Which of the following is a true statement?
1/3 > 3/8
4/8< 8/24 4/8<9/16 4/16>3/8
The Correct Answer and Explanation is:
Let’s evaluate each of the given statements one by one.
- 1/3 > 3/8 To compare these two fractions, we can find a common denominator or convert them to decimals. Let’s first convert both fractions into decimals.
- ( \frac{1}{3} \approx 0.3333 )
- ( \frac{3}{8} = 0.375 ) Since ( 0.3333 < 0.375 ), the statement 1/3 > 3/8 is false.
- 4/8 < 8/24 To compare these two fractions, let’s simplify both fractions.
- ( \frac{4}{8} ) simplifies to ( \frac{1}{2} ) (since both the numerator and denominator can be divided by 4).
- ( \frac{8}{24} ) simplifies to ( \frac{1}{3} ) (since both the numerator and denominator can be divided by 8). Now, compare ( \frac{1}{2} ) and ( \frac{1}{3} ). Since ( \frac{1}{2} = 0.5 ) and ( \frac{1}{3} \approx 0.3333 ), it’s clear that ( \frac{1}{2} > \frac{1}{3} ). Therefore, the statement 4/8 < 8/24 is false.
- 4/8 < 9/16 We simplify ( \frac{4}{8} ) to ( \frac{1}{2} ) as before. Now, let’s compare ( \frac{1}{2} ) with ( \frac{9}{16} ).
- To compare these fractions, we can either convert them to decimals or find a common denominator. Let’s convert to decimals:
- ( \frac{1}{2} = 0.5 )
- ( \frac{9}{16} = 0.5625 ) Since ( 0.5 < 0.5625 ), the statement 4/8 < 9/16 is true.
- 4/16 > 3/8 Let’s simplify ( \frac{4}{16} ) to ( \frac{1}{4} ). Now compare ( \frac{1}{4} ) and ( \frac{3}{8} ).
- To compare these, we can find a common denominator. The least common denominator (LCD) of 4 and 8 is 8.
- ( \frac{1}{4} = \frac{2}{8} ) (by multiplying both the numerator and denominator by 2).
- ( \frac{3}{8} ) remains as is. Since ( \frac{2}{8} < \frac{3}{8} ), the statement 4/16 > 3/8 is false.
Conclusion:
The true statement is 4/8 < 9/16.