24 divided by 48 and show work
The Correct Answer and Explanation is:
Problem:
What is 24 divided by 48?
Step-by-Step Work:
We are asked to divide 24 by 48, or find:2448\frac{24}{48}4824
Step 1: Identify the relationship
24 is smaller than 48, so the result will be less than 1.
Step 2: Simplify the fraction
2448\frac{24}{48}4824
We look for the greatest common factor (GCF) of 24 and 48.
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- The greatest common factor is 24
Now simplify the fraction:24÷2448÷24=12\frac{24 \div 24}{48 \div 24} = \frac{1}{2}48÷2424÷24=21
Step 3: Convert to decimal (if needed)
12=0.5\frac{1}{2} = 0.521=0.5
Final Answer:
24÷48=12=0.524 \div 48 = \frac{1}{2} = 0.524÷48=21=0.5
Textbook-Style Explanation (300 words):
Division is the process of splitting a number into equal parts. In this problem, we are dividing 24 by 48, which can be written as the fraction 2448\frac{24}{48}4824. This represents how many times 48 can fit into 24. Since 24 is smaller than 48, we expect the result to be a number less than 1.
To simplify the fraction, we find the greatest common factor (GCF) of the numerator and the denominator. The GCF of 24 and 48 is 24 because 24 is the largest number that evenly divides both 24 and 48. We divide both the numerator and the denominator by 24 to simplify:2448=24÷2448÷24=12\frac{24}{48} = \frac{24 \div 24}{48 \div 24} = \frac{1}{2}4824=48÷2424÷24=21
This tells us that 24 is half of 48. In fractional form, this is written as 12\frac{1}{2}21, and in decimal form, it is equal to 0.5.
To verify the result, we can multiply 48 by 0.5:48×0.5=2448 \times 0.5 = 2448×0.5=24
So, 24 divided by 48 equals 0.5. Understanding how to simplify fractions and convert between fractions and decimals is an important part of basic arithmetic and helps build skills for more advanced math topics.
