Concept of fractions

Question

5 children are each running an equal part of a 3 mile race. How far will each child run?

Answer 1

First I would ask a student how far each of the 5 children would go if they each ran an equal part of a 1 mile race. I would ask the student to draw a picture. If not apparent at first, I would emphasize that each child runs PART of the mile. How many equal parts do we have to divide that one mile into? It is important to give a student time to think, draw and figure this out. If the one mile is divided into 5 equal parts, what FRACTIONAL part does each child run? 1/5

Now let's try this with THREE miles . . . I would give the student time to draw the 3 pictures and figure out that each child runs 1/5 + 1/5 + 1/5 of a mile, or 3/5 of a mile.

If we drew out the 3 miles in a line, dividing each mile into 5 pieces, and progressed 3/5 five times, we would reach the finish line. (I would draw this for them if they did not already have it drawn).

Answer 2

Using tools that are currently employed in teaching this:

Dividing the miles into 5ths, the children evenly split the 3 miles into 3/5 of a mile pieces

Answer 3

There are 3 miles divided among 5 children = 3/5 (3 divided by 5).

To check, add them: 3/5 + 3/5 + 3/5 + 3/5 + 3/5 = 15/5 = 5.

Multiply by 5 to check: 5 * 3/5 = 15/5 = 5.

Answer 4

For this sort of question, I like to start by taking away the extra words to leave just the parts that are the math parts.

If we do that, we get:

1. 5 children running
2. equal parts
3. 3 miles

The total race is 3 miles, so we start there. Each child is running an equal part, so we separate those 3 miles into 5 equal parts, which is 3 divided by 5. That can be shown as 3 ÷ 5.

With fractions, the top part, or the part above the line, is called the numerator. That's the number were splitting into parts. Here that's 3. The bottom part, the part below the line, is called the denominator. That's the number of pieces we're splitting the top part into. Here that's 5.

So 3 split into 5 parts is 3 ÷ 5. Or, as a fraction, it's ⅗.

Please ask any questions if that isn't clear.