Question

in the example, a rectangle was drawn to represent the problem. then partial - products multiplication was used to record the work in a simpler way. use partial products multiplication to solve problems 1 and 2. example: partitioned rectangle partial - products multiplication practice write the numbers in expanded form. ③ 905,603 ④ 589,043 ⑤ 2,599,002 ⑥ 8,003,452

Explanation:

Step1: Solve Problem 1 (48 * 3)

First, expand 48 into 40 + 8. Then multiply each part by 3:

• 40 * 3 = 120
• 8 * 3 = 24

Now, add the partial products: 120 + 24 = 144.

Step2: Solve Problem 2 (653 * 8)

Expand 653 into 600 + 50 + 3. Multiply each part by 8:

• 600 * 8 = 4800
• 50 * 8 = 400
• 3 * 8 = 24

Add the partial products: 4800 + 400 + 24 = 5224.

Step3: Expand 905,603

Break down by place values:

• Hundred thousands: 900,000 (9 * 100,000)
• Thousands: 5,000 (5 * 1,000)
• Hundreds: 600 (6 * 100)
• Ones: 3 (3 * 1)

So, 905,603 = 900,000 + 5,000 + 600 + 3.

Step4: Expand 589,043

Break down by place values:

• Hundred thousands: 500,000 (5 * 100,000)
• Ten thousands: 80,000 (8 * 10,000)
• Thousands: 9,000 (9 * 1,000)
• Tens: 40 (4 * 10)
• Ones: 3 (3 * 1)

So, 589,043 = 500,000 + 80,000 + 9,000 + 40 + 3.

Step5: Expand 2,599,002

Break down by place values:

• Millions: 2,000,000 (2 * 1,000,000)
• Hundred thousands: 500,000 (5 * 100,000)
• Ten thousands: 90,000 (9 * 10,000)
• Thousands: 9,000 (9 * 1,000)
• Ones: 2 (2 * 1)

So, 2,599,002 = 2,000,000 + 500,000 + 90,000 + 9,000 + 2.

Step6: Expand 8,003,452

Break down by place values:

• Millions: 8,000,000 (8 * 1,000,000)
• Thousands: 3,000 (3 * 1,000)
• Hundreds: 400 (4 * 100)
• Tens: 50 (5 * 10)
• Ones: 2 (2 * 1)

So, 8,003,452 = 8,000,000 + 3,000 + 400 + 50 + 2.

Answer:

1. \( 48 \times 3 = 144 \)
2. \( 653 \times 8 = 5224 \)
3. \( 905,603 = 900,000 + 5,000 + 600 + 3 \)
4. \( 589,043 = 500,000 + 80,000 + 9,000 + 40 + 3 \)
5. \( 2,599,002 = 2,000,000 + 500,000 + 90,000 + 9,000 + 2 \)
6. \( 8,003,452 = 8,000,000 + 3,000 + 400 + 50 + 2 \)