Final answer:
The student's mathematical questions involve comparing pairs of fractions and decimals to determine which is larger or smaller, and this requires converting to common denominators or decimals and understanding sign rules for operations.
Step-by-step explanation:
The subject of the student's question is number comparison in mathematics, specifically comparing fractions and decimals to determine which is larger or smaller. Comparing such numbers requires understanding of how to find common denominators for fractions or converting fractions to decimals.
Step-by-step Comparison:
- To compare -3/8 and -2/5, find a common denominator or convert to decimals. -3/8 = -0.375, and -2/5 = -0.4. Since -0.375 is closer to zero than -0.4, -3/8 is greater.
- For 3/4 and 7/9, you may also convert to decimals or compare directly by finding a common denominator. 3/4 = 0.75, and 7/9 is approximately 0.777. Thus, 7/9 is greater than 3/4.
- Comparing 1/3 and 3/10 involves converting these to decimals or finding a common denominator; 1/3 = 0.333... and 3/10 = 0.3. So, 1/3 is larger than 3/10.
- Finally, -0.4 and -5/12 can be converted to the same form; -0.4 is -0.4 as a decimal, and -5/12 is approximately -0.4167. Since -0.4 is closer to zero than -0.4167, -0.4 is greater than -5/12.
This illustrates the importance of understanding how to manipulate different forms of numbers in mathematics. Knowledge of signs when adding, subtracting, multiplying, and dividing is crucial to accurate number comparison. Remember that the sign rules for multiplication and division follow the same pattern; two numbers of the same sign result in a positive, while numbers of opposite signs result in a negative outcome when multiplied or divided.