What Is a Percentage? A Grade 6 Guide

A percentage is a number out of 100. When I say 25%, I mean 25 parts out of every 100 parts of the whole. A percentage is the same idea as a ratio with 100 as the whole, so 25% is the ratio 25:100. That one idea turns test marks, sale prices and survey results into numbers a child can compare at a glance.

What Is a Percentage?

A percentage is a part of a whole written as a number out of 100. The word comes from Latin, and it means per hundred. So 25% means 25 parts out of every 100 parts. I tell children to picture a class of 100, because 25 of them is easy to see.

I start with a class of 100 children. If 25 wear glasses, I write 25%. If 60 pass a test, I write 60%. The number in front of the sign counts the parts, and the sign tells you the whole is always 100.

Children meet percentages long before Grade 6, on sale signs and test papers. I build on that memory, not on a rule. Once a child sees that % always means out of 100, the rest of the topic falls into place.

What Does “Per Cent” Mean?

Per cent means out of every hundred. Per means for each, and cent means a hundred, just like a century is a hundred years. The sign % is short for per cent, so it always means out of 100. Whenever you see %, read it as out of 100.

I break the word in two on the board. Per means for each, and cent means a hundred. A century is a hundred years, and a centimetre is one hundredth of a metre. The same cent sits inside the word percent.

Shops use the same idea every day. I show how discounts work in my How Percentages Work in Shopping guide.

How Is a Percentage Like a Ratio?

A percentage is a ratio with 100 as the second number. The ratio 25:100 says the same thing as 25%, because both mean 25 parts out of 100. The whole always stands for 100 in a percentage, and that is why percentages let you compare two different wholes fairly.

Two test scores show why this matters. Ali scores 18 out of 20, and Sara scores 36 out of 40. As ratios they look different, but as percentages both are 90%. The percentage puts both scores on the same scale, so a child can compare them in one glance.

This is the skill Common Core standard 6.RP.A.3 asks for: find a percent of a quantity as a rate per 100, and a percentage is the simplest rate of all.

How Do You Write a Fraction as a Percentage?

To write a fraction as a percentage, make the bottom number 100, or divide the top by the bottom and multiply by 100. For 3/4, multiply top and bottom by 25 to get 75/100, which is 75%. Both paths land on the same answer, so pick the one that feels easier.

Some fractions are easy. Halves, quarters and fifths all fit 100 neatly, so 1/2 is 50%, 1/4 is 25% and 1/5 is 20%. I ask children to learn these three by heart, because they come up in almost every sum.

Other fractions need the divide step. For 3/8, divide 3 by 8 to get 0.375, then multiply by 100 to get 37.5%. The method never changes: divide first, multiply by 100 second.

How Do You Write a Percentage as a Fraction or a Decimal?

To write a percentage as a fraction, put it over 100 and simplify. So 25% is 25/100, which simplifies to 1/4. To write it as a decimal, divide by 100, which moves the point two places left. 25% is 0.25, and 1/4, 0.25 and 25% are the same number in three clothes.

I teach the fraction first, because it shows the meaning. Put the percentage over 100, then simplify by dividing top and bottom by the same number. For 40%, write 40/100, then divide by 20 to get 2/5.

The decimal is quicker. Divide by 100, which moves the point two places left. So 40% is 0.4, 7% is 0.07, and 125% is 1.25. The point moves two places, never one and never three.

What Mistakes Do Children Make Most With Percentages?

The biggest mistake is treating a percentage as a number on its own without naming the whole. A child also thinks a percentage can never pass 100%, and writes 0.5 as 0.5% instead of 50%. Each mistake comes from forgetting the whole, so I always ask: percent of what?

The whole is the key. A child who says 25% without asking 25% of what has lost the meaning. I make children say the whole out loud: 25% of the class, 25% of the price, 25% of the marks.

A percentage can pass 100%. If a shop sells 120% of last year’s stock, it sold more than last year. And 0.5 is 50%, not 0.5%: the decimal point moves two places, so 0.5 means 50 parts out of 100.

A Real-Life Case: A Spelling Test

Here is one case, worked in full, the way I do it in class.

Step 1: Sara spells 15 words right out of 25. The part is 15, and the whole is 25.

Step 2: Divide the part by the whole: 15 ÷ 25 = 0.6.

Step 3: Multiply by 100 to get the percentage: 0.6 × 100 = 60%. Sara scores 60% on her spelling test.

My Ratio, Rate and Percentage Application worksheet works the same move with 36 out of 50, which is 72%.

Try It Yourself: 3 Practice Questions

Cover the answers, try all three, then check.

1. Write 25% as a fraction in its simplest form.
2. What is 40 out of 100 as a percentage?
3. Write 3/4 as a percentage.

Answers

1. 1/4. Write 25% as 25/100, then divide top and bottom by 25 to get 1/4.
2. 40%. Write 40 out of 100 as 40/100, which is 40%.
3. 75%. Multiply top and bottom by 25 to get 75/100, which is 75%.

Key Takeaways

• Percentage: a number out of 100.
• Per cent: per means for each, cent means a hundred.
• Ratio link: 25% is the ratio 25:100.
• Fraction to percentage: make the bottom 100, or divide and multiply by 100.
• Percentage to fraction: put it over 100 and simplify.
• Name the whole: a percentage means nothing without it.

If your child answered all three questions, she is ready for a longer page. For more free practice at this level, browse our Grade 6 math worksheets page. Every sheet is free to print.