Certainly! Let's compare each of the given pairs using the appropriate mathematical symbol ([tex]${data-answer}gt;$[/tex], [tex]$=$[/tex], or [tex]${data-answer}lt;$[/tex]).
a. Compare 3 and -3:
- When comparing positive and negative numbers, the positive number is always greater.
- Therefore, [tex]\(3\)[/tex] is greater than [tex]\(-3\)[/tex].
- Symbol: [tex]\(3 > -3\)[/tex]
b. Compare 12 and 24:
- When comparing two positive numbers, the larger number is the greater one.
- Therefore, [tex]\(12\)[/tex] is less than [tex]\(24\)[/tex].
- Symbol: [tex]\(12 < 24\)[/tex]
e. Compare 7.2 and 7:
- When comparing two positive decimals and whole numbers where the decimal part adds value, you can see 7.2 is slightly more than 7 due to the additional 0.2.
- Therefore, [tex]\(7.2\)[/tex] is greater than [tex]\(7\)[/tex].
- Symbol: [tex]\(7.2 > 7\)[/tex]
f. Compare -7.2 and -7:
- When comparing two negative numbers, the number with the smaller absolute value is greater.
- Therefore, [tex]\(-7.2\)[/tex] is less than [tex]\(-7\)[/tex].
- Symbol: [tex]\(-7.2 < -7\)[/tex]
i. Compare [tex]\(\frac{-3}{5}\)[/tex] and [tex]\(\frac{-6}{10}\)[/tex]:
- First, simplify both fractions:
- [tex]\(\frac{-3}{5}\)[/tex] is already in its simplest form.
- [tex]\(\frac{-6}{10}\)[/tex] simplifies to [tex]\(\frac{-3}{5}\)[/tex] after dividing the numerator and the denominator by 2.
- Since both fractions are equal after simplification.
- Therefore, [tex]\(\frac{-3}{5}\)[/tex] is equal to [tex]\(\frac{-6}{10}\)[/tex].
- Symbol: [tex]\(\frac{-3}{5} = \(\frac{-6}{10}\)[/tex]\)
j. Compare [tex]\(\frac{-2}{3}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- When comparing a negative fraction to a positive fraction, the positive fraction is always greater.
- Therefore, [tex]\(\frac{-2}{3}\)[/tex] is less than [tex]\(\frac{1}{3}\)[/tex].
- Symbol: [tex]\(\frac{-2}{3} < \(\frac{1}{3}\)[/tex]\)
To summarize:
a. [tex]\(3 > -3\)[/tex]
b. [tex]\(12 < 24\)[/tex]
e. [tex]\(7.2 > 7\)[/tex]
f. [tex]\(-7.2 < -7\)[/tex]
i. [tex]\(\frac{-3}{5} = \(\frac{-6}{10}\)[/tex]\)
j. [tex]\(\frac{-2}{3} < \(\frac{1}{3}\)[/tex]\)
