Part, whole, and percent proportion word problems! In this video I go over solving percent problems in which I find the whole amount given the part and percentage. I use the proportion method to determine the whole number when given the part and percent in word problems. This proportion strategy is an easy way to solve all types of percentage problems, and it is the main strategy I teach my tutoring students!
Understanding Percent Problems: Finding the Whole
In this post, we’re tackling one of the most common types of percent problems:
How do you find the total (or whole) when you know the part and the percentage?
This is Part 2 of my Percentages Series, where we break down all types of percent problems step by step.
If you’ve ever asked yourself, “378 is 72% of what number?” — this post is for you!
Method 1: Using a Proportion to Solve Percent Problems
Let’s look at the first example:
Example 1
Problem:
378 is 72% of what number?
Step 1: Set up a proportion
We’ll use the proportion method, where we set up two fractions equal to each other:
Here’s a helpful hint:
- The number next to “of” usually represents the total (denominator).
- The number next to “is” usually represents the part (numerator).
Step 2: Cross multiply
Step 3: Solve for x
✅ Answer: 378 is 72% of 525.
Example 2: Percent Word Problem
Let’s look at a real-world example involving discounts and sales.
Problem:
Davin bought a shirt for $28.90. The shirt was marked 15% off.
What was the original price of the shirt?
Step 1: Understand the situation
If the shirt is 15% off, that means Davin paid 85% of the original price (because 100%−15%=85%.
So in this case:
- Part (the amount Davin paid) = 28.90
- Percentage = 85%
- Total (the original price) = ?
Step 2: Set up your proportion
Step 3: Cross multiply
Step 4: Solve for x
✅ Answer: The original price of the shirt was $34.00.
Key Takeaways
- When finding the total, use the proportion:
- The word “is” usually represents the part.
- The word “of” usually represents the total.
- In discount problems, always subtract the discount percent from 100% to find what percent was actually paid.
Related Lessons
This post is Part 2 of 3 in my Percentages Series:
- Part 1 – Finding the Percentage When Given the Total and Part
- Part 2 – Finding the Total (You’re here!)
- Part 3 – Finding the Part When Given the Percentage and Total
You can also check out my Pre-Algebra Series on YouTube for video explanations, practice problems, and math tips!
Watch the Video Lesson 🎥
You can watch the full video that goes with this blog post on my YouTube channel:
👉 My Tutoring Bee on YouTube
Related Videos:
If you are looking for other math YouTube videos that pair well with this skill, try these:
🤩Finding Percent in Word Problems: https://youtu.be/V4oSYtoXEjE
🤩How to Work with Percent Word Problems: https://youtu.be/u6mX6KcRJPs
🤩How to Round Decimals Nearest Tenth & More!: https://youtu.be/27W1zhXDh1M
🤩Fractions Percent Decimal Conversion: https://youtu.be/5V6RpRSP1dA
🤩Fraction and percentage conversion (short): https://youtube.com/shorts/1VAy4JYqg54?feature=share
🤩Convert decimal to percent or percent to decimal (short): https://youtube.com/shorts/0zccmKcefg8?feature=share
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For Teachers:
Teachers, thank you so much for watching! I hope that my videos have helped you help your students. If you are looking for downloadable online resources to help your students practice and grow, these may help you out:
🎉Basic Algebra Concepts Introduction and Overview Google Forms: https://www.teacherspayteachers.com/Product/Basic-Algebra-Concepts-Introduction-and-Overview-Google-Forms-11043670
🎉Adding and Subtracting Integers Quiz FREEBIE: https://www.teacherspayteachers.com/Product/Adding-and-Subtracting-Integers-Quiz-FREEBIE-for-distance-learning-5524609
🎉6th Grade Math Spiral Review BUNDLE Plus Boom Cards: https://www.teacherspayteachers.com/Product/6th-Grade-Math-Spiral-Review-BUNDLE-Plus-Boom-Cards-5542680
🎉Order of Operations WITH EXPONENTS Boom Cards and Google Slides Set 3: https://www.teacherspayteachers.com/Product/Order-of-Operations-WITH-EXPONENTS-Boom-Cards-and-Google-Slides-Set-3-6445584
🎉Solve Linear Equations Activity Mystery Pixel Picture Digital Google Slides: https://www.teacherspayteachers.com/Product/Solve-Linear-Equations-Activity-Mystery-Pixel-Picture-Digital-Google-Slides-8540224
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