To verify the commutative property for addition using the given values [tex]\( x = \frac{1}{2} \)[/tex] and [tex]\( y = \frac{3}{5} \)[/tex], follow these steps:
1. Identify the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- [tex]\( x = \frac{1}{2} \)[/tex]
- [tex]\( y = \frac{3}{5} \)[/tex]
2. Calculate [tex]\( x + y \)[/tex]:
- [tex]\( x + y = \frac{1}{2} + \frac{3}{5} \)[/tex]
3. To add the fractions, find a common denominator:
- The denominators are 2 and 5. The least common multiple (LCM) of 2 and 5 is 10.
4. Convert the fractions to have a common denominator:
- [tex]\( \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \)[/tex]
- [tex]\( \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \)[/tex]
5. Add the fractions:
- [tex]\( \frac{5}{10} + \frac{6}{10} = \frac{5 + 6}{10} = \frac{11}{10} = 1.1 \)[/tex]
6. Calculate [tex]\( y + x \)[/tex]:
- [tex]\( y + x = \frac{3}{5} + \frac{1}{2} \)[/tex]
7. Again, find a common denominator and convert the fractions:
- This step is identical to step 3 and 4 since addition is commutative:
- [tex]\( \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \)[/tex]
- [tex]\( \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \)[/tex]
8. Add the fractions:
- [tex]\( \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} = 1.1 \)[/tex]
9. Compare the results from both additions:
- [tex]\( x + y = \frac{11}{10} = 1.1 \)[/tex]
- [tex]\( y + x = \frac{11}{10} = 1.1 \)[/tex]
10. Conclusion:
- Since [tex]\( x + y \)[/tex] and [tex]\( y + x \)[/tex] both equal 1.1, the commutative property [tex]\( x + y = y + x \)[/tex] is verified.
Therefore, for the given values [tex]\( x = \frac{1}{2} \)[/tex] and [tex]\( y = \frac{3}{5} \)[/tex], the commutative property holds true.
