Answer :
We begin by simplifying each fraction:
1. Simplify
[tex]$$\frac{24}{36}.$$[/tex]
The greatest common divisor (GCD) of 24 and 36 is 12. Dividing the numerator and the denominator by 12, we have
[tex]$$\frac{24 \div 12}{36 \div 12} = \frac{2}{3}.$$[/tex]
2. Simplify
[tex]$$\frac{8}{12}.$$[/tex]
The GCD of 8 and 12 is 4. Dividing by 4, we obtain
[tex]$$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}.$$[/tex]
3. Simplify
[tex]$$\frac{12}{16}.$$[/tex]
The GCD of 12 and 16 is 4. Dividing by 4 gives
[tex]$$\frac{12 \div 4}{16 \div 4} = \frac{3}{4}.$$[/tex]
4. Simplify
[tex]$$\frac{4}{6}.$$[/tex]
The GCD of 4 and 6 is 2. Dividing by 2, we have
[tex]$$\frac{4 \div 2}{6 \div 2} = \frac{2}{3}.$$[/tex]
5. Simplify
[tex]$$\frac{18}{20}.$$[/tex]
The GCD of 18 and 20 is 2. Dividing by 2 yields
[tex]$$\frac{18 \div 2}{20 \div 2} = \frac{9}{10}.$$[/tex]
Now, observe that the fractions
[tex]$$\frac{24}{36}, \quad \frac{8}{12}, \quad \text{and} \quad \frac{4}{6}$$[/tex]
all simplify to
[tex]$$\frac{2}{3}.$$[/tex]
Thus, these three fractions are equivalent.
In summary, the equivalent fractions are:
[tex]$$\frac{24}{36}, \quad \frac{8}{12}, \quad \frac{4}{6}.$$[/tex]
1. Simplify
[tex]$$\frac{24}{36}.$$[/tex]
The greatest common divisor (GCD) of 24 and 36 is 12. Dividing the numerator and the denominator by 12, we have
[tex]$$\frac{24 \div 12}{36 \div 12} = \frac{2}{3}.$$[/tex]
2. Simplify
[tex]$$\frac{8}{12}.$$[/tex]
The GCD of 8 and 12 is 4. Dividing by 4, we obtain
[tex]$$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}.$$[/tex]
3. Simplify
[tex]$$\frac{12}{16}.$$[/tex]
The GCD of 12 and 16 is 4. Dividing by 4 gives
[tex]$$\frac{12 \div 4}{16 \div 4} = \frac{3}{4}.$$[/tex]
4. Simplify
[tex]$$\frac{4}{6}.$$[/tex]
The GCD of 4 and 6 is 2. Dividing by 2, we have
[tex]$$\frac{4 \div 2}{6 \div 2} = \frac{2}{3}.$$[/tex]
5. Simplify
[tex]$$\frac{18}{20}.$$[/tex]
The GCD of 18 and 20 is 2. Dividing by 2 yields
[tex]$$\frac{18 \div 2}{20 \div 2} = \frac{9}{10}.$$[/tex]
Now, observe that the fractions
[tex]$$\frac{24}{36}, \quad \frac{8}{12}, \quad \text{and} \quad \frac{4}{6}$$[/tex]
all simplify to
[tex]$$\frac{2}{3}.$$[/tex]
Thus, these three fractions are equivalent.
In summary, the equivalent fractions are:
[tex]$$\frac{24}{36}, \quad \frac{8}{12}, \quad \frac{4}{6}.$$[/tex]
