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Chapter 1: Problem 12

The USA Today crossword puzzle is a rectangle containing 15 rows with 15 squares in each row. How many squares does the puzzle have altogether?

Short Answer

Expert verified
The puzzle has 225 squares.

Step by step solution

01

Understand the Problem

The problem states that there is a rectangle divided into 15 rows with 15 squares in each row. We are asked to find the total number of squares in the puzzle.
02

Recall the Formula for Area of a Rectangle

To find the total number of squares in a rectangle, we can use the formula for the area of a rectangle. The area is given by the product of the number of rows and the number of squares per row.
03

Apply the Formula

The number of rows is 15 and the number of squares in each row is also 15. So, we multiply these two numbers to find the total number of squares: \[ \text{Total squares} = 15 \times 15 \]
04

Calculate the Total

Compute the multiplication: \[ 15 \times 15 = 225 \] So, the total number of squares in the puzzle is 225.

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Key Concepts

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

Multiplication
Multiplication is a fundamental arithmetic operation. It helps us find the total number when we combine equal groups. For example, in this problem, we have 15 rows, each with 15 squares. To find the total, we multiply the two numbers: 15 times 15. This is expressed as: \[ 15 \times 15 \] When we compute this multiplication, we get 225, meaning there are 225 squares in total.

Multiplication is not just for this problem. It's used in various real-life scenarios:
  • Calculating the total cost of items when each costs the same.
  • Finding the area when we know the length and width.
  • Determining the total quantity in repeated scenarios.
By practicing multiplication, you can solve many problems efficiently.

Remember these steps:
  • Identify the quantities to be multiplied.
  • Set up the multiplication equation.
  • Compute the result.
Area of a Rectangle
The area of a rectangle is a measure of the space contained within its borders. To find the area, you use the formula: \[ \text{Area} = \text{Length} \times \text{Width} \] In this exercise, the length and width of the rectangle are both 15 squares because it is a square-shaped puzzle.

To calculate the area:
  • Take the number of rows (15).
  • Multiply it by the number of squares in each row (15).
This gives us: \[ 15 \times 15 = 225 \] Therefore, the area of the rectangle is 225 square units.

Understanding the area is essential for:
  • Designing floor plans or gardens.
  • Planning how much material is needed for construction.
  • Solving geometry problems.
Make sure to always check that your measurements are in the same units before multiplying.
Problem-Solving Steps
Effective problem-solving requires a systematic approach. Here is how you can approach problems like the crossword puzzle math problem:
  • Step 1: Understand the Problem
    Identify what is being asked. In our case, we need to find the total number of squares in the rectangle.
  • Step 2: Recall Relevant Formulas
    Identify the formula that applies. For rectangles, the area is the product of length and width.
  • Step 3: Apply the Formula
    Substitute the given values into the formula. We use 15 for both length and width here.
  • Step 4: Calculate the Total
    Solve the multiplication to find the total.
For our puzzle, this means:
\[ \text{Total squares} = 15 \times 15 = 225 \] Developing this step-by-step habit will make complex problems easier to handle. Regular practice and breaking down problems are key to becoming proficient.

Remember:
  • Understand the problem fully before starting.
  • Identify and use the right formulas.
  • Break down the problem into smaller, manageable steps.

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