How to calculate percentages

Learn how to calculate percentages in this easy lesson! When you're asked to calculate an (unknown) percentage ("What percentage...?"), you need to first write the fraction PART/TOTAL, and then simply write that fraction as a decimal and as a percentage. See many examples below.

The concepts and ideas of this lesson are also explained in this video:

What percentage
of the height of
a 15-ft tree is
a 3-ft sapling?

A choir has 22 women and 18
men. Find what percentage
of the choir’s members are
men.

One pair of jeans costs $25 and another
costs $28. How many percent is the
price of cheaper jeans of the price of
the more expensive jeans?

Look carefully at the questions above. Notice that the problems don’t tell you the percentage; in other words, there is no number in the problem written as x%. Instead, they ask you to find it!

Questions with “What percentage ... ?” or "How many percent ... ?"

Asking “What percentage?” or "How many percent?" is the same as asking “How many hundredth parts?”

We can solve these questions in a two-part process:

First find out the part that is being asked for as a fraction. The denominator probably won’t be 100.
Convert that fraction to a decimal. Then you can easily convert the decimal to a percentage!

Example 1. A choir has 22 women and 18 men. Find what percentage of the choir’s members are men.

Find out what part (fraction) of the choir’s members are men. That is 18/40, or 9/20.
Write 9/20 as a percent. Use equivalent fractions: 9/20 = 45/100 = 45%.

Example 2. One pair of jeans costs $25 and the other costs $28. How many percent is the price of cheaper jeans of the price of the more expensive jeans?

Write what part the cheaper price is of the more expensive price. The answer is 25/28.
Write 25/28 as a percentage. A calculator gives 25/28 = 0.8928... Rounded to the nearest whole percent, that’s 89%.

1. a. What percentage of a 15-ft tree is a little 3-ft sapling?

b. How many percent is $12 of $16?

2. Find how many percent the smaller object’s height is of the taller object’s height.

6 m

8 m

300 cm

120 cm

3. A 2-year old child measures 32 inches tall and weighs 24 pounds. A 10-year old child measures 52 inches tall and weighs 96 pounds.

a. How many percent is the smaller child’s age of the older child’s age?

b. How many percent is the smaller child’s height of the older child’s height?

4. Write the percentages into the sectors in the circle graphs Think of fractions!

5. The circle graph at the right gives the angle measure of each sector of the circle. Find what percentage each sector is of the whole circle, and write the percentage in the sector. Remember, the whole circle is 360°.

Place Value Grade 1 Using a 100-bead abacus in elementary math Teaching tens and ones Practicing with two-digit numbers Counting in groups of ten Skip-counting practice (0-100) Comparing 2-digit numbers Cents and dimes Grade 2 Three-digit numbers Comparing 3-digit numbers Grade 3 Place value with thousands Comparing 4-digit numbers Rounding & estimating Rounding to the nearest 100 Grade 4 Place value - big numbers	Add & subtract lessons Grade 1 Missing addend concept (0-10) Addition facts when the sum is 6 Addition & subtraction connection Grade 2 Fact families & basic addition/subtraction facts Sums that go over over the next ten Add/subtract whole tens (0-100) Add a 2-digit number and a single-digit number mentally Add 2-digit numbers mentally Regrouping in addition Regrouping twice in addition Regrouping or borrowing in subtraction Grade 3 Mental subtraction strategies Rounding & estimating	Multiplication Grade 3 Multiplication concept as repeated addition Multiplication on number line Commutative Multiply by zero Word problems Order of operations Structured drill for multiplication tables Drilling tables of 2, 3, 5, or 10 Drilling tables of 4, 11, 9 Grade 4 Multiplying by whole tens & hundreds Distributive property Partial products - the easy way Partial products - video lesson Multiplication algorithm Multiplication Algorithm — Two-Digit Multiplier Scales problems - video lesson Estimation when multiplying
Division Grade 3 Division as making groups Division/multiplication connection Division is repeated subtraction Zero in division Division that is not exact (remainder) Divisibility Grade 4 How to teach long division Long division as repeated subtraction Why long division works Zero in dividend Remainder & long division Two-digit divisor Review of division topics Divisibility Divisibility within 0-1000 Divisibility rules Prime factorization 1 Prime factorization 2 Sieve of Eratosthenes	Fraction Lessons Understanding fractions Finding fractional parts with division Mixed numbers Fractions to mixed numbers and vv. Adding like fractions Equivalent fractions Adding unlike fractions 1 Adding unlike fractions 2: Finding the common denominator Adding mixed numbers Subtracting mixed numbers Subtracting mixed numbers 2 Measuring in inches Comparing fractions Simplifying fractions Multiply fractions by whole numbers Multiply fractions by fractions Multiplication and area Simplify before multiplying Dividing fractions by whole numbers Dividing fractions: fitting the divisor Dividing fractions: reciprocal numbers Dividing fractions: using the shortcut	Geometry Lessons Lines, rays, and angles Measuring angles Parallel & perpendicular Acute, obtuse, and right triangles Angle sum of a triangle Equilateral & isosceles triangles Circles Symmetry Altitude of a triangle Polygons Perimeter Area of rectangles Area of right triangles Area of parallelograms Area of triangles Area versus Perimeter Angles in Polygons (PDF) Review: Area of Polygons (PDF) Surface Area (PDF)
Decimals Lessons Decimals videos Decimals (1 decimal digit) Decimal place value (1 decimal digit) Decimals (2 decimal digits) Decimal place value (2 decimal digits) Decimals (3 decimal digits) Add & subtract (1 decimal digit) Add & subtract (2 decimal digits) Add and subtract decimals — practice Comparing decimals Multiply a decimal by a whole number Multiply decimals by decimals Divide decimals—mental math Divide decimals by decimals Multiply and divide decimals by 10, 100, and 1000 Decimals review lesson	Percents Lessons How to teach proportions Percent - the basic concept Percentage of a number—mental math How to calculate a percentage of a number How to calculate percentages Basics of percent of change	General Four habits of highly effective math teaching Why are math word problems SO difficult for children? Hint: it has to do with a "recipe" that many math lessons follow. The do's and don'ts of teaching problem solving in math Advice on how you can teach problem solving in elementary, middle, and high school math. How to set up algebraic equations to match word problems Students often have problems setting up an equation for a word problem in algebra. To do that, they need to see the RELATIONSHIP between the different quantities in the problem. This article explains some of those relationships. Seven reasons behind math anxiety and how to prevent it Mental math "mathemagic" with Arthur Benjamin (video) Keeping math skills sharp in the summer Geometric vanish puzzles Science resources Short reviews of the various science resources and curricula I have used with my own children.

How to calculate percentages

See also