Math Problem Statement

Ed needed to extend the string on his kite. The current string was eight and three fourths feet. He cut a piece of string that measured 4.5 feet and added it to the existing string. What is the new length of the string?

Solution

To find the new length of the string after Ed adds the additional piece, we need to add the length of the existing string to the length of the added string.

The current string length is 8 and 3/4 feet, which can be written as a mixed number: 834 feet8 \frac{3}{4} \text{ feet} We can convert this mixed number into an improper fraction: 834=8×4+34=32+34=354 feet8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \text{ feet}

The additional string length is given as 4.5 feet. We can convert 4.5 into a fraction: 4.5=92 feet4.5 = \frac{9}{2} \text{ feet}

Now, let's add these two fractions: 354+92\frac{35}{4} + \frac{9}{2}

To add these fractions, we need a common denominator. The least common denominator between 4 and 2 is 4. We convert 92\frac{9}{2} to 184\frac{18}{4}: 354+184=534 feet\frac{35}{4} + \frac{18}{4} = \frac{53}{4} \text{ feet}

Finally, we can convert 534\frac{53}{4} back into a mixed number: 534=1314 feet\frac{53}{4} = 13 \frac{1}{4} \text{ feet}

So, the new length of the string is 13 and 1/4 feet.

Would you like more details on this solution or have any other questions?

Here are 5 related questions:

  1. How do you convert between mixed numbers and improper fractions?
  2. What is the process for finding the least common denominator?
  3. How do you add or subtract fractions with different denominators?
  4. Can you multiply or divide mixed numbers directly, or do you need to convert them first?
  5. How can you simplify improper fractions back into mixed numbers?

Tip: Always ensure that fractions have a common denominator before adding or subtracting them.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Adding Fractions

Formulas

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Theorems

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Suitable Grade Level

Grades 4-6