What is a Tape Diagram?
In tape diagrams, we observe that rectangles are used to visually represent the parts of a ratio or a fraction. Tape diagrams are used to represent and solve complex math problems in a simpler way.
They are shown as a strip of paper or as a piece of tape.
Let’s consider an example:
The given tape diagram shows 3 sections with 1 section that is shaded. So, the ratio of the shaded section to the total number of sections represented by the tape diagram is 1:3.
Let’s consider another example: Chocolates in the ratio 2:3 can be represented as:
for part 2 of the ratio and
for part 3 of the ratio.
So, we can also use a combination of 2 or more tape diagrams to solve math problems.
How do we Use a Tape Diagram?
In order to solve a math problem using the tape diagram we follow these steps:
Step 1: Draw a horizontal rectangle and divide it into groups. (The number of groups depends on what is given in the problem.)
Step 2: Write the number of items for each group.
Step 3: Perform the addition, subtraction, multiplication or division operation as applicable.
Learn More About Tape Diagrams in This Video
Solved Examples
Example 1: Find \(\frac{2}{5}\) 25 of 10 using a tape diagram.
Solution:
To find \(\frac{2}{5}\) divide 10 into 5 equal parts.
Each of the 5 equal parts is 2.
To find \(\frac{2}{5}\) take 2 of the parts.
So, \(\frac{2}{5}\) of 10 is 4.
Example 2: Find \(\frac{1}{3} \times \frac{1}{4}\) using a tape diagram.
Solution:
Model \(\frac{1}{4}\). Divide 1 whole into 4 parts.
To find \(\frac{1}{3} of \frac{1}{4}\), divide each \(\frac{1}{4}\) into 3 equal parts.
Since, 12 parts make 1 whole, 1 part represents \(\frac{1}{12}\)
So, \(\frac{1}{3} \times \frac{1}{4}=\frac{1}{12}\)
Example 3: Two students, Tom and Charles have pencils in the ratio 2:3. How many pencils does each student have if they have a total of 50 pencils with them?
Solution:
The ratio of pencils with Tom and Charles = 2:3
Let’s represent the ratio using tape diagrams.
Total sections in the two tape diagrams = 2 + 3 = 5
We know, total number of pencils = 50, so,
5 sections represent 50 pencils.
1 section represents \(\frac{50}{5}=10\) pencils
So,
Number of pencils with Tom \(=2 \times 10 = 20\) [2 sections]
Number of pencils with Charles \(=3\times 10 = 30\) [3 sections]
Therefore, Tom has 20 pencils and Charles has 30 pencils.
Students find tape diagrams helpful as a tape diagram as a pictorial model to better grasp a math idea. Such tape diagrams are frequently applied to solve problems involving fractions or ratios. Students usually find it easier to explain their math ideas and arrange information using tape diagrams.
A tape diagram is a visual representation that looks like a piece of tape and is used to help with calculations linked to ratio and fractions, operations such as addition, subtraction, and most frequently the multiplication of fractions. These diagrams help students better visualize math problems.
A bar model, a length model, a strip diagram or a fraction strip, are other names for tape diagrams that are commonly used.