Category: Math Around Us

  • 10 Ways Getting Married is Like Doing Math

    10 Ways Getting Married is Like Doing Math

    10 Ways Getting Married is LikeDoing Math www.MathFour.com

    One of my very best friends got married last weekend. On my way home from her wedding I started thinking about the similarities of getting married and doing math.

    1. Doing it while other people watch can make you nervous.

    Being at the board or being at the altar is a freaky experience. The pressure’s on.

    2. Taking classes can make you better at it.

    Couples counseling, Marriage Encounter and marital classes are available. You learn stuff. You grow.

    If you find the right math class, you can improve your math learning. Even if you find the wrong math class, you’ll learn something. And grow.

    3. It’s not easy, but it’s worth it.

    Anyone who’s ever been married will tell you there are challenges. And sometimes those challenges are downright painful. But sticking together and pushing through will make your marriage stronger.

    And every math student will tell you there are challenges. Even students to which math seems natural can hit walls. If you push through, you’ll be a stronger math student.

    4. It’s about communication. Sometimes.

    There are two parts to love and marriage: your feelings, and the communication of those feelings. If you don’t have both, your marriage is doomed.

    There are two parts to mathematics: the math itself, and the communication of the math. What we teach is really only the communication of math. But if a student doesn’t have a basic understanding of the math itself, his mathematical success is doomed.

    5. Some people are better for you than other people.

    If you’ve ever been in a bad relationship, you know what I’m talking about. It’s a similar feeling when you have to sit through a math class with a teacher who’s mean, intellectually inferior, or smells bad.

    Choosing a good partner in math learning is important. So is a choosing a good partner in life.

    6. Trial and error is involved. A lot.

    Marriage involves trial and error. With a heavy emphasis on error.

    You’re going to mess up. But each time you err, try again. Learning and growing is part of the marriage process.

    For math: ditto.

    7. Going all in makes a big difference.

    When you get married you make a huge commitment. On the outside.

    If you also make that huge commitment on the inside, with your heart and soul and all your being, your marriage will be better for it.

    For math, you can buy books, hire tutors, sign-up for classes. But you have to make the commitment, on a heart and soul level, to go all in.

    8. It can be frightening and intimidating.

    Marriage is a huge commitment. It means vulnerability – full out. And that’s pretty scary.

    Children learn early on, for better or worse, that grown-ups expect right answers when they do math. And since there’s an awful lot of failure in math, this means serious vulnerability.

    (And for some, doing math is a lot more scary than getting married!)

    9. It’s tough, but if you stick with it, it pays off.

    Marriage is hard. Really hard. Mostly because of that vulnerability thing, though. As you push through, your marriage gets better.

    Math is hard. Sort of. And strangely, it’s because of the vulnerability thing. Once you settle in and embrace the failures as learning moments, your math learning skyrockets.

    10. Joking about how dreadful it is can be damaging to your children.

    Your children look up to you. Everything you say influences them.

    If you talk about your marriage as if it’s the albatross around your neck, your kids will grow up believing it.

    If you talk about math like it’s frightening and weird, your kids will believe that too.

    So don’t. For either.

    Congrats! You’re in the club!

    It’s a whole new ballgame from here. But if you can be a math student, you can tackle the marriage thing!

    Congratulations, Theresa and JP. May you have a wonderful life together!

  • Making Sausage with Math

    Making Sausage with Math

    The Math in Making Sausage

    I’m into trying new things. And I’m always curious where I’ll find math in them. So I agreed to help process the deer my husband brought home from hunting.

    We don’t have a sausage processor, though. So Husband went to a sausage making party at his cousin’s house.

    We needed to get everything ready — venison cubes, pork cubes and spices. I decided to put them in “matching” bags so it would be easy for him.

    Pounds and Pounds of Meat

    The recipe called for 6 pounds of cubed venison and 4 pounds of cubed pork.

    But our bags of cubed venison were anywhere from 4 to 7 pounds. And there were lots of 1/2’s and 3/4’s in there, too.

    After all, it’s our first time. We never thought to bag up sausage-makin’s the same!

    I had two options.

    1. I could move the meat around until all but one bag was exactly 6 pounds. Then do the math to scale down the other bag.
    2. Or I could do some really fun math approximations. And by fun I mean… weird, strange, and not even close to being exact.

    Guess which I picked…

    It’s about ratios.

    The ratio of venison to pork is 6 to 4. “Reducing” the fraction gives the ratio 3 to 2.

    Going the other way gives 9 pounds venison to 6 pounds pork.

    But I had 4 pounds, 7 pounds and all sorts of weird numbers in between!

