Final answer:
To determine if fractions are equivalent, you compare them by either multiplying or dividing their numerators and denominators by the same number. 5/7 is equivalent to 15/21, but 3/12 is not equivalent to 2/16, and 4/8 is not equivalent to 6/24.
Step-by-step explanation:
When comparing fractions to determine if they are equivalent, we look to see if one is a multiple of the other. The key is whether you can multiply or divide both the numerator and denominator of one fraction by the same number to get the other fraction.
- 5/7=15/21: To check this, you can multiply the numerator (5) and the denominator (7) of the first fraction by 3 to see if it equals the second fraction (5*3=15 and 7*3=21), or you can divide the numerator and denominator of the second fraction by 3 (15/3=5 and 21/3=7). Both methods show these fractions are equivalent.
- 3/12=2/16: If we try to find a number to multiply or divide both parts of one fraction to get the other, we won't find it. 3 cannot be multiplied to get 2, nor can 12 be multiplied to get 16. Therefore, these fractions are not equivalent.
- 4/8=6/24: Here, if you multiply the numerator (4) and denominator (8) of the first fraction by 3, you get the second fraction (4*3=12 and 8*3=24), which is not quite the same. However, if you divide the numerator and denominator of the second fraction by 4 (6/4=1.5 and 24/4=6), you also don't get the first fraction. Again, these fractions are not equivalent.
This process of finding equivalent fractions is based on the principle that multiplying or dividing both the numerator and the denominator by the same number (a non-zero number) will not change the value of the fraction.