#anatomy/physiology - Keto eating and measuring weight loss

Question

I started following a Keto way of eating (if you aren't familiar with this concept, you can look to the videos of Dr. Ken Berry, Dr. Anette Bosworth (she calls herself Dr. Boz), and Nurse Cindy (sorry - don't know her full name), among others.

One of the hard parts of researching this way of eating, there is a lot of testimonials concerning weight loss. There are a lot of claims about various amounts of weight lost, but it's hard to look at all these numbers and try to figure out what's what - someone who loses a little bit of weight vs someone who loses a lot of weight and different starting points. Is there a way to help make some sense of it? Help!

Answer

There is a way - use percentages. See below for how...

Analysis

First off, I totally hear you on having to deal with a sea of numbers and trying to find a way to make sense of what is being reported.

Also, my wife and I started eating Keto a couple of months ago and so I am familiar with Keto. Further, my wife runs a Facebook support group for Keto called Keto Living for Health and so you can access support through her group, if you are looking for a Facebook group that speaks to you.

Before I start the weight discussion, I would like to point out that weight is a very difficult metric - there is so much going on inside our 100 trillion cells of our body that weight will fluctuate, and sometimes wildly, with no apparent reason. (Keep in mind that only 10% of those cells are actually you - or in other words has DNA that is your human DNA, and the other 90% is all the flora and fauna that live within us that do all the work (such as the gut flora that actually break down food we consume into the constituent nutrients that get absorbed by our intestines)).

Ok - so weight is not a reliable indicator on a day-to-day basis to see what is happening inside your body. However, every house has a weight scale and it's easy to use, so oftentimes people will use day-to-day weight change as a way to track progress. However, as you lose size, weight will start to follow.

With all that understood about weight, let's now talk about measuring weight loss.

Let's talk about my weight loss. I started at 87.5 kg and I recently measured my progress at 78.7 kg. How much have I lost? Well... we can do the subtraction:

87.5 - 78.7 = 8.8 kg

And I'll note I lost that over the course of 10 or so weeks.

Ok... 8.8 kg isn't a lot compared to some of the reported weight losses online. But 8.8 kg is actually quite a bit compared to where I started. If I divide my weight loss by my starting weight and then multiply by 100, that will give a percentage weight loss:

8.8 / 87.5 x 100 = 10.0

This number is my percentage - I've lost 10.0%. To have lost 10% of my weight in 10 weeks - that's pretty amazing.

Ok - so let's do another person. Let's say they start at 350 pounds and they now weight 330 pounds. What percentage of their body weight have they lost?

First we look at how much weight was lost:

350 - 330 = 20 pounds.

For someone who is 330 pounds, they may think that they've "only lost" 20 pounds and might not be happy with that number. But let's look at the percentage they've lost:

Divide 20 by 350 and then multiply by 100 to get the percentage:

20 / 350 x 100 = 5.7%

A weight loss of 5.7% of their starting weight is amazing.

I hope this helps!

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And now time for shameless plugs - this blog has other "household math" topics and opinion pieces - I invite you to look around.

I have another resource that is an online inter-connected textbook. It's focused pretty much on math topics right now but will continue to expand outward called Fact-orials.

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And as always, questions and comments are always welcome!

 

 

 

#Admin - Refocusing my efforts

Hi all,

Projects, like life, evolve and change. Goals are evaluated, re-evaluated. Reasons are examined, values tested. And then, after much thought and deliberation, actions are taken to bring that new evolution to fruition.

When I first started Math Fact-orials, I was seeking to re-create the experience I was having at Socratic.org - an experience of engaging with students, answering their questions, and finding within myself a feeling of satisfaction and accomplishment.

Then came the realization that where my heart really lay was in creating an online, inter-linked, education resource that would help show not just how things work, but why they work and where they came from. From this came the birth of Fact-orials. While that project envisions being able to explain everything at a level where a pre-teen can understand any given subject, it's also designed for curious adults who wonder "How is it that the Pythagorean Theorem, a^2 + b^2 = c^2, works?". (The answer is - I don't know. But I intend to write about it when I do find out...).

My heart also lies in creating content that helps adults live their lives. Helping people understand just what it means where a $100 shirt is 10% off (you pay $90 before any sales taxes), how to work that out on a calculator (1 - 0.1 x 100 = 90) and then to understand if it's actually a good deal (the same shirt in a different store for full retail of $85 is still a better deal than the one on sale) - these are topics that are of interest to me.

