Liz has different lengths of ribbon
(in feet) shown by the amounts
below:

Ask by Ramirez Pierce. in the United States

Jan 23,2025

Question

Liz has different lengths of ribbon (in feet) shown by the amounts below: $$ \quad 3 \frac{1}{3}+5 \frac{3}{4} $$

UpStudy AI · Accepted Answer

Sure, let's calculate the total length of ribbon Liz has by adding the two lengths together.

Liz has:
- **3 ⅓ feet** of ribbon
- **5 ¾ feet** of ribbon

**Step 1: Convert Mixed Numbers to Improper Fractions**

First, convert the mixed numbers to improper fractions for easier addition.

1. **3 ⅓ feet**
   - Multiply the whole number by the denominator: $$ 3 \times 3 = 9 $$
   - Add the numerator: $$ 9 + 1 = 10 $$
   - So, $$ 3 \frac{1}{3} = \frac{10}{3} $$

2. **5 ¾ feet**
   - Multiply the whole number by the denominator: $$ 5 \times 4 = 20 $$
   - Add the numerator: $$ 20 + 3 = 23 $$
   - So, $$ 5 \frac{3}{4} = \frac{23}{4} $$

**Step 2: Find a Common Denominator**

To add the two fractions, they must have the same denominator. The least common denominator (LCD) of 3 and 4 is 12.

- Convert $$ \frac{10}{3} $$ to twelfths:
  $$
  \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12}
  $$
  
- Convert $$ \frac{23}{4} $$ to twelfths:
  $$
  \frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12}
  $$

**Step 3: Add the Fractions**

Now, add the two fractions:

$$
\frac{40}{12} + \frac{69}{12} = \frac{109}{12}
$$

**Step 4: Convert Back to a Mixed Number**

Divide the numerator by the denominator to convert back to a mixed number:

$$
109 \div 12 = 9 \text{ with a remainder of } 1
$$

So,

$$
\frac{109}{12} = 9\ \frac{1}{12}
$$

**Final Answer:**

Liz has a total of **9 ⅙ feet** of ribbon.
Liz has a total of $$ 9 \frac{1}{12} $$ feet of ribbon.

Liz has different lengths of ribbon
(in feet) shown by the amounts
below:

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