Tag: math on the fly

Brief Site and Blog Update

Posted on by Nathaniel

UPDATE 10/10/2025:

Things have moved at a snail’s pace. I still plan to get back to releasing videos, but working 50+ hours a week on a full-time job has slowed things down quite a bit.

I have been steadily working on the newly updated ACT math book for the digital exam every day, but it’s a longgggggg book and every problem and solution needs to be checked.

(I needed to use a lot of g’s. Not really sure why.)

You can be rest assured that AI has not written a single page of the book. I write every page of the book myself. And yes, it felt necessary to say this.

I will be finished with the book very soon.

There will be more than 1,200 math problems in the book with revised sections and added problems on functions, standard deviation, logarithms, rational functions and other important concepts. There will be a new 30+ section on hyperbolas, which will complete the ACT’s coverage of conic sections (circles, parabolas, ellipses and hyperbolas).

Once, the book is finished, I will continue making worksheets, revising and making videos weekly, and updating the newsletter more frequently.

Changes will start to accelerate across social media and the entire website.

Feel free to contact me if you have any questions.

I’m always watching. I’ve got my eyes on you like a sensei. 👀

Take care. Peace.

 

 

FROM 3/29/2025: 

Hello everyone! I hope all is well!

I am shifting the site to cover ALL math topics ranging from Prealgebra/Math Basics, Algebra/College Algebra, Geometry, Trigonometry, Algebra II, Precalculus, Calculus I, Calculus II, Calculus AB/BC, Finite Mathematics, Financial Mathematics, Statistics and Probability.

Obviously, there are a lot of topics contained in those subjects. It will take time to make the videos and worksheets.

In the meantime, the ACT worksheets will always be available and the ACT videos I have already made will also be available.

All of the videos can be found on my Math on the Fly YouTube Page at https://www.youtube.com/@mathonthefly

Ok, I’m done. Gotta go make my coffee with 2 Splendas and Hazelnut cream. (Caramel Macchiato is also ridiculously great but I’m running off topic ☕)

Have a great 2025!

REGULAR MATH VIDEOS:

→ Prealgebra, Making Factor Trees
https://www.youtube.com/watch?v=LyxWbYTASCY

→ Prealgebra, Making Factor Tables
https://www.youtube.com/watch?v=Tixp-CWdHmw

→ Prealgebra, Prime Factorization
https://www.youtube.com/watch?v=MXKMP-3UEAY

→ Prealgebra, Rounding Decimals
https://www.youtube.com/watch?v=Er8EtAKA1N0

→ Prealgebra, Divisibility Rules from 1 to 10
https://www.youtube.com/watch?v=GgnO1-Hc19Y

ACT MATH VIDEOS:

→ Algebra, Solving Exponential Equations by Changing Bases
https://www.youtube.com/watch?v=KjfVJ4jnjwA

→ Geometry, Area of Compound Figures
https://www.youtube.com/watch?v=Msjf9f5h034

→ Trigonometry, The Law of Sines
https://www.youtube.com/watch?v=CG1gemouHB4

→ Geometry, Midpoints and Finding Unknown Endpoints
https://www.youtube.com/watch?v=z_ouoqu-Cic

→ Algebra, Solving Quadratic Equations, the Quadratic Formula and Factoring
https://www.youtube.com/watch?v=uYP2Ebq9Ga0

→ Algebra/Precalculus, Analyzing Geometric Series
https://www.youtube.com/watch?v=sMbBVrvwUDo

→ Algebra, Distance, Rate and Time
https://www.youtube.com/watch?v=GeKD8v80WCU

→ Geometry/Trigonometry, Right Triangle Trigonometry & The Pythagorean Theorem
https://www.youtube.com/watch?v=UamQEIIu9TQ

→ Prealgebra, Factors and Primes
https://www.youtube.com/watch?v=SsyGowpFOkQ

→ Probability, Multiple Events and Complements
https://www.youtube.com/watch?v=qdJdzZakiks

→ Geometry, Ratios and Areas of Polygons
https://www.youtube.com/watch?v=5MhsasVz1ys

→ Statistics, Arithmetic Mean and Averages
https://www.youtube.com/watch?v=_JDphxKZX48

→ Prealgebra, Combining and Creating New Ratios
https://www.youtube.com/watch?v=hdx3_PajAWc

→ Prealgebra, Finding Fractions of Amounts
https://www.youtube.com/watch?v=5GwyeWa23h8

Pre-Algebra & Math Basics: Math Operations of Decimals

Posted on by Nathaniel

In the video I cover adding decimals, subtracting decimals, multiplying decimals, and dividing decimals. When adding and subtracting decimals, the key is to keep the decimal places lined up. When multiplying decimals, you add up the total number of decimal places to get the answer. For dividing decimals, I quickly cover the situations of dividing decimals by whole numbers and dividing decimals by decimals.

The following problems are covered in the video:

Adding Decimals
→ 15 + 0.4 + .9251
→ 13.829 + 6 + .7

Subtracting Decimals
→ 17.912 – 4.5
→ 5.6 – 0.3991
→ 100 – 0.72

Multiplying Decimals
→ 1.2 × 11
→ 1.2 × 1.1
→ 12 × 1.1
→ .12 × 1.1
→ .12 × .11

Dividing Decimals
→ 2.67 ÷ 3
→ 2.67 ÷ 0.3
→ 2.67 ÷ 0.003

Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Dividing Decimals

Posted on by Nathaniel

In this video, I go into detail the correct way to divide decimals. I go through the difference between terminating and repeating decimals. I also handle the situations of dividing decimals by whole numbers, dividing decimals by decimals, and when to stop the division in both situations.

