To explain why these calculations are true using a place value chart, we need to break down the multiplication into more manageable parts. Here's a step-by-step solution for each equation.
### Part (a): 4 x 38.125 = 152.5
#### Step 1: Decompose 38.125
Let's break down \(\( 38.125 \)\) by place value:
- 3 tens (30)
- 8 units (8)
- 1 tenths (0.1)
- 2 hundredths (0.02)
- 5 thousandths (0.005)
So, \(\( 38.125 = 30 + 8 + 0.1 + 0.02 + 0.005 \)\)
#### Step 2: Multiply each component by 4
Next, we multiply each part by 4:
- \(\( 4 \times 30 = 120 \)\)
- \(\( 4 \times 8 = 32 \)\)
- \(\( 4 \times 0.1 = 0.4 \)\)
- \(\( 4 \times 0.02 = 0.08 \)\)
- \(\( 4 \times 0.005 = 0.02 \)\)
#### Step 3: Add all the results
Now, we add all these parts together:
\(\[ 120 + 32 + 0.4 + 0.08 + 0.02 = 152.5 \]\)
This confirms that \(\( 4 \times 38.125 = 152.5 \)\).
### Part (b): 9 × 53.191 = 478.719
#### Step 1: Decompose 53.191
Let's break down \(\( 53.191 \)\) by place value:
- 5 tens (50)
- 3 units (3)
- 1 tenths (0.1)
- 9 hundredths (0.09)
- 1 thousandths (0.001)
So, \(\( 53.191 = 50 + 3 + 0.1 + 0.09 + 0.001 \)\)
#### Step 2: Multiply each component by 9
Next, we multiply each part by 9:
- \(\( 9 \times 50 = 450 \)\)
- \(\( 9 \times 3 = 27 \)\)
- \(\( 9 \times 0.1 = 0.9 \)\)
- \(\( 9 \times 0.09 = 0.81 \)\)
- \(\( 9 \times 0.001 = 0.009 \)\)
#### Step 3: Add all the results
Now, we add all these parts together:
\(\[ 450 + 27 + 0.9 + 0.81 + 0.009 = 478.719 \]\)
This confirms that \(\( 9 \times 53.191 = 478.719 \)\).
By breaking down each component and multiplying by the coefficient, we can see how the calculations align and demonstrate that these products are indeed correct.
