Which of the following pairs of numbers contain like fractions? A. 3 /2 and 2 /3 B. 6 /7 and 15 /7 C. 5 /6 and 10/12 D. 31 /2 and 43 /4
The Correct Answer and Explanation is:
Correct Answer: B. 6/7 and 15/7
Explanation:
Fractions are called like fractions when they have the same denominator. The denominator is the number below the fraction bar and tells how many equal parts the whole is divided into.
Let’s analyze each option:
- Option A: 3/2 and 2/3
The denominators are 2 and 3. Since they are not the same, these are unlike fractions. - Option B: 6/7 and 15/7
Both fractions have the denominator 7. This means they are like fractions. - Option C: 5/6 and 10/12
The denominators are 6 and 12. These are different, so the fractions are unlike fractions, even though they can be compared or simplified. The key idea is that their denominators must be exactly the same to be like fractions. - Option D: 31/2 and 43/4
The denominators are 2 and 4. Since they are different, these are unlike fractions.
Only option B has both fractions with the same denominator of 7, which is the defining characteristic of like fractions.
Why Like Fractions Matter:
Like fractions are important in arithmetic because they are easier to add and subtract. When fractions have the same denominator, only the numerators (top numbers) need to be added or subtracted, and the denominator remains unchanged. This simplifies the calculation process and is especially useful in solving equations, comparing values, or converting to decimals.
For example:
- 6/7 + 15/7 = (6 + 15)/7 = 21/7 = 3
Operations like this are not possible directly with unlike fractions without first finding a common denominator. Therefore, recognizing like fractions makes fraction work more efficient and accurate.
