144 divided by 8 in distributive property
The correct answer and explanation is:
Correct Answer:
Using the distributive property,
144 ÷ 8 can be rewritten as:
(80 + 64) ÷ 8 = (80 ÷ 8) + (64 ÷ 8) = 10 + 8 = 18
Explanation (300 words):
The distributive property in arithmetic is a useful tool that breaks down a complex operation into simpler parts. It states that for any numbers aa, bb, and cc: a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times c
While it is most often used for multiplication, it can also help with division, especially when dividing a sum by a number. The division version of the distributive property says: b+ca=ba+ca\frac{b + c}{a} = \frac{b}{a} + \frac{c}{a}
This means that if you want to divide a number (which is the sum of two parts) by another number, you can split the dividend into two smaller parts, divide each separately, and then add the results.
For example, consider 144 ÷ 8.
Breaking 144 into two numbers that are easier to divide by 8 is key. We can split 144 as 80 + 64 because both 80 and 64 are divisible by 8.
- Divide 80 by 8:
80÷8=1080 ÷ 8 = 10 - Divide 64 by 8:
64÷8=864 ÷ 8 = 8
Adding these results:
10+8=1810 + 8 = 18
So, 144÷8=(80+64)÷8=80÷8+64÷8=10+8=18144 ÷ 8 = (80 + 64) ÷ 8 = 80 ÷ 8 + 64 ÷ 8 = 10 + 8 = 18
This method is especially helpful when working with mental math, as it breaks a large division problem into smaller, easier calculations.
In summary, the distributive property helps simplify division by splitting the number into manageable chunks, dividing each, then adding the results to find the answer efficiently.