Question

what fraction of a group?

1. compare the lengths of ropes b, c, and d to the length of rope a, and complete each statement. then use the measurements shown on the grid to write a multiplication equation and a division equation for each statement.

a. rope b is ______ times as long as rope a.
multiplication equation: division equation:

Explanation:

Step1: Determine Rope A's length

Assume each grid square has a side length of 1 unit. Rope A spans from column 2 to column 5 (let's say the first dot is at column 2, row A, and the second at column 5, row A). So length of Rope A is \( 5 - 2 = 3 \) units.

Step2: Determine Rope B's length

Rope B starts at column 2, row B, and ends at column 14, row B (from the grid). So length of Rope B is \( 14 - 2 = 12 \) units.

Step3: Find the multiplier for Rope B relative to A

To find how many times Rope B is as long as Rope A, divide Rope B's length by Rope A's length: \( \frac{12}{3} = 4 \). So Rope B is 4 times as long as Rope A.

Step4: Write multiplication equation

Let \( L_A \) be length of Rope A, \( L_B \) be length of Rope B. Then \( L_B = 4 \times L_A \). Since \( L_A = 3 \), \( 3 \times 4 = 12 \).

Step5: Write division equation

From multiplication, we can get division: \( L_B \div L_A = 4 \) or \( 12 \div 3 = 4 \), and also \( L_B \div 4 = L_A \) or \( 12 \div 4 = 3 \).

Answer:

a. Rope B is \( \boldsymbol{4} \) times as long as Rope A.
Multiplication equation: \( 3 \times 4 = 12 \) (or \( L_A \times 4 = L_B \))
Division equation: \( 12 \div 3 = 4 \) (or \( L_B \div L_A = 4 \))