To determine if the fractions 7 63 and 7 630 are equivalent, it’s essential to compare them systematically.
First, let’s convert both numbers into improper fractions for clearer comparison:
1. The mixed number 7 63 can be converted as follows:
- Multiply the whole number (7) by the denominator (63): 7 * 63 = 441.
- Add the numerator (0, since 7 63 does not change any actual value in the fraction part): 441 + 0 = 441.
- So, 7 63 as an improper fraction is 441/63.
2. Now, let’s check 7 630:
- Again, multiply the whole number (7) by the denominator (630): 7 * 630 = 4410.
- Add the numerator (0, same reason): 4410 + 0 = 4410.
- Thus, 7 630 as an improper fraction is 4410/630.
Now, let’s simplify both fractions:
- For 441/63, we can divide both numerator and denominator by 63: 441 ÷ 63 = 7. Therefore, 441/63 simplifies to 7.
- For 4410/630, both numbers can be simplified by dividing by 630: 4410 ÷ 630 = 7. Therefore, 4410/630 also simplifies to 7.
Since both fractions simplify to 7, we can conclude that 7 63 is equivalent to 7 630.