Nathaniel – Math On The Fly

Author: Nathaniel

Hi, this is Nathaniel. I sell Math Books for the ACT. I have helped students pass the test for nearly 15 years. We all know students have a lot to worry about. Not understanding math should not be one of them.

Brief Update About Site and Blog

Posted on March 29, 2025April 1, 2025 by Nathaniel

Hello everyone! I hope all is well!

As you can tell, 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, so it will take time to populate and make the videos. In the coming weeks and months I am going to be assertive about getting videos made and posted to social media. Stay tuned.

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

Join the mailing list to get updates to the website, news in the world of math, discounts and more!

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: Divisibility Rules

Posted on March 23, 2025March 23, 2025 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!

Pre-Algebra & Math Basics: Rounding Decimals

Posted on March 23, 2025 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!

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.

Geometry ACT Math Prep: Area of Compound Figures

Posted on October 17, 2024March 12, 2025 by Nathaniel

In this ACT Math video, we delve into Geometry and cover compound figures, which are also called composite figures. Compound figures are figures that when cut are made up of common shapes such as squares, rectangles, circles, triangles and trapezoids.

When the ACT test gives problems like this, you will usually need to find unknown sides of the figure before you can proceed to find the area. For this ACT Math example, we find missing sides of the compound figure, and then show four different ways to get the area.

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

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.

Trigonometry ACT Math Prep: The Law of Sines

Posted on October 14, 2024March 12, 2025 by Nathaniel

In this ACT Math video, we cover The Law of Sines. The rules of SOH-CAH-TOA and hypotenuse, opposite and adjacent sides only apply to right triangles. When we don’t have a right triangle, other formulas sometimes need to be used to find sides and angles. One of those formulas is The Law of Sines.

A brief overview of the formula is given, and then two different methods using the formula are used to solve the problem.

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

Click here to see the problem.

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

Because this is a formula that students do not use often, the practice problem is considered a HARD difficulty problem.

Geometry ACT Math Prep: Midpoints and Endpoints

Posted on October 10, 2024March 12, 2025 by Nathaniel

In this ACT Math prep video, we cover a classic ACT math problem that shows up all the time on the ACT. You are given the midpoint and one of the endpoints of a segment, and you must find the coordinates of the other endpoint of the segment.

This problem continues to show up on the ACT, mainly because students continue to get it incorrect. In the video, we show three different methods for using the given midpoint to find the missing endpoint.

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

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.