    Sausage making isn’t exact.

    Recipes in general are merely suggestions of what and how much. I wanted to get close, but there was no reason to drag out pencil and paper to do the math.

    If 3 pounds of venison needs 2 pounds of pork, then 1 pound venison needs 2/3 pounds pork. And since 2/3 is more than a half and less than a whole, I could “eyeball” this.

    3 pounds venison + 1 pound venison NEEDS 2 pounds pork + 2/3 pounds pork

    So…

    4 pounds venison NEEDS a little less than 3 pounds pork

    The Math in Making Sausage

    And I can use this approximation to do 7 pounds…

    3 lbs venison + 4 lbs venison NEEDS 2 lbs pork + less than 3 lbs pork

    So…

    7 pounds venison NEEDS a little less than 5 pounds pork

    Time for the spices.

    I lined up the spice bags according to their corresponding volumes of meat. The ones in the middle (with 6 pounds of venison and 4 pounds of pork) got the amount of spices the recipe called for.

    Then I went up and down in spices according to how much the meat volume went up or down.

    And… yum!

    When I take out a handful of links for dinner, I can’t tell which mix it is.

    But isn’t that the nature of sausage?

    Have you ever made sausage? The next time you do, make sure you mention the math you’re doing to your kids!

    Share your thoughts in the comments or on twitter/x. And don’t forget to pin this on Pinterest!

  • Positive, Negative and Zero Numbers — And Dove Body Wash!

    Positive, Negative and Zero Numbers — And Dove Body Wash!

    Every real number can be classified as positive, negative or zero. And you can use bath products to teach this!

    We attended the Dad 2.0 Summit a couple of weeks ago. Husband scored some really neat Dove Men Care products. I asked for a set too.

    I was lathering myself up in the shower and starting to smell rather manly. I wondered if there was an equivalent Dove product that had a super intense, feminine smell.

    Which made me think of the number line.

    Negative, Positive and Zero.

    People often ask me about zero — is it positive or negative?

    Every number is is either positive, negative or zero. Those are the three possible “states” — and each number is exactly one of them.

    That’s why we sometimes use the term “non-negative.” Non-negative doesn’t mean positive. It means a number that is either positive or zero.

    It’s a subtle difference but super important.

    But teaching it with Dove Body Wash? Really?

    Yes!

    There are three general marketing tactics for body wash — male, female and “neutral.”

    This can correspond with the positive, negative and zero of the numbers!

    (Of course which you choose as positive or negative depends on you — my favorite person happens to be my husband — a male — so I picked for men as the positive numbers in my graph.)

    You can even reinforce the math language.

    Suppose you’re in the shower and you notice you’re out of body wash. You can call to your child and ask, “Will you bring me some Dove Men Care body wash.”

    Which is like saying, “Bring me some positive body wash.”

    Or you can say, “Please bring me some body wash — anything as long as it’s not that girly-smelling Dove Purely Pampering stuff your mom uses!”

    Which is equivalent to saying, “I want the non-negative body wash.”

    How about it?

    What do you have in your shower or tub that you can illustrate positive, negative and zero with? Will you give it a shot?

    Share your thoughts in the comments or on twitter/x. And don’t forget to pin this on Pinterest!

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  • How Long Does it Take to Follow Up after a Conference?

    How Long Does it Take to Follow Up after a Conference?

    As I slowly recover from my Dad 2.0 Summit adventure this weekend, I’m faced with a stack of business cards a mile high.

    How long does it REALLY take to follow up after a conference?

    Every time I attend a conference or convention I end the weekend with the same anxiety: “When am I going to have time to follow up with all these people?”

    Understanding the problem is half the solution.

    Instead of wallowing in a pool of anxiety and worry, I’m going to get a better grip on what it means to “follow up with all these people.”

    And the way I do that is with a little arithmetic and mathematical modeling.

    How long does it take to connect with one person?

    To find out how long it takes to follow up with one person, I picked a business card from my stack at random. It happened to be from one of the MilkMustache.com ladies.

    It took me 16 minutes to reach out to her. This included the email, researching the site and following her on Twitter.

    How many times do I have to do this?

    I have 32 more business cards in my stack. I’m going to assume they’re all unique, and that I’ll connect with them in about the same way as I did with Milk.

    So to connect with everyone, it will take me

    32 people x 16 minutes/person = 512 minutes

    I can divide that number by 60 and see that it will take me about 8 1/2 hours to connect with everyone I met at the Dad 2.0 Summit.

    Now it’s time to work!

    Everyone I met there was pretty amazing. And I’m a lot less anxious now that I know that connecting with all of them will not take forever.

