Compare $7 / 8$ with $14 / 16$ using ( $<,>,=$ ).
Answer (1)
Simplify the fraction 16 14 by dividing both numerator and denominator by 2: 16 14 = 8 7 .
Compare the simplified fraction with 8 7 .
Since 8 7 = 8 7 , the two fractions are equal.
Therefore, 8 7 = = 16 14 .
Explanation
Problem Analysis We are given two fractions, 7/8 and 14/16 . Our goal is to compare them using the symbols , ="> < , > , = to determine their relationship.
Simplifying the Fraction To compare the fractions, we can simplify 14/16 . Both the numerator and denominator are divisible by 2. Dividing both by 2, we get:
16 14 = 16 ÷ 2 14 ÷ 2 = 8 7
Comparing the Fractions Now we compare the simplified fraction 7/8 with the original fraction 7/8 . Since they are the same, the two fractions are equal.
8 7 = 8 7
Final Answer Therefore, 7/8 is equal to 14/16 .
8 7 = 16 14
Examples
Understanding fraction equality is crucial in everyday situations, such as sharing a pizza. If you cut a pizza into 8 slices and take 7, you have 7/8 of the pizza. If you cut the same pizza into 16 slices and take 14, you have 14/16 of the pizza. Since 7/8 = 14/16 , you're getting the same amount of pizza in both scenarios, just divided into smaller slices in the second case. This concept applies to various real-life situations, from cooking to measuring ingredients.
