Business Math Basics: percentages, profit, margin, markup and break-even

01

Percentages and percent change

In simple words

A percent is "out of 100". If a pizza is cut into 100 tiny slices and you eat 25 of them, you ate 25 percent. Percent change just asks: did the number go up or down, and by how many hundredths of where it started?

Key facts

Percent means "per hundred". 25% = 25/100 = 0.25.
To change a percent into a decimal, divide by 100. To change a decimal into a percent, multiply by 100.
Percent of a number = number x (percent / 100).
Percent change = (new value - old value) / old value x 100. Always divide by the OLD value (the starting point).
A positive answer is an increase. A negative answer is a decrease.
A percent up and the same percent down do not cancel out, because the starting number is different each time.

Question	Working	Answer
25% of CA$80	0.25 x 80	CA$20
20% off CA$40	0.20 x 40 = 8, then 40 - 8	pay CA$32
Rice goes from PHP 50 to PHP 56	(56 - 50) / 50 = 6 / 50 = 0.12	+12%
Price goes from CA$60 down to CA$50	(50 - 60) / 60 = -10 / 60 = -0.1667	about -16.7%

Step by step

Write the two numbers you are comparing. Label them old (start) and new (end).
Subtract: new minus old. Example: 56 - 50 = 6.
Divide that answer by the OLD number: 6 / 50 = 0.12.
Multiply by 100 to get a percent: 0.12 x 100 = 12%.
Look at the sign. Positive means up, negative means down.
For "percent of a number", change the percent to a decimal first (20% = 0.20) and multiply.
Check: 12% of the old number (0.12 x 50 = 6) should equal the change you found (6).

Watch on YouTube

Finding a percentageKhan Academy · YouTube · youtube.com

Percent change: percent increase and percent decreaseMath with Mr. J · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01Percentages and percent change

LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:00

Voice

Read the video script

[Host] "Percent just means out of one hundred. So 25 percent is 25 out of 100, or 0.25."
[Text on screen: 25% of 80 = 0.25 x 80 = 20] "To find 25 percent of 80, change 25 percent to 0.25 and multiply. You get 20."
[Screen: rice from 50 to 56 pesos] "Now percent change. Rice goes from 50 pesos to 56 pesos. That is 6 more."
[Text on screen: 6 / 50 = 0.12 = 12%] "Divide the change by the OLD price, 50. You get 0.12, which is 12 percent."
[Host] "Always divide by where you started. Do that, and percent change gets easy."

Try it now

Find a price you know that changed (rice, bus fare, a phone plan, rent). Write the old and new price and calculate the percent change with the five steps above. Then find 15% of your last grocery receipt total.

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Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

I'm learning "Business Math Basics: percentages, profit, margin, markup and break-even" on The Future Market. Lesson 1: "Percentages and percent change".

What the lesson teaches:
- Percent means "per hundred". 25% = 25/100 = 0.25.
- To change a percent into a decimal, divide by 100. To change a decimal into a percent, multiply by 100.
- Percent of a number = number x (percent / 100).
- Percent change = (new value - old value) / old value x 100. Always divide by the OLD value (the starting point).
- A positive answer is an increase. A negative answer is a decrease.
- A percent up and the same percent down do not cancel out, because the starting number is different each time.
- Question - Working - Answer

The exercise I'm working on:
Find a price you know that changed (rice, bus fare, a phone plan, rent). Write the old and new price and calculate the percent change with the five steps above. Then find 15% of your last grocery receipt total.

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.

I'm a parent helping my child (about 8 years old) with a lesson called "Percentages and percent change" from the course "Business Math Basics: percentages, profit, margin, markup and break-even".

Here's what the lesson says:
A percent is "out of 100". If a pizza is cut into 100 tiny slices and you eat 25 of them, you ate 25 percent. Percent change just asks: did the number go up or down, and by how many hundredths of where it started?

The activity:
Find a price you know that changed (rice, bus fare, a phone plan, rent). Write the old and new price and calculate the percent change with the five steps above. Then find 15% of your last grocery receipt total.

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.

Open Claude

Sources

Well-known textbook definitions of percent and percent change (no statistics are used in this lesson).

My notes

I learned this

02