Whole numbers as fractions

A fraction tells you about parts of a whole. The number on the bottom tells how many equal parts the whole is cut into. The number on the top tells how many of those parts you have.

When the top number and the bottom number are the same, the fraction equals 1 whole. Two halves make a whole, so 2/2 = 1. Three thirds make a whole, so 3/3 = 1. Five fifths make a whole, so 5/5 = 1.

You can use this pattern to find bigger whole numbers too. If one whole is 4/4, then two wholes is 8/4, because 8 is two groups of 4. Three wholes is 12/4, and four wholes is 16/4.

A whole number can also be written as a fraction with 1 on the bottom. The number 3 is the same as 3/1, because 3 wholes still count as 3. So 6/1 = 6 and 10/1 = 10.

Try it yourself: what whole number is 10/5? Think, 5/5 is one whole, so 10/5 is two wholes.

A number line is a great tool for fractions. Mark 0 at the start and 1 one step along. Now split the space between 0 and 1 into equal parts. If you split it into 4 equal parts, each part is one quarter, or 1/4.

Count the quarters with hops: 1/4, 2/4, 3/4, and then 4/4. Where does 4/4 land? Right on the 1 mark. That means 4/4 and 1 are the same point on the number line, so 4/4 = 1.

Keep hopping in quarters: 5/4, 6/4, 7/4, 8/4. Where does 8/4 land? On the 2 mark. So 8/4 = 2. Every 4 quarters you hop, you reach one more whole number.

You can do this with any fraction. Split the space into thirds and 3/3 lands on 1, while 6/3 lands on 2. Split it into halves and 2/2 lands on 1, while 4/2 lands on 2.

So when you see a fraction on a number line, start at 0 and count the parts. If your hop lands exactly on a whole number mark, the fraction equals that whole number.

Did you know a plain whole number like 4 can dress up as a fraction? It is easy, and it works for every whole number.

Step 1: write the whole number on top. For 4, the top number is 4.

Step 2: write 1 on the bottom. That makes 4/1.

Why does this work? The bottom number tells you the size of each piece. A bottom number of 1 means each piece is a whole one. So 4/1 means 4 whole pieces, which is just 4.

You can write any whole number this way. 7 = 7/1. 12 = 12/1. 100 = 100/1. The value never changes.

You can also go the other way. When you see a fraction with 1 on the bottom, like 9/1, you can take off the bottom and just say 9.

Try it: write 6 as a fraction. Put 6 on top and 1 on the bottom. You get 6/1. You did it!

Fractions can look different and still mean the same amount. We call these equivalent fractions.

Try it with a picture. Draw a rectangle and split it into 2 equal parts. Shade 1 part. That shows 1/2.

Now split the same rectangle into 8 equal parts instead. How many parts do you shade to show the same amount? Count them: 1, 2, 3, 4. You shade 4 of the 8 parts, which is 4/8. So 1/2 = 4/8. Same amount, different look.

A number line works too. Mark 0 and 1. Split the space into halves and find 1/2. Then split the same space into eighths. The fraction 4/8 lands on exactly the same spot as 1/2.

The big idea: if two fractions land on the same point, or shade the same amount, they are equal. This is the key to seeing that 4/4 lands right on 1, and 8/4 lands right on 2.