Use the distributive property to express 24 40
The Correct Answer and Explanation is:
To apply the distributive property, you can break down 24 and 40 into smaller, more manageable factors. Here’s how you can do it:
Problem:
Express 24 × 40 using the distributive property.
Step-by-Step Solution:
- Break down 40 into a sum of simpler numbers:
One easy way to break 40 down is as the sum of 30 and 10: 40=30+1040 = 30 + 1040=30+10 - Apply the distributive property:
Now, apply the distributive property. The distributive property says: a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times ca×(b+c)=a×b+a×c In this case, a=24a = 24a=24, b=30b = 30b=30, and c=10c = 10c=10. So, we distribute 24 to both 30 and 10: 24×40=24×(30+10)24 \times 40 = 24 \times (30 + 10)24×40=24×(30+10) This gives: 24×40=(24×30)+(24×10)24 \times 40 = (24 \times 30) + (24 \times 10)24×40=(24×30)+(24×10) - Calculate each term:
Now calculate each multiplication: 24×30=72024 \times 30 = 72024×30=720 24×10=24024 \times 10 = 24024×10=240 - Add the results together:
Finally, add the two results: 720+240=960720 + 240 = 960720+240=960
Final Answer:
24×40=96024 \times 40 = 96024×40=960
Explanation:
The distributive property is a very useful tool for simplifying calculations, especially when dealing with large numbers. By breaking down 40 into two smaller, easy-to-multiply numbers (30 and 10), you can perform simpler multiplications and then add the results together. This method is particularly helpful when multiplying mentally or when you want to avoid complex multiplication.
