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Chapter 1: Problem 11

A concrete block weighs \(37 \frac{1}{2}\) pounds. How much will 30 of these blocks weigh?

Short Answer

Expert verified
The total weight of 30 concrete blocks is 1125 pounds.

Step by step solution

01

Identify the Weight of One Block

The problem states that one concrete block weighs \(37 \frac{1}{2}\) pounds. This weight is equivalent to 37.5 pounds when written as a decimal.
02

Multiply to Find the Total Weight

To find the total weight of 30 blocks, multiply the weight of one block (37.5 pounds) by 30. This results in a total weight of \(37.5 \times 30 = 1125\) pounds.

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Key Concepts

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

Fractions to Decimals Conversion
Fractions and decimals are two ways of representing numbers. Sometimes, it is easier to work with decimals, especially in calculations. To convert a fraction to a decimal, you need to divide the numerator (the top number) by the denominator (the bottom number).
For example, the fraction \(\frac{1}{2}\) means you take the number 1 and divide it by 2. Doing this gives you 0.5. Thus, \(37 \frac{1}{2}\), which is 37 plus \(0.5\), becomes 37.5 in decimal form.
  • Identify the fraction part of the number.
  • Divide the numerator by the denominator to get the decimal.
  • Add this decimal to the whole number part.
This simple conversion is crucial in ensuring that all arithmetic operations can be performed smoothly, as decimals are universally used in multiplication and division.
Weight Calculation
Weight calculation is essential when you need to find how heavy several items are together. In this problem, you want to know the weight of 30 concrete blocks. Each block weighs 37.5 pounds.
First, write down the weight of one block. Then multiply it by the number of blocks you have.
  • Single block weight: 37.5 pounds.
  • Number of blocks: 30.
  • Total weight calculation: 37.5 (weight of one block) multiplied by 30.
This multiplication gives you the cumulative weight of all blocks, which is 1125 pounds. This process highlights the importance of a systematic approach in weight calculation, an everyday practical skill.
Arithmetic Operations
Arithmetic operations are basic math calculations that include addition, subtraction, multiplication, and division. Here, multiplication is the key operation. It helps in determining the total when you have a quantity of items with the same value and need to find the sum of all those values.
To calculate the total weight of the blocks:
  • Take the weight of one block.
  • Multiply it by the number of blocks.
  • Result provides the total weight.
This illustrates how multiplication simplifies finding totals when multiple identical items are involved. It turns repeated addition into a single, concise operation, making calculations quicker and more efficient.

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Most popular questions from this chapter

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