Which of the following pairs of numbers contain like fractions? a. 5 / 6 and 10 / 12 b. 3 / 2 and 2 / 3 c. 3 1 / 2 and 4 3 / 4 d. 6 / 7 and 1 5 / 7
The Correct Answer and Explanation is:
Correct Answer: d. 6 / 7 and 1 5 / 7
Explanation:
Like fractions are fractions that have the same denominator. The denominator is the bottom part of a fraction, and it shows the total number of equal parts. When comparing two fractions, if their denominators are equal, the fractions are considered like fractions.
Let’s evaluate each pair:
a. 5/6 and 10/12
These fractions do not have the same denominator. The first has a denominator of 6, and the second has 12. Even though these can be compared or simplified, they are not like fractions.
b. 3/2 and 2/3
These fractions have different denominators: 2 and 3. Therefore, they are not like fractions.
c. 3 1/2 and 4 3/4
These are mixed numbers. To compare, we look at the fractional parts: 1/2 and 3/4. Their denominators are different. So, these are not like fractions either.
d. 6/7 and 1 5/7
The first number is a proper fraction. The second is a mixed number. To compare their fractional parts, we focus on the denominators.
- 6/7 is already a fraction with denominator 7.
- 1 5/7 includes a whole number (1) and the fraction 5/7.
Both 6/7 and 5/7 have the same denominator of 7. This means they can be added or subtracted easily. So, these two values contain like fractions.
Even though one of them is a mixed number, the fraction parts can still be compared because they share the same denominator. Therefore, option d is the correct answer.
Understanding like fractions helps with operations like addition and subtraction of fractions. It is easier to perform these operations when the denominators are the same, as only the numerators need to be considered.
