What are Equivalent Fractions?

Any number divided by itself is 1
2/5 is a reduced form of 4/10
Dividing by 1 does not change the value of the number you're dividing
4/10 must be equal to 2/5, since all we did was divide by 1
Fractions with the same value are called EQUIVALENT FRACTIONS
Multiplying by 1 also does not change the value of a number
8/20 is also equivalent to 4/10
We can multiply by any number over itself to give us an infinite number of equivalent fractions

1. Let's take a look at a fraction first as an example
1. Any number divided by itself is 1
2. So dividing 4/10 by 2/2 is the same as dividing 4/10 by 1
3. When you divide by 1, you don't change the value of the number you're dividing
1. When you divide by 1, you don't change the value of the number you're dividing
2. Since we got 2/5 when we divided 4/10 by 2/2 (which we know is just 1), it must be equal to 4/10
1. 4/10 and 2/5 are equivalent fractions
2. If you divide 4 by 10, you get 0.4 as a decimal
3. But if you divide 2 by 5, you also get 0.4 as a decimal!
4. These two fractions have the same value, so they are equivalent!
1. A 'fancy form of 1' is just a number divided by itself
2. So 2/2 is an example of a number we could multiply or divide by to find equivalent fractions
1. Let's try finding some other equivalent fractions, this time by multiplying
1. Remember, multiplying by 1 also does not change the value of a number
2. In fact, 1 is what we call the 'multiplicative identity'
3. Since we know that 2/2 is just 1, multiplying 4/10 by 2/2 should give us another equivalent fraction
1. 4/4 is another 'fancy form of 1'
2. Multiplying 4/10 by 4/4 gives us another equivalent fraction, 16/40
1. There are an infinite number of 'fancy forms of 1' that we could create by dividing numbers by themselves
2. Multiplying 4/10 by any one of these will give us a different equivalent fraction
3. So there is no limit to the number of equivalent fractions we could make!

What are equivalent fractions?