

In the following exercises, evaluate the following expressions. $$ b h \text { when } b=7, h=8 $$

Short Answer

Expert verified
The value of \( b h \) is 56.

Step by step solution

01

Identify the given values

Identify the values provided for the variables in the expression. Here, we have \( b = 7 \) and \( h = 8 \).
02

Substitute the values into the expression

Substitute the given values of \( b \) and \( h \) into the expression \( b h \). This gives us \( 7 \times 8 \).
03

Perform the multiplication

Multiply the numbers obtained from the substitution. Calculate \( 7 \times 8 = 56 \).
04

Write the final answer

Write down the final value obtained after performing the multiplication. Therefore, \( b h = 56 \).

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Key Concepts

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

Substitution in algebra
In algebra, substitution is a fundamental concept. It means replacing variables with their given numerical values. This allows us to solve and simplify expressions. For example, if we have the expression, \( b h \) and are given that \( b = 7 \) and \( h = 8 \), then we can substitute these values in place of \( b \) and \( h \). This helps in breaking down the problem into simpler numerical operations. Substitution is very useful because it transforms an abstract expression into concrete numbers we can work with. Remember to always double-check the values being substituted to avoid mistakes.
Multiplication
Multiplication is one of the core operations in algebra. Once the substitution is done, the next step usually involves performing basic arithmetic operations like multiplication. For the exercise at hand, after substituting the given values into the expression, we end up with \( 7 \times 8 \). Multiplying numbers can be thought of as repeated addition, where \( 7 \times 8 \) means adding 7 to itself 8 times, resulting in 56. Knowing your multiplication tables can greatly speed up your calculations and help in avoiding errors.
Step-by-step problem solving
Breaking down a problem into clear and manageable steps is crucial in algebra. Here鈥檚 a brief overview of the step-by-step approach used in this problem:
  • **Step 1: Identify the given values**: This involves recognizing the values provided for each variable in the problem. For instance, we identified that \( b = 7 \) and \( h = 8 \).
  • **Step 2: Substitute the values into the expression**: After identifying the values, we substitute these values into the expression \( b h \), transforming it into a numerical problem, such as \( 7 \times 8 \).
  • **Step 3: Perform the multiplication**: The next step is to carry out the multiplication of the numbers, giving us \( 56 \).
  • **Step 4: Write the final answer**: Finally, we write down the final answer obtained after performing the multiplication, which in this case is \( b h = 56 \).
Following a step-by-step approach ensures that each part of the problem is handled correctly, reducing the chance of errors and making the solution process clearer.

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