Find the address

The idea

To mark p/q (q ≠ 0) on the number line, divide the unit interval into q equal parts and move p parts from 0, to the right if the number is positive and to the left if negative.

Where is 3/4?

Integers sit on the number line one unit apart. A rational number can sit between two integers. Where does 3/4 live?

Between which two integers is 3/4?

• 0 and 1
• 1 and 2
• 3 and 4

Cut and move

Mark each number: cut every unit into q equal parts, then move p parts from 0.

q parts, p moves

To mark p/q (q ≠ 0) on the number line, divide the unit interval into q equal parts. Then move p parts from 0, to the right if the number is positive and to the left if it is negative.

Fractions greater than 1 work the same way. 9/4 = 2 1/4 lies between 2 and 3: after 2 whole units, move 1 more of the 4 parts.

Notes

To mark p/q on the number line, divide each unit interval into q equal parts and move p parts from 0: right if p is positive, left if it is negative.

Check yourself

To mark 5/6, into how many equal parts do you cut each unit interval?

Answer: 6

The denominator is 6, so each unit is cut into 6 equal parts. Then move 5 parts to the right.

How do you mark −3/4?

9/4 = 2 1/4. Between which two integers does 9/4 lie?

Move 7 parts of 3 from 0. After 2 whole units you have moved 6 parts. How many more parts do you move?

Answer: 1

7 − 6 = 1 more part, so 7/3 = 2 1/3 lies between 2 and 3.

• Cut each unit into 4 parts and move 3 parts to the left of 0 — correct. Yes. The number is negative, so move left.
• Cut each unit into 4 parts and move 3 parts to the right of 0. A negative number is to the left of 0.
• Cut each unit into 3 parts and move 4 parts to the left of 0. The denominator 4 gives the number of parts. The numerator 3 gives the number of moves.
• 1 and 2. 9/4 is more than 2, because 8/4 = 2.
• 2 and 3 — correct. Yes. 2 whole units, and then 1 more part of 4.
• 9 and 10. 9/4 is a little more than 2, not more than 9.