    So I’m off to connect!

    How about you?

    When’s the last time you went to a conference or convention? Were you overwhelmed with the number of contacts you made? Would it have helped to do what I did?

    Share your thoughts in the comments. And don’t forget to mention this “convention math” to your kids!

    Share your thoughts in the comments or on twitter/x. And don’t forget to pin this on Pinterest!

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  • How to Answer “When am I going to use this?”
  • 5 Phases of Learning Math
  • 7 Ways to Wrangle a Word Problem
  • How to Find the Cheapest Price per Unit

    How to Find the Cheapest Price per Unit

    I’m heading to the Dad 2.0 Summit tomorrow so last week I ordered more of my super cool playing card business cards.

    Business Cards - using playing cards!

    I had to decide how many decks to buy — and I wanted to pay the cheapest price per deck.

    I had to work within my constraints.

    I had only one and a half weeks to get them in. And less than $50 budgeted for them.

    And I needed at least 100 of them.

    These playing card business cards aren’t cheap — about $10 per deck of 54, plus shipping costs. But I love them.

    I was willing to pay the premium price.

    But I still wanted to get the cheapest price of the premium price that I could!

    So I did the math!

    Here’s a screenshot of the price structure from YourPlayingCards.com:

    Pricing structure breakdown for playing-card business cards.

    Since my budget was $50, I had to go with four or fewer decks.

    I started looking at the per-deck cost of shipping.

    • If you order 1 deck, the cost is $4/deck to ship it.
    • If you order 2 decks, the cost is $3/deck.
    • If you order 3 decks, shipping is $3.33/deck.
    • And getting 4 decks cost $2.50/deck for shipping.

    Four decks is the winner — or is it?

    Four decks would be right at $50 — and give me 216 cards. But if I went even more under budget with 2 decks — my total comes to $26.

    Since I only plan on using 50-100 cards at this conference, two decks would be fine.

    “But that’s not the cheapest price per unit,” you say?

    The cheapest price per unit sometimes isn’t the cheapest!

    If I buy two decks now, and two decks later, it costs me $52 ($26 + $26). But if I buy four decks now it only costs me $50.

    Even though I want to get the cheapest price per unit, I’m focused on the the “out the door” cost, too.

    What I really need right now is two decks. And the “out the door” cost on those is $26. Just about half of the $50.

    Which means that, for now, two decks is the cheapest for what I need!

    How about you?

    What have you found is cheaper in theory but not in reality? Share it in the comments or on twitter/x. And don’t forget to pin this on Pinterest!

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  • How to Find 20% of a Rectangle — The Facebook Page Cover Photo

    How to Find 20% of a Rectangle — The Facebook Page Cover Photo

    I’m struggling with the new Facebook cover photo rules. You can’t have more than 20% of the cover photo as text.

    But what IS 20% of the cover photo?

    Let’s do the math!

    The cover photo is 851 pixels wide by 315 pixels tall. Which is a total of 268,065 pixels. That’s a lot of pixels!

    And 20% of that is…

    268,065 x 0.20 = 53,613

    Still, that’s an awful lot of pixels!

    To figure out what that could be in reality, I picked on old Wolfram Alpha. Plugging it in there, I can get the prime factorization of 53,613.

    3 x 3 x 7 x 23 x 37

    Which breaks down into about five reasonable areas. And because this is all about seeing what those are (instead of just numbers), I created a handy infographic.

    The light areas are the 20% rectangles — and you can move them anywhere.

    Wow - finally some way to SEE what the max text of 20% of my Facebook Page cover photo should be!

    Like it? Share it on Pinterest! And if you use it, leave your Facebook fan page link in the comments so we can see how you applied it.

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  • Does Santa Exist — Mathematically?

    Does Santa Exist — Mathematically?

    Every year people try to prove or disprove the existence of Santa. There are sites like iCaughtSanta.com for grownups to create “proof” and write-ups like Keith Devlin’s The Mathematics of Christmas that counter any proof that photos might provide.

    I used the super cute service at www.iCaughtSanta.com to create this. You gotta love how Husband doesn’t even see Santa because he’s too busy on the iPhone!

    But to really prove anything about Mr. Jolly-Red-Boy, we must think about what it really means to prove something — mathematically.

    Say what you want to prove.

    The first thing you need for a nice mathematical proof is a “conjecture.”

    A conjecture is a statement that you think can be proven. Or that you want to prove. According to the google dictionary a conjecture is

    an opinion or conclusion formed on the basis of incomplete information

    Our working conjecture here is: Santa exists.

