Ratio
In short: Ratio is a comparison of two quantities by division, written 7 to 4, 7:4 or 7/4, as in 7 violins for every 4 cellos in an orchestra.
6th GradeRatios and Percents6.RP.A.1
What is Ratio?
A ratio tells how much of one thing there is next to another thing. It answers questions such as “how many violins for each cello?” without needing the total.
Precisely, it pairs two numbers \(a\) and \(b\) that describe quantities in the same situation. It can be written \(a \text{ to } b\), \(a : b\) or \(\frac{a}{b}\), and the order matters: \(7 : 4\) and \(4 : 7\) describe different comparisons.
How to spot it
- A sentence says “for every”, “to” or “per” between two amounts, such as 9 sopranos for every 6 altos.
- You are asked to compare a part with another part, or a part with the whole group.
- A recipe, a mixture or a team roster lists two counts that must stay balanced.
- A question asks for the ratio of one named group to another named group, in that order.
The method
- Read the order of the words: “violins to cellos” puts violins first and cellos second.
- Count or read the two quantities, for example 14 violins and 8 cellos.
- Write them as \(14 : 8\), as \(14 \text{ to } 8\) or as \(\frac{14}{8}\).
- Simplify by dividing both numbers by their greatest common factor: \(14 : 8 = 7 : 4\).
Ratio: solved example
Problem
A marching band in Ohio has 18 trumpets and 30 drums. Write the ratio of trumpets to drums in simplest form.
Solution
Trumpets come first, so the ratio is \(18 : 30\).
The greatest common factor of 18 and 30 is 6. Divide both numbers: \(18 \div 6 = 3\) and \(30 \div 6 = 5\). The comparison of trumpets to drums is \(3 : 5\).
Try it
Question 1
A bakery sold 24 muffins and 16 bagels. Compare bagels to muffins in simplest form.
Show the answer
Bagels first: \(16 : 24\). Dividing by 8 gives \(2 : 3\).
Question 2
A class has 11 left-handed and 14 right-handed students. What is the ratio of left-handed students to all students?
Show the answer
The whole group is \(11 + 14 = 25\), so the part-to-whole comparison is \(11 : 25\).
Ratio vs. Rate
It compares two quantities and may use the same unit, such as violins and cellos. A rate is a special comparison of two quantities with different units, such as 150 miles per 3 hours. Every rate is a ratio, but two plain counts are not usually called a rate.
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Related words
Whole dictionary: A–Z · 6th Grade · Ratios and Percents