Percents of numbers: word problems
key notes :
📌 What is Percent?
Percent means “per 100”.
Symbol: %
Example: 25% = 25 out of 100 = 25/100 = 0.25
🧮 Formula to Find Percent of a Number:
Percent of a number = (Percent ÷ 100) × Whole Number
Example: Find 20% of 150 → (20 ÷ 100) × 150 = 30 ✅
💰 Word Problem Steps:
Read the problem carefully 📖
Identify the whole (the total amount)
Identify the percent (how much out of 100)
Use the formula to find the part or amount
Check your answer for reasonableness ✔️
🔄 Converting Percent to Decimal:
Move decimal two places left
Example: 75% → 0.75, 8% → 0.08
🔢 Types of Word Problems:
Finding the Percent of a Number
Example: What is 15% of 200?
Finding the Whole Number
Example: 30 is 20% of what number?
Formula: Whole = Part ÷ (Percent ÷ 100)
Finding the Percent
Example: 50 out of 200 is what percent?
Formula: Percent = (Part ÷ Whole) × 100
💡 Tips & Tricks:
Always underline the numbers in the problem
Watch out for keywords: of → multiply, is → equal to, what → unknown
Use estimations to quickly check your answer
📊 Examples with Emojis:
A shop sold 120 🍎 apples. 25% were red 🍎. How many red apples?
25% of 120 → (25 ÷ 100) × 120 = 30 🍎 red apples
A student got 45 marks out of 60 📝. What percent did he score?
Percent = (45 ÷ 60) × 100 = 75% ✅
Learn with an example
Tucker’s Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 10 espressos in all, 10% of which were single-shot. How many single-shot espressos did the cafe sell?
———-single-shot espressos.
Find 10% of 10.
The whole is 10.
The percent is 10%.
Let n represent the part.
Write a proportion to solve for n.
n/10=10/100
100n=10 . 10
100n=100
n=100/100
n=1
The cafe sold 1 single-shot espresso.
You could also find the answer by writing and solving an equation:
part=percent of whole
n=10% . 10
n=0.1 . 10
n=1
The cafe sold 1 single-shot espresso.
Javier ordered a set of beads. He received 35 beads, and 40% of them were purple. How many purple beads did Javier receive?
—————— beads.
Find 40% of 35.
The whole is 35.
The percent is 40%.
Let n represent the part.
Write a proportion to solve for n.
n/35=40/100
100n=35 . 40
100n=1400
100n/100=1400/100
n=14
Javier received 14 purple beads.
You could also find the answer by writing and solving an equation:
part=percent of whole
n=40% . 35
n=0.4 . 35
n=14
Javier received 14 purple beads.
The lunch choices last Friday were mushroom or pepperoni pizza. The canteen made 42 pizzas in all, 50% of which were mushroom pizzas. How many mushroom pizzas did the canteen make?
—————————-mushroom pizzas.
Find 50% of 42.
The whole is 42.
The percent is 50%.
Let n represent the part.
Write a proportion to solve for n.
n/42=50/100
100n=42 . 50
100n=2100
100n/100=2100/100
n=21
The canteen made 21 mushroom pizzas.
You could also find the answer by writing and solving an equation:
part=percent of whole
n=50% . 42
n=0.5 . 42
n=21
The canteen made 21 mushroom pizzas.
let’s practice!
