How to use double number lines to represent equivalent ratios?
The following diagram shows how to use a double number line diagram to find equivalent ratios and solve word problems.
Find the value of each product mentally.
(4.5) • 4
(4.5) • 8
1/10 • 65
2/10 • 65
The other day, we made drink mixtures by mixing 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe:
Recall that a perfect square is a number of objects that can be arranged into a square. For example, 9 is a perfect square because 9 objects can be arranged into 3 rows of 3. 16 is also a perfect square, because 16 objects can be arranged into 4 rows of 4. In contrast, 12 is not a perfect square because you can’t arrange 12 objects into a square.
Here is a diagram showing Elena’s recipe for light blue paint.
double number line diagram
A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. The locations of the tick marks match on both number lines. The tick marks labeled 0 line up, but the other numbers are usually different.
a. Complete the diagram to show the amount of flour and eggs needed for 2, 3, and 4 batches of cookies.
b. What is the ratio of cups of flour to eggs?
c. How much flour and how many eggs are used in 4 batches of cookies?
d. How much flour is used with 6 eggs?
e. How many eggs are used with 15 cups of flour?
3. Here is a representation showing the amount of red and blue paint that make 2 batches of purple paint.
a. On the double number line, label the tick marks to represent amounts of red and blue paint used to make batches of this shade of purple paint.
b. How many batches are made with 12 cups of red paint?
c. How many batches are made with 6 cups of blue paint?
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