Evaluating Mathematical Expression for 18-Year-Old Students

To evaluate the expression –1 × –1/2 ÷ –2/3 – 1/5, we will break it down step by step:

1. Identify the components: The expression consists of three main parts: multiplication, division, and subtraction involving negative fractions.
2. Start with the multiplication:
   –1 × –1/2 = 1/2
   (because multiplying two negative numbers gives a positive number).
3. Now we substitute this back into the expression:
   1/2 ÷ –2/3 – 1/5
4. Next, perform the division:
   Dividing by a fraction is the same as multiplying by its reciprocal:
   1/2 ÷ –2/3 = 1/2 × –3/2 = –3/4
5. Now substitute this result into the expression:
   –3/4 – 1/5
6. To subtract these fractions, we need a common denominator:
   The least common denominator (LCD) of 4 and 5 is 20.
7. Convert the fractions:
   –3/4 = –15/20
   (because –3 times 5 is –15, and 4 times 5 is 20)
   –1/5 = –4/20
   (because –1 times 4 is –4, and 5 times 4 is 20)
8. Now, combine the fractions:
   –15/20 – 4/20 = –19/20

Thus, the final evaluated expression is:

–19/20