Solve this equation. \( 10 d=32 \) Draw a hanger or a tape dagram if it helps wifh your thinking.

Sure! Let's solve the equation \( 10d = 32 \) using a **tape diagram** to visualize the problem. ### Step 1: Understand the Equation The equation \( 10d = 32 \) means that **10 times** a certain number \( d \) equals **32**. We need to find the value of \( d \). ### Step 2: Draw a Tape Diagram A **tape diagram** helps us visualize the equation by representing the unknown value and how many times it appears. ``` |--- d ---|--- d ---|--- d ---|--- d ---|--- d ---|--- d ---|--- d ---|--- d ---|--- d ---|--- d ---| Total: 32 ``` - Each **`|--- d ---|`** represents one \( d \). - There are **10** \( d \)'s in total. - The entire length of the tape diagram equals **32**. ### Step 3: Calculate the Value of \( d \) To find the value of one \( d \), divide the total by the number of \( d \)'s (which is 10): \[ d = \frac{32}{10} \] \[ d = 3.2 \] ### Step 4: Verify the Solution Let's check if \( d = 3.2 \) satisfies the original equation: \[ 10d = 10 \times 3.2 = 32 \] Since both sides equal **32**, our solution is correct. ### Summary \[ 10d = 32 \implies d = \frac{32}{10} = 3.2 \] Using the tape diagram helped us visualize that **10 equal parts** make up the total **32**, so each part \( d \) is **3.2**.