Is 3/4 between 7/12 and 18/24 on the number line?
3/4 = 18/24
True?
3/4 is the same as the largest number on the number line.
To determine if 3/4 is between 7/12 and 18/24 on the number line, we need to compare their numerical values.
First, let's simplify the fractions:
- 7/12 cannot be simplified any further.
- 18/24 can be simplified to 3/4 by dividing both numerator and denominator by their greatest common divisor, which is 6.
Now we compare the simplified fractions:
- We have 3/4 and 7/12.
- To compare them, we can either find a common denominator or convert them to decimals.
Method 1: Finding a common denominator
To compare fractions with different denominators, we can find a common denominator. The least common multiple (LCM) of 4 and 12 is 12.
Now let's convert 3/4 and 7/12 to fractions with a common denominator of 12:
- 3/4 becomes 9/12 (multiply numerator and denominator by 3).
- 7/12 remains the same.
Now we compare 9/12 and 7/12. Clearly, 9/12 is greater than 7/12.
Method 2: Converting to decimals
Another way to compare these fractions is by converting them to decimals:
- 3/4 as a decimal is 0.75 (divide the numerator by the denominator).
- 7/12 as a decimal is approximately 0.5833 (divide the numerator by the denominator).
Comparing these decimals, we can see that 0.75 is greater than 0.5833.
Both methods indicate that 3/4 is greater than 7/12. Therefore, 3/4 is not between 7/12 and 18/24 on the number line.