which is greater -1 3/4 or -1 1/4
The Correct Answer and Explanation is:
To determine which number is greater between -1 3/4 and -1 1/4, we need to compare these two mixed numbers. A mixed number consists of a whole number and a fraction, and to compare them, we will first convert both mixed numbers to improper fractions, then compare their values.
Step 1: Convert -1 3/4 to an improper fraction.
A mixed number like -1 3/4 can be rewritten as:
-1 3/4 = – (1 + 3/4) = – (4/4 + 3/4) = -7/4.
So, -1 3/4 becomes -7/4 when written as an improper fraction.
Step 2: Convert -1 1/4 to an improper fraction.
Similarly, -1 1/4 can be rewritten as:
-1 1/4 = – (1 + 1/4) = – (4/4 + 1/4) = -5/4.
Thus, -1 1/4 becomes -5/4 when written as an improper fraction.
Step 3: Compare the improper fractions.
Now we have:
- -1 3/4 = -7/4
- -1 1/4 = -5/4
When comparing negative fractions, the fraction with the smaller absolute value is greater. This is because the negative fractions are less “negative.” For example, -7/4 is farther away from zero than -5/4, meaning -7/4 is less than -5/4.
Conclusion:
Since -5/4 is closer to zero than -7/4, -1 1/4 is greater than -1 3/4.
In summary, when comparing negative numbers, the one that is less negative (closer to zero) is the larger number. Hence, -1 1/4 is greater than -1 3/4.
