Let's say we're given the fraction 3/5.
Fraction to a Percent: Multiply or divide both the numerator and the denominator by a certain number that will make the denominator 100. So we have to multiply 20 with 5 in order to make the denominator equal to 100. But as a rule of fractions, you also have to multiply the numerator by the same number, 20, which will give us 60/100. After making your denominator 100, whatever number you get from your numerator will be your percent. So 3/5 = 60%.
Fraction to a Decimal: Do the same thing as above, except the last step. So you should have 60/100 at this point. Notice the denominator has 2 zeros, correct? 100 has 2 zeros. That means that if you wanted to convert 60/100 to a decimal, you have to take the numerator and move the decimal point TWO places to the left. Meaning you just shift it two numbers to the left. But where is the decimal? It's right after the zero. That's always the case for whole numbers - the decimal point is right after the last digit in whole numbers. So now that we know what to do, shifting two decimal places to the left of 60 will give us .60, and can be written as 0.6. So 3/5 = 0.6.
Fraction to an Equivalent: This just means find a fraction that has the same value as the given fraction, which is 3/5 in this case. In order to do this, you can either multiply or divide both the numerator and denominator by the same number. This does NOT work with addition and subtraction, however. Observe:
Multiplying by 2:
(3 * 2)/(5 * 2) = 6/10 <- Equivalent to 3/5, you can check using a calculator.
Dividing by 2:
(3/2)/(5/2) = 1.5/2.5 <- Equivalent to 3/5, you can check using a calculator.
Adding by 2:
(3 + 2)/(5 + 2) = 5/7 <- NOT equivalent because it's larger than 3/5.
Subtracting by 2:
(3 - 2)/(5 - 2) = 1/3 <- NOT equivalent because it's smaller than 3/5.