Let's look at how to make equivalent fractions. Here we have a shape divided into three equal parts with one part shaded. That's the fraction 1/3. Now let's split each of the three parts in half. The hole is now divided into six parts and two of them are shaded. The shaded area is the same size which means 1/3 is equivalent to 2 sixths. Let's try it again. Starting with 1/3. This time we'll divide the hole into 12 smaller triangles. To shade the same amount, we now need to fill in four of those triangles. So 1/3 is also equivalent to 4 12ths.
Notice the pattern here. We started with three total parts and ended up with 12.
That's four times as many parts. To keep the fractions value the same, we also need to have four times as many shaded parts. 1 shaded part * 4 gives us four shaded parts. We can find an equivalent fraction by multiplying the top and bottom of a fraction by the same number.
Here 1 * 4als 4 and 3 * 4 = 12.
Let's look at a different problem.
This shape is divided into 16 triangles and eight of them are shaded. So 1/2 is equivalent to 86.
What number did we have to multiply 1 and two by to get to 86.
To get from a numerator of 1 to a numerator of 8, we multiply by 8. To get from a denominator of 2 to a denominator of 16, we also multiply by 8. As long as we multiply the top and bottom by the same number, we create an equivalent fraction. Let's use this idea to make another fraction. Here we start with a shape that shows 3/8. Let's make a fraction that's equal to 3/8. If we multiply the denominator 8 by 2, we get 16 total parts. To keep the fraction equivalent, we must also multiply the numerator 3 by 2. That gives us 6. This means 3/8 is equivalent to 616.
You can always find an equivalent fraction by multiplying the numerator and the denominator by the same number.
This changes how many pieces the hole is divided into and how many of those pieces are counted, but it doesn't change the overall portion of the hole.
Whether it's 3/8 or 616, the value remains exactly the same.
