Solving Percentage Problems

Student Summary

In a situation that involves percentages, there are often three questions we are interested in answering.

Suppose a tank is filled with some water.

  1. If we know that the tank is 25% filled and can hold 36 liters, we can ask: What is 25% of 36 liters?
  2. If we know that the tank has 9 liters and is 25% filled, we can ask: How many liters are in a full tank?
  3. If we know that the tank has 9 liters but can hold 36 liters when full, we can ask: What percentage of 36 liters is 9 liters?

We can use a double number line diagram, a table, or a tape diagram to help us reason about each question.

Double number line, 5 evenly spaced tick marks. Top line, volume, liters. Scale 0 to 36, by 9’s. Bottom line, percent. Scale 0 to 100, by 25’s.

We can also use our knowledge of fractions or relationships between numbers. For instance, we know that 9 is 14\frac{1}{4} of 36, or 36÷436 \div 4, so it is 14\frac{1}{4} of 100% or 25%.

In general, in a situation where AA% of BB is CC, we can find the value of AA, BB, or CC if we know the other two values.

Visual / Anchor Chart

Standards

Building On
5.NF.B

5.NF.B

Addressing
6.RP.3.c

6.RP.A.3.c

6.RP.3.c

6.RP.A.3.c