Key takeaway: A tape diagram is a drawing of rectangular bars divided into equal units that shows how quantities in a ratio or a word problem are related, so the unknown can be found by division.
Grade 66.RP.A.3Ratios, Rates and Percents
Definition of Tape Diagram
A tape diagram is a strip-shaped drawing that models a problem with bars. Each bar is cut into equal pieces, and one piece stands for the same amount everywhere in the picture.
For a ratio such as 4 to 7, you draw one bar with 4 pieces and another with 7 pieces. If you know the total or the difference, you can find what one piece is worth by division, then use it to find every other amount. Tape diagrams are also called bar models.
Formula and notation
There is no formula, only a method. Label each bar with its name, mark the equal pieces, and write the known number on the bar it belongs to.
With a ratio \(a : b\) and a total \(T\), one piece is worth
\[\text{one piece} = \frac{T}{a + b}\]
and the two bars are worth \(a\) pieces and \(b\) pieces.
Key facts
- All pieces in one diagram must be the same size, even when they sit in different bars.
- A total is the sum of all pieces; a difference compares the lengths of two bars.
- A tape diagram turns a ratio problem into a one-step division problem.
- The drawing does not need to be exact, but the number of pieces must be correct.
Tape Diagram example
A bake sale table holds muffins and cookies in the ratio \(4 : 7\). There are 88 items in all. How many cookies are on the table?
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Draw a bar of 4 equal pieces for muffins and a bar of 7 equal pieces for cookies.
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Count the pieces: \(4 + 7 = 11\). These 11 pieces hold 88 items.
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One piece: \(88 : 11 = 8\) items.
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Cookies take 7 pieces: \(7 \times 8 = 56\).
There are 56 cookies (and \(4 \times 8 = 32\) muffins).
Common mistake
Watch out
Tess divides 88 by 7 to get a piece of \(12.57\) and says the diagram is wrong.
Why it is wrong
88 is the total of both bars, not the value of the 7-piece bar. Divide the total by all the pieces in the picture, \(4 + 7 = 11\), to get one piece of 8. Only then multiply by the number of pieces in the bar you want.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Ratios, Rates and Percents