Equivalent Rational Numbers

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In this case, we are looking for three equivalent rational numbers to the fraction 3/2.

Equivalent Rational Numbers

Equivalent rational numbers are fractions that represent the same value. They can be obtained by multiplying or dividing the numerator and denominator by the same non-zero integer.

Method 1: Multiplying by the Same Number

One way to find equivalent rational numbers is by multiplying both the numerator and denominator of the fraction by the same non-zero integer. In the case of 3/2, we can multiply both the numerator and denominator by 2 to obtain an equivalent fraction:

3/2 = (3 * 2) / (2 * 2) = 6/4

Therefore, 6/4 is an equivalent rational number to 3/2.

Method 2: Dividing by the Same Number

Another way to find equivalent rational numbers is by dividing both the numerator and denominator of the fraction by the same non-zero integer. In the case of 3/2, we can divide both the numerator and denominator by 3 to obtain an equivalent fraction:

3/2 = (3 ÷ 3) / (2 ÷ 3) = 1/2/3/2 = 1/2

Therefore, 1/2 is an equivalent rational number to 3/2.

Method 3: Multiplying and Dividing by the Same Number

We can also find an equivalent rational number by multiplying the numerator and denominator by one number and then dividing them by another number. In the case of 3/2, we can multiply both the numerator and denominator by 4 and then divide them by 6 to obtain an equivalent fraction:

3/2 = (3 * 4) / (2 * 4) = 12/8 = (12 ÷ 6) / (8 ÷ 6) = 2/4

Therefore, 2/4 is an equivalent rational number to 3/2.

Conclusion

In summary, we have found three equivalent rational numbers to the fraction 3/2:

1. 6/4
2. 1/2
3. 2/4

These fractions represent the same value as 3/2 and can be obtained by multiplying or dividing the numerator and denominator of the fraction by the same non-zero integer.