Which one of the following pairs of numbers contains like fractions? A. 5/4 and 4/5 B. 4/8 and 12/16 C. 6/7 and 60/70 D. 1/2 and 3/2
The Correct Answer and Explanation is:
Explanation:
To determine which pair contains like fractions, first understand what “like fractions” are. Like fractions are fractions that have the same denominator. This is a key rule in fraction comparison and arithmetic. Fractions with the same denominator are easier to add, subtract, or compare because they represent parts of the same whole.
Now, examine each choice:
A. 5/4 and 4/5
- Denominators: 4 and 5
- These are unlike fractions because the denominators are different.
B. 4/8 and 12/16
- Denominators: 8 and 16
- At first glance, they look different. However, reduce both to their simplest forms:
- 4/8 simplifies to 1/2
- 12/16 simplifies to 3/4
- Even after simplification, the denominators remain different.
However, this looks incorrect initially because they do not have the same denominator. Let’s reevaluate other options more carefully.
C. 6/7 and 60/70
- Denominators: 7 and 70
- Not the same.
- 60/70 simplifies to 6/7
- So, 6/7 and 60/70 represent the same value, but not like fractions since their denominators differ.
D. 1/2 and 3/2
- Denominators: 2 and 2
- These fractions have the same denominator, so they are like fractions.
Thus, the most accurate answer is:
Corrected Answer: D. 1/2 and 3/2
These fractions are like fractions because they share the same denominator, which is 2. Even though their numerators differ, the fact that the denominators are identical makes them easy to compare and work with. They represent different amounts, but they are built from the same-sized parts. The concept of like fractions is important in addition and subtraction because such operations require matching denominators to proceed correctly.
