Tape Diagram
In short: A tape diagram is a sketch made of side-by-side strips cut into identical boxes, used to see how the amounts in a story problem add up to a total or differ.
6th GradeRatios and Percents6.RP.A.3
What is Tape Diagram?
A tape diagram pictures a situation with strips, like pieces of measuring tape lined up. Every strip is cut into units of the same size, so you can see which quantity is bigger and by how many units.
Precisely, for a ratio \(a : b\) you draw one tape with \(a\) equal units and another with \(b\) equal units. The whole is \(a + b\) units, and one unit equals the known amount divided by the number of units it covers.
How to spot it
- A word problem gives a ratio of two groups and either a total or a difference between them.
- The question wants a total or a gap between two comparable amounts in the same story.
- Numbers in the story seem too big to guess, but they split evenly into small equal chunks.
- A classmate’s solution would be clearer as a picture of parts and a whole.
The method
- Draw one bar for each quantity, using the ratio to decide how many equal units each bar gets.
- Label the bar or the total with the number given in the problem.
- Find the value of one unit by dividing the labeled amount by the units it covers.
- Multiply that unit value by the boxes in the bar you need, then label your answer.
Tape Diagram: solved example
Problem
At a school book fair in Tulsa, the ratio of fiction to nonfiction books is 3 : 5. There are 96 books in all. How many nonfiction books are there?
Solution
Draw 3 units for fiction and 5 units for nonfiction, so the whole tape has \(3 + 5 = 8\) units.
One unit is \(96 \div 8 = 12\) books. Nonfiction covers 5 units: \(5 \times 12 = 60\). The fair has 60 nonfiction books, and \(36 + 60 = 96\) confirms it.
Try it
Question 1
Dogs and cats at a shelter are in the ratio 4 : 7. If there are 21 more cats than dogs, how many dogs are there?
Show the answer
The gap is \(7 – 4 = 3\) units, so one unit is \(21 \div 3 = 7\). Dogs cover 4 units: \(4 \times 7 = 28\) dogs.
Question 2
Red and blue marbles are in the ratio 2 : 9. There are 18 red marbles. How many marbles are there in all?
Show the answer
Two units equal 18, so a unit is 9. All 11 units give \(11 \times 9 = 99\) marbles.
Tape Diagram vs. Double Number Line
A tape diagram compares quantities as bars made of equal units, which is ideal for part-whole problems with a total. A double number line places matching values on two scales, which is ideal for rates, prices and conversions where both numbers keep growing together.
Keep going
Lessons
Worksheets and quizzes
- Ratios and Ratio Language – Worksheet
- Ratios and Ratio Language – Quiz
- Ratio Tables and Graphs of Ratios – Worksheet
- Ratio Tables and Graphs of Ratios – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Ratios and Percents