A double number line is two lines drawn one above the other, marked so the pairs line up.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Equal steps on both
If the top line goes up by 3 each mark, the bottom goes up by 2 each mark. Every column is the same ratio.
What it is for
Find the column you know, then read the answer off the other line.
Why bother drawing it
A table hides the spacing. A double number line shows that halfway along the top is halfway along the bottom.
Two number lines, kept in step
A double number line puts one quantity on the top line and the other underneath, aligned so that matching values sit above each other. Move along the top by a factor and the bottom moves by the same factor. It is a ratio table drawn to scale.
Reading a value off it
If 3 kg costs £12, mark 3 above 12. Halving gives 1.5 above 6. Doubling gives 6 above 24. To find the cost of 4 kg, get to 1 kg first — 1 above 4 — then multiply up. The line makes the intermediate steps visible.
When to use it rather than a table
A table is quicker to write; a double number line shows the relative sizes, so it is better when you need to judge whether an answer is sensible. Many people sketch the line to think and use the table to record.
The spacing has to be honest
Equal steps along the line must represent equal amounts. A line where 1, 2 and 3 are close together and 10 is just after 3 will mislead you about size. If you are drawing it to think with, draw it roughly to scale.
Step 2: Try It Yourself
Change the ratio and watch both lines re-mark themselves.
| Cups of juice | Cups of water |
|---|---|
| 3 | 4 |
| 6 | 8 |
| 9 | 12 |
| 12 | 16 |
Every row is the same ratio. 3 to 4 is the same comparison as 12 to 16.
Step 3: Watch an Example
One step at a time.
Watch Ana Use a Double Number Line
Juice to water is 3 : 4. Ana needs 12 cups of juice.
- Step 1
She marks the top line 0, 3, 6, 9, 12 and the bottom 0, 4, 8, 12, 16.
Step 4: Your Turn
Practice makes it stick.
The Paint Mix
Problem 1 of 2
Blue to white is 2 : 5. For 8 litres of blue, how much white?
The Same Mix
Problem 2 of 2
Blue to white is 2 : 5. For 15 litres of white, how much blue?
Read Across the Lines
1 of 4
Ratio 3 : 5. If the top shows 9, what does the bottom show?
2 of 4
Ratio 4 : 7. If the top shows 12, what does the bottom show?
3 of 4
Ratio 5 : 2. If the bottom shows 8, what does the top show?
4 of 4
On a double number line, do both lines take the same number of steps?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Ratio 2 : 9. If the top shows 6, what does the bottom show?
What You Learned
- A double number line marks two quantities so their pairs line up.
- Both lines take the same number of steps.
- Find the value you know, then read straight across.