Also important is having a way to talk about things that aren't strictly financial, but more of opinion pieces where I can try to break down complicated (and often deliberately obfuscated) issues into what I hope are thought-provoking simple ideas that everyone can relate to.

As a result, while my goals for Fact-orials have't changed and that project will continue to steam along, Math Fact-orials will change signifcantly:

• Math Fact-orials will now be focused on what I like to call Household Math and also on opinion pieces,
• Math Fact-orials will no longer accept nor answer questions from students,
• The academic content currently on Math Fact-orials, as Fact-orials expands, may become part of that project, but will no longer be hosted on Math Fact-orials,
• Entries on Math Fact-orials will no longer be daily (not that they've been for the last little while, but now I'm officially comfortable with that state of affairs).

I want to thank you, one and all, for reading this and continuing to support me as I continue to explore my interests, my passions, and my heart's desire.

#PreAgebra - Which fraction is bigger? Smaller?

Questions:



We'll be doing 3c, 4c, 5c, 6b, 6c

Answers:

See below:

Analysis:

In all of these questions, we're dealing with what appears to be a bunch of random numbers dividing other rather numbers. It's all quite confusing! But if we work with these numbers, they'll tell us which of them is bigger and which is smaller.

There are a bunch of ways to think of fractions and to understand what they are telling us, but one of my favourites is a pizza pie analogy. All of these questions have three fractions, so let's imagine three pizza pies all the same size. We're going to cut those pies into some number of same sized pieces - it's the denominator, or the bottom number, that tells us how many. Keep in mind that as the number of pieces increases, the size of those pieces drops (if I cut a pizza in half, 1 slice is really big. If I cut that same pizza into 100 pieces, the pieces are really really small).

After we've cut the pizza into the number of pieces we want, then we'll pick out some number of those pieces. It's the numerator, or the top number, that tells us that. Let's start working 3C so you can see what I mean:



That first pizza has been cut into 7 pieces and we'll take 3, the second pizza has been cut into 2 pieces and we'll take 1, and the third pizza has been cut into 5 pieces and we get 3. Ok - so which option gives us the most amount of pizza? Right now it's a little hard to tell, isn't it? The slices are all different sizes and we're taking different amounts. What would really help is if the slices were all the same size - if we cut the pizza into slices that are all the same size - then all we'd need to do is pick the fraction with the largest numerator (the top number).

Now, as we cut the pizza into smaller and smaller slices, we still want to get the same amount of pizza! So as we increase the number of slices, we get more of them.

As an example, look at the  and think about a pizza where it's cut into 2 and you get 1 slice. If we cut the pizza into quarters, so 4 pieces, how many pieces of pizza do you get now? 2. Getting 2 slices when it's cut into 4 is the same as when you get 1 slice when the pizza is cut into 2 (image from chilimath.com):



This is where the idea of a Common Denominator comes into play - and all that means is that we want the bottom numbers to all be the same (so that the pizza slices are all the same size).

So how do we get to the Common Denominator? One way is to simply multiply all the denominators together (this may not get you to the Lowest Common Denominator, which you'll need to find in other questions, but it'll work well here):

7 x 2 x 5 = 70

Ok - so our denominator will be 70.

Now - we need to remember a couple of things at this point. The first is that we can always multiply by the number 1 and end up with the same number we started with. 3 x 1 = 3. I can multiply by 1 and not change the value of the fraction.

The other thing we need to remember is that 1 doesn't always look like 1. If I divide a number by itself, what do I get? 1. And so:



So now we can multiply the different fractions by versions of the number 1 so that we get our denominators to all be 70:







Remember, these are all equivalent to the fractions I had before - all I did is multiply by 1.

Ok - which amount of pizza is most? The one with 42 slices in it. And which fraction was that? 

All the other questions can be worked this same way:

4C



The Common Denominator is 8 x 6 x 3 = 144:





The one with 36 pieces is the smallest, and that is 

5C



The common denominator is 7 x 6 x 5 = 210



And now they can be arranged easily from largest to smallest:



6B

This question has a little twist to it - they include the number 1 as a fraction. Let's change it's look slightly so that it really does look like a fraction:



This says I cut the pizza into 1 piece (or in other words, it's the whole pizza) and I get that one piece (again, the whole pizza).

Now let's work this the same we have the others:



The common denominator is 5 x 1 x 8 = 40:



From smallest to largest, it's the one with 20, then 24, then 40, or:



6C



The common denominator is 7 x 9 x 3 = 189



From smallest to largest it's the one with 27, then 63, then 84, or:



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Questions and comments always welcome!