Math Problem Statement

Multiple Choice Question Fiona made a wall hanging with pockets for holding the classroom calculators. Each pocket is 3 1/4 inches wide, and the pockets are separated by 1/4 inch with a 1/4 -inch border around the outside. One row of pockets holds 4 calculators, as shown below. What is the total number of inches across each row?

Solution

Let's break this problem down step by step.

  1. Each pocket is 3 1/4 inches wide. In fractional terms, this is: 314=134inches3 \frac{1}{4} = \frac{13}{4} \, \text{inches}

  2. There are 4 pockets in a row. So, the total width of just the pockets is: 4×134=13inches4 \times \frac{13}{4} = 13 \, \text{inches}

  3. The pockets are separated by 1/4 inch. Since there are 4 pockets, there are 3 spaces between them. So, the total space between the pockets is: 3×14=34inches3 \times \frac{1}{4} = \frac{3}{4} \, \text{inches}

  4. There is also a 1/4-inch border on each side. The total width of the borders is: 2×14=24=12inches2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \, \text{inches}

  5. Now, sum everything together to get the total width across the row: 13+34+12=13+34+24=13+54=13+114=1414inches13 + \frac{3}{4} + \frac{1}{2} = 13 + \frac{3}{4} + \frac{2}{4} = 13 + \frac{5}{4} = 13 + 1 \frac{1}{4} = 14 \frac{1}{4} \, \text{inches}

So, the total number of inches across each row is 14 1/4 inches.

Would you like further clarification on any step or more details?

Here are some related questions for practice:

  1. How many inches would a row of 5 pockets take with the same dimensions?
  2. What if each pocket was 4 inches wide instead of 3 1/4 inches?
  3. How would the total width change if there was no border?
  4. What is the total width if the spaces between pockets were 1/2 inch instead of 1/4 inch?
  5. How many rows of 4 pockets would fit in a space that is 60 inches wide?

Tip: When calculating total width, always account for both pockets and the spaces between them, as well as any borders.

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Math Problem Analysis

Mathematical Concepts

Measurement
Fractions
Addition of mixed numbers

Formulas

Total width = (Number of pockets × Pocket width) + (Number of spaces × Space width) + (2 × Border width)

Theorems

Addition of fractions and mixed numbers

Suitable Grade Level

Grade 5-6