Math Problem Statement

Multiply. Write your answer using the smallest numbers possible.

9 miles 7 feet times 734

miles feet

Solution

To multiply the mixed measurement (9 miles and 7 feet) by 734, follow these steps:

  1. Convert miles to feet:
    Since there are 5280 feet in a mile:
    9 miles=9×5280=47520 feet9 \text{ miles} = 9 \times 5280 = 47520 \text{ feet}.
    Add the 7 feet to this:
    47520+7=47527 feet47520 + 7 = 47527 \text{ feet}.

  2. Multiply by 734:
    47527×734=34892718 feet47527 \times 734 = 34892718 \text{ feet}.

  3. Convert back to miles and feet:

    • Divide 34892718 feet34892718 \text{ feet} by 5280 feet/mile5280 \text{ feet/mile} to find the total miles:
      34892718÷5280=6606 miles and a remainder of 2138 feet34892718 \div 5280 = 6606 \text{ miles and a remainder of } 2138 \text{ feet}.

Final Answer:

6606 miles 2138 feet

Would you like further clarification or help with another problem?

Related Questions:

  1. How do you convert between miles and feet?
  2. How can you simplify large multiplications?
  3. Why is converting to a single unit before multiplying more efficient?
  4. What is the significance of using the smallest possible numbers in measurements?
  5. Can you explain other examples of converting between mixed units?

Tip: Always check if your final result in mixed units makes logical sense by recalculating the larger unit and the remainder.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Multiplication
Mixed Units

Formulas

1 mile = 5280 feet
Total feet = (miles × 5280) + feet
Division for conversion back: total feet ÷ 5280 = miles, remainder = feet

Theorems

Basic Arithmetic Operations
Unit Conversion Principles

Suitable Grade Level

Grades 5-8