Question

calculate in many ways
here are some different diagrams that represent 315 × 24. for each diagram, write a multiplication expression inside each rectangle to represent the product.
1
300 10 5
20
4
2
315
20
4
3
300 10 5
24
4 use one of the diagrams to find the value of 315 × 24.
5 explain why you chose that diagram to find the product.

Explanation:

Step1: Analyze the first diagram (for 315 = 300 + 10 + 5 and 24 = 20 + 4)

We can use the area model (distributive property) here. Calculate each sub - rectangle:

• For \(300\times20\): \(300\times20 = 6000\)
• For \(300\times4\): \(300\times4=1200\)
• For \(10\times20\): \(10\times20 = 200\)
• For \(10\times4\): \(10\times4 = 40\)
• For \(5\times20\): \(5\times20=100\)
• For \(5\times4\): \(5\times4 = 20\)

Step2: Sum up all the sub - products

Now, sum all these values: \(6000 + 1200+200 + 40+100 + 20\)
First, \(6000+1200 = 7200\)
Then, \(7200+200=7400\)
Then, \(7400 + 40=7440\)
Then, \(7440+100 = 7540\)
Then, \(7540+20=7560\)

Or we can use the second diagram: \(315\times20=6300\) and \(315\times4 = 1260\), then \(6300+1260=7560\)

Or the third diagram: \(300\times24 = 7200\), \(10\times24=240\), \(5\times24 = 120\), then \(7200+240 + 120=7560\)

Answer:

The value of \(315\times24\) is \(7560\)