Which fraction is not equivalent to 9/12 1. 24/32 2. 6/8 3. 15/20 4.16/24
The Correct Answer and Explanation is:
The correct answer is: 4. 16/24
To determine which fraction is not equivalent to 9/12, we must first simplify 9/12 to its lowest terms. To do this, find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 9 and 12 is 3.912=9÷312÷3=34\frac{9}{12} = \frac{9 \div 3}{12 \div 3} = \frac{3}{4}129=12÷39÷3=43
So, 9/12 simplifies to 3/4. The next step is to check which of the given fractions also simplify to 3/4. If a fraction simplifies to 3/4, then it is equivalent to 9/12.
- 24/32
The GCD of 24 and 32 is 8.
2432=24÷832÷8=34\frac{24}{32} = \frac{24 \div 8}{32 \div 8} = \frac{3}{4}3224=32÷824÷8=43
Equivalent.
- 6/8
The GCD of 6 and 8 is 2.
68=6÷28÷2=34\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}86=8÷26÷2=43
Equivalent.
- 15/20
The GCD of 15 and 20 is 5.
1520=15÷520÷5=34\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}2015=20÷515÷5=43
Equivalent.
- 16/24
The GCD of 16 and 24 is 8.
1624=16÷824÷8=23\frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}2416=24÷816÷8=32
Not equivalent to 3/4.
Therefore, the only fraction that is not equivalent to 9/12 is 16/24.
Explanation:
In mathematics, equivalent fractions represent the same value or proportion, even if their numerators and denominators are different. To determine if two fractions are equivalent, simplifying them to their lowest terms is a reliable method. Simplification involves dividing both the numerator and the denominator by their greatest common divisor.
Once a fraction is reduced to its simplest form, it can easily be compared with others. In this case, 9/12 simplifies to 3/4. All the given choices must also reduce to 3/4 to be equivalent. Fractions like 24/32, 6/8, and 15/20 all reduce to 3/4, confirming their equivalency. However, 16/24 simplifies to 2/3, which differs from 3/4. Therefore, it does not represent the same value and is not equivalent to 9/12.