The following problems are covered in the video:

Dividing Decimals by Whole Numbers:
→ 38.72 ÷ 4
→ 5.0 ÷ 8
→ 1.48 ÷ 20
→ 2.6 ÷ 3
→ 14.0 ÷ 11

Dividing Decimals by Decimals:
→ 41.35 ÷ 0.5
→ 4.32 ÷ 0.009
→ 0.158 ÷ 0.06

Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Finding Factors of Numbers

Posted on by Nathaniel

Factors are whole numbers that divide evenly into another whole number. In this video I explain what factors are, and show how to easily make a list to find the factors of any number.

The following problems are covered in the video:

→ Find the Factors of 40
→ Find the Factors of 100 (Perfect Square)

Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Divisibility Rules

Posted on by Nathaniel

In the math video, divisibility rules is covered. Divisibility rules are shortcuts that allow us to quickly figure out if a number divides evenly into another whole number. This skill can be used for reducing fractions, finding factors of numbers, finding the GCF, factoring polynomials, simplifying square roots and much more. Most students know the divisibility rule for 2 (the number must be even), the rule for 5 (the number must end in 0 or 5) and the rule for 10 (the number must end in 0). I cover all the divisibility rules from 1 to 10. Without using a calculator, you will be able to easily tell for example, if 3 divides evenly into 1,232,251 or if 4 divides evenly into a number like 5,385,414.

This topic is usually covered one time in middle school, and then it is never covered again. Some school systems never cover the topic at all, which I think is ridiculous. All of the rules can be proven algebraically through modular arithmetic, which is an area of mathematics that is usually only covered in math competitions or accelerated math classes. We will simply cover the shortcuts.

We cover the following problems in the video:

→ Are 8 and 5397 divisible by 1?
→ Are 3516 and 2847 divisible by 2?
→ Are 24, 6702 and 3335 divisible by 3?
→ Are 5916, 7508, 4442, 61592 and 37900 divisible by 4?
→ Are 4830, 1965 and 50502 divisible by 5?
→ Are 2574, 9128, 4920 and 5133 divisible by 6?
→ Are 364, 717, 105 and 3546 divisible by 7?
→ Are 4800, 39056, 6009, 17078, 450388 and 21000 divisible by 8?
→ Are 36, 7425 and 9199 divisible by 9?
→ Are 9170, 1005 and 80002 divisible by 10?

Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Rounding Decimals

Posted on by Nathaniel

In this video, I cover the topic of rounding decimals, a topic that confuses many students. I cover the 3 steps of rounding decimals and use those steps to round decimals to the nearest tenth, hundredth, thousandth and ten thousandth. I also cover the special situations of rounding up on 9, rounding to the nearest dollar and whole number, as well as rounding repeating decimals.

The following problems are covered in the video:

→ Round 8.2748 and 0.9468 to the nearest tenth
→ Round 0.1652 and 6.083 to the nearest tenth
→ Round 1.3975 to the nearest hundredth (Round up on 9)
→ Round 7.615 and 0.8016 to the nearest thousandth
→ Round 9.1738 to one, two, three and four decimal places
→ Round 3.499 and 49.82 to the nearest whole number
→ Round $7.61 to the nearest dollar
→ Round $24.19 to the nearest dollar

The following examples of repeating decimals are also covered:


Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Prime Factorization

Posted on by Nathaniel

Prime factorization is when you write a whole number as a multiplication problem using only prime numbers. In this short math video on prime factorization, I cover what prime factorization looks like for a whole number and how to find it step-by-step using factor trees and factor tables. I also cover how to find the prime factorization of a prime number.

We cover the following problems in the video:


Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Making Factor Tables

Posted on by Nathaniel

In this math video, I show how to quickly and easily make factor tables. Similar to factor trees, they can used to find the GCF and LCM of numbers, simplify square roots, find prime factorizations and more! All students should learn how to make factor trees and factor tables. They are also good practice for recognizing prime numbers as well.

We cover the following problem in the video:

Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Pre-Algebra & Math Basics: Making Factor Trees

Posted on by Nathaniel

In this math video, I quickly cover how to make factor trees. All students should learn how to make them since they can be used to find factors, find the GCF and LCM of groups of numbers, simplify square roots, factor polynomials, and much more! They also help you quickly learn and recognize prime numbers.

We cover the following problems in the video:



Below is the video. Enjoy!

Feel free to provide comments or math topic suggestions to nathaniel@mathonthefly.com. Your feedback is always appreciated!

Algebra ACT Math Prep: Exponential Equations

Posted on by Nathaniel

In this ACT Math video, we cover Exponential Equations. In these types of problems, you have bases that are raised to powers and we need to find the value of x that makes both sides equal to each other.

We show how to change the bases to make the problem easier to solve. We also show how to use the answer choices to solve the problem.

The example used in the video will be based off the following ACT math problem:

Click here to see the problem.

This is the practice exercise we will work out in the video:

This practice problem is considered a MEDIUM difficulty problem.