compare 7/8 with 14/16 using greater than less than or equal to
The correct answer and explanation is:
Correct Answer:
7/8 = 14/16
Explanation:
To compare the fractions 7/8 and 14/16, first check if they can be written with the same denominator. This allows a direct comparison between numerators. The denominators here are 8 and 16. The least common denominator (LCD) of 8 and 16 is 16.
Convert 7/8 to a fraction with a denominator of 16. Multiply both the numerator and the denominator by 2:
- 7 × 2 = 14
- 8 × 2 = 16
So, 7/8 becomes 14/16
Now compare:
- 14/16 and 14/16
Both fractions are exactly the same. This means they are equal.
Another way to verify this is to simplify 14/16. Divide both numerator and denominator by their greatest common factor, which is 2:
- 14 ÷ 2 = 7
- 16 ÷ 2 = 8
So, 14/16 simplifies to 7/8
This confirms that 14/16 = 7/8
Fractions can often look different but represent the same value. When the numerator and denominator of one fraction are both multiplied or divided by the same nonzero number, the value of the fraction stays the same. This is called simplifying or scaling.
In practical terms, 7/8 of a cake and 14/16 of the same cake mean the same portion is eaten. Understanding how to compare fractions helps when working with measurements, recipes, budgeting, and in many parts of daily life and academics.
Final comparison:
7/8 = 14/16