    It’s pretty straight up. But this isn’t quite enough. We need to know what “Santa” means.

    Then define and refine.

    Before we can work with the conjecture, it’s important to know the details. The details are usually definitions and assumptions.

    So this is where it gets fun. I often tell people that mathematicians “make all this crap up.” This is because we start with definitions and assumptions — not reality.

    So define Santa to be a human male who can enter the living room of every house with Christian children within a span of 24 hours.

    We can refine our conjecture to be:

    In the set of all human males, there exists x such that x can enter the living room of every house with Christian children within a span of 24 hours.

    Now think about how to prove it.

    There are many ways to prove something. Some of the common ones are:

    • Direct proof
    • Proof by contradiction
    • Proof by blatant assertion

    Here is a quick definition of each:

    Direct proof — proving it without using any fancy logical methods. This is more difficult that you would think.

    Proof by contradiction — proving it by saying if the conclusion weren’t true, then it would be really stupid. Or the earth would implode. Or 1 would be the same as 0. Etc.

    Proof by blatant assertion — proving it by saying it is true. Usually in a really loud voice and with a shaking of the fist. It’s helpful in this method to use swear words, but not required. (Note: all mathematicians attempt this type of proof at least once in their lives. But they never accept this method from others.)

    A myth is that mathematicians (and math teachers) know how to do something before they tackle it. In fact, they typically never know how to do something or what will happen when they try something.

    So as good Christmas mathematicians, we’ll give these our best shots…

    Play with the proofs and see what shakes out!

    A direct proof would be to show that everything in our known world supports the existence of Santa. Without doing any calculations, we can easily see that no standard human would be able to visit every living room in a small country, much less the whole world.

    So a direct proof won’t work for us.

    A proof by contradiction would be “if Santa doesn’t exist, then the world doesn’t really exist either. Well, at least in the way we know it.”

    This one doesn’t quite work either.

    Of course if we adjust our conjecture to say the opposite of what it does, a proof by contradiction would work.

    New Conjecture: In the set of all human males, there does not exist x such that x can enter the living room of every house with Christian children within a span of 24 hours.

    Proof: Suppose Santa does exist. Using some calculations regarding physics (found in this article on the Math in Christmas), we can see that Santa must be able to time travel or break the general laws of physics.

    Since breaking the laws of physics cannot be done, we have just shown (by contradiction) that Santa doesn’t exist.

    Well that’s certainly not good for our original, and preferred, conjecture. But we have one more proof method left.

    Say “Santa exists!” regardless of what the logic says.

    Now we get to turn to proof by blatant assertion.

    I believe in Santa in a way that can’t be shaken. But to be honest, my belief uses a different definition.

    It doesn’t matter — if you want to believe you can. People all over believe in God, the spirit of the trees and some people even believe that the real line doesn’t exist. There are tons of ways to “prove” the opposite of all of these.

    But these are things from the heart. Not from any logical or mathematical standpoint.

    So go ahead, believe in Santa. Ignore the physics and go print out proof of Santa for your kids!

    And don’t forget to talk about logic and proofs. At least on the surface.

    Share your thoughts in the comments or on twitter/x.

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  • Salvation Army Donation Math

    Salvation Army Donation Math

    I have the privilege to be one of The Salvation Army Angel Tree Ambassadors this season. This is especially meaningful because my family benefited from the Angel Tree when I was a kid.

    But of course, donating also has math in it. So if you donate to those in need, you can integrate math learning into it.

    And if you haven’t had a chance to donate in a while, check out the math below to see how easy it is!

    Donate your time.

    Volunteering with Qpon Junkie at The Salvation Army Angel Tree Secret Warehouse

    Head to a local shelter, Salvation Army, or church to volunteer. Talk to your kids about how much time they spend each week playing, doing sports and gaming.

    1. Suppose your family donates a half day — how much of their free time will they be giving up?

    Say they have 18 hours a week to play: 1-2 hours/day during the week and 3-5 hours/day on the weekend.

    A half day, or four hours, is \(\frac{4 \text{ hours}}{18 \text{ hours}}\) or 22%. So less than a quarter of their free time is taken as a volunteer.

    If that’s the only time all year you volunteer, the math is a little different. The play time for the year is 52 weeks x 18 hours/week = 936 hours.

    Volunteering 4 of those hours means they’ve given \(\frac{4 \text{ hours}}{936 \text{ hours}}\) or 0.5% (less than 1%) of their free time away!

    Donate some money.

    How much money are you budgeting for gifts this holiday season? $250? $500?

    2a. If you donate $5 to The Salvation Army online, what percentage of your budget of $250 would be donated to them?

