Both fractions have the same numerator, which is 5. A fraction (a)/(b) represents taking a parts out of an object divided into b equal parts.

why 5/6 is greater than 5/7

Answer: $\frac{5}{6} > \frac{5}{7}$ because both fractions have the same numerator, and dividing a whole into 6 equal parts yields larger individual parts than dividing it into 7 equal parts ( $5 \times \frac{1}{6} > 5 \times \frac{1}{7}$ ). Equivalently, with common denominators, $\frac{35}{42} > \frac{30}{42}$ .

Step-by-step solution

Step 1: Analyze the Numerators and Denominators

Both fractions have the same numerator, which is $5$ . A fraction $\frac{a}{b}$ represents taking $a$ parts out of an object divided into $b$ equal parts.

Step 2: Understand the Meaning of the Denominator

The denominator tells us how many equal parts the whole is divided into. Dividing a whole into fewer parts makes each part larger, so each $\frac{1}{6}$ piece is larger than each $\frac{1}{7}$ piece.

Step 3: Compare the Same Number of Parts

Since each $\frac{1}{6}$ part is larger than each $\frac{1}{7}$ part, taking $5$ of the larger parts will always give a greater total than taking $5$ of the smaller parts. For fractions with the same numerator, the fraction with the smaller denominator is always greater.

Step 4: Verify Using a Common Denominator

To confirm arithmetically, we convert both fractions to like fractions using their common denominator, $42$ . Comparing the numerators, since $35 > 30$ , it confirms that $\frac{35}{42} > \frac{30}{42}$ , so $\frac{5}{6} > \frac{5}{7}$ .

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