A piece of blue yarn is 4 
3
10
 yards long. A piece of pink yarn is 4 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?


To solve this problem, let's first determine the lengths of both pieces of yarn and then find the difference.

### Step 1: Length of the Pink Yarn
The length of the blue yarn is given as:
\[
4 \frac{3}{10} \text{ yards}
\]

This can be converted into an improper fraction:
\[
4 \frac{3}{10} = \frac{40 + 3}{10} = \frac{43}{10} \text{ yards}
\]

Since the pink yarn is 4 times the length of the blue yarn, we calculate:
\[
4 \times \frac{43}{10} = \frac{172}{10} = 17.2 \text{ yards}
\]

### Step 2: Difference in Length
Now, to find how much longer the pink yarn is than the blue yarn, we subtract the length of the blue yarn from the length of the pink yarn:
\[
17.2 - 4.3 = 12.9 \text{ yards}
\]

### Answer
The pink yarn is **12.9 yards longer** than the blue yarn.

Would you like more details or have any questions?

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Here are some related questions:
1. What would be the total length if both pieces of yarn were combined?
2. How would the answer change if the blue yarn were only 3 times longer than its current length?
3. If a third yarn piece is half the length of the pink yarn, what would its length be?
4. What is the length difference if the pink yarn were 5 times the length of the blue yarn instead?
5. How would you convert the answer to feet?

**Tip:** When multiplying fractions, simplify the fraction after converting to ensure accuracy.

A piece of blue yarn is 4 3/10 yards long. A piece of pink yarn is 4 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?

Solve a step-by-step problem to determine the difference in length between a 4.3-yard blue yarn and a pink yarn four times as long. Ideal for students in Grades 5-6, covering key concepts in fractions, multiplication, and subtraction.

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