Are the following fractions equivalent? justify your answer
18/24 9/12 15/20 6/9
Three of the fractions = 3/4
One does not.
18=2*3*3
24=2*2*2*3
18/24=(2*3*3)/(2*2*2*3)=3/(2*2)=3/4
9=3*3
12=2*2*3
9/12=(3*3)/(2*2*3)=3/(2*2)=3/4
15=3*5
20=2*2*5
15/20=(3*5)/(2*2*5)=3/(2*2)=3/4
6=2*3
9=3*3
6/9=(2*3)/(3*3)=2/3
To determine if the fractions are equivalent, we need to simplify each fraction and compare them. Fractions are equivalent if their simplified forms have the same numerator and denominator.
Let's simplify each fraction:
1. 18/24:
- Divide both the numerator and denominator by their greatest common divisor (GCD), which is 6.
- Dividing both by 6, we get 3/4.
2. 9/12:
- Divide both the numerator and denominator by their GCD, which is 3.
- Dividing both by 3, we get 3/4.
3. 15/20:
- Divide both the numerator and denominator by their GCD, which is 5.
- Dividing both by 5, we get 3/4.
4. 6/9:
- Divide both the numerator and denominator by their GCD, which is 3.
- Dividing both by 3, we get 2/3.
Now, let's compare the simplified fractions:
- The fractions 18/24, 9/12, and 15/20 all simplify to 3/4.
- The fraction 6/9 simplifies to 2/3.
Since the simplified forms of 18/24, 9/12, and 15/20 are all equal to 3/4, but 6/9 is different, we can conclude that the given fractions are not all equivalent.
Therefore, the fractions 18/24, 9/12, 15/20, and 6/9 are not equivalent.