    Five dollars out of $250 is \(\frac{\$5}{\$250}\) or 2% of your budget.

    2b. What percentage of your budget of $500 would be donated to The Salvation Army online if you gave $50?

    Fifty dollars out of $500 is \(\frac{\$50}{\$500}\) or 10%.

    3. If the average present cost for you is $25 and you donated 10% of that to The Salvation Army online, what would the new average present cost be?

    Ten percent of $25 is the same as 10% x $25 (remember “of” means multiply). This is 0.10 x $25 or $2.50.

    So your new average present cost is $25 – $2.50 or $22.50. That’s still pretty good!

    Share the experience.

    Suppose you just don’t have a half day, and you’re working on a budget of $0 this Christmas. You can still help your children see the beauty of giving and share some math with them.

    4. The Houston Salvation Army Secret Warehouse (where they keep all the toys) is 24,000 square feet. It serves about 6,000 families. About how much space is that for the toys for each family?

    So \(\frac{24,000 \text{ square feet}}{6,000 \text{ families}} = 4 \text{ square feet/family}\) in that warehouse! That’s the size of a square with each side roughly the length of your arm.

    Check out the bags of donated gifts behind the bike in the picture and you can see that it’s totally true!

    Share a smile.

    Michael J. Ivery, one of the famous Salvation Army Bell Ringers

    The Salvation Army Bell Ringers have a tough job encouraging people to drop their loose change into the famous Red Kettle. They spend hours on their feet. And many times people don’t even look their way.

    So give them a big smile when you pass by. Have your children stop and shake their hand and tell them thanks for helping others.

    When you leave, talk about how big the bell ringer’s smile was at having someone interact with them. Remember, the size of a smile could be measured in inches (another math thing) — but often it’s measured in happiness!

    Create a math model.

    A math model is an equation that represents reality. Or something close to reality.

    You can model how good you would feel based on how you share.

    5. Can you create a formula for how good you feel when you donate your time, money or do other nice things for others?

    For me, I used a scale from 1 to 10. I assigned numbers to each of the activities:

    • Giving one toy makes me feel as good as 6.
    • Giving one book makes me feel as good as an 8.
    • Giving one hour of my time makes me feel a 4.
    • Giving a smile and handshake to a bell ringer makes me feel like a 10.
    • Giving one dollar makes me feel like a 5.

    So my formula for how good I feel this season looks like this:

    \(\frac{(6 \times \text{Toys}) + (8 \times \text{Books}) + (4 \times \text{Hours}) + (10 \times \text{Smiles}) + (5 \times \text{Dollars})}{\text{Toys } + \text{ Books } + \text{ Hours } + \text{ Smiles } + \text{ Dollars}}\)

    Your turn!

    So how about it? What will you do this holiday season to help you feel good and teach your children math? Share your thoughts in the comments and don’t forget to tweet about it.

    And of course, visit your local Salvation Army and donate online!

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  • Fractions Aren't Exact!

    Fractions Aren't Exact!

    I make Texas shaped waffles every Saturday morning. But this weekend I ran into a snag. The recipe called for 2 cups of Bisquick and I only had 1 1/4 cups left!

    Break out the fractions!

    “This shouldn’t be a problem,” I thought. “I’m good with fractions. I’ll just scale down the whole recipe.”

    2 cups is the same as 8 quarter cups. I have 1 1/4 cups of Bisquick — or five quarter cups.

    So I need to break the other ingredients down into eight pieces and only use five of them.

    This is the thinking that most math people would translate into, “I need 5/8 of the whole recipe.”

    Sounds good!

    Until I saw the other ingredients…

    • 1 1/3 cups milk
    • 1 egg
    • 2 tablespoons oil

    For real?!

    Here’s how I thought about the fractions in the 1 1/3 cups milk:

    Since I need 5 of the eight pieces, I need 5 of the 1/6 cups. Grief!

    “Don’t panic,” I thought, “4 of the 1/6 cups give me 2/3. And 5/6 is pretty close to 1. So let’s just estimate the milk as almost a cup.”

    Now what about the egg?

    I was not about to find 5/8 of an egg. So I thought:

    The recipe doesn’t say a large egg or a medium egg. And the variations of eggs are huge. So what would it matter if I used one egg or 5/8 of an egg? It’s still pretty close.

    I dumped the whole egg in.

    And I threw caution to the wind.

    At this point, my fractions were so far gone I just tipped the bottle of oil up and let it go.

    And wouldn’t you know — we had some pretty awesome waffles!

    Share your thoughts in the comments or on twitter/x.

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  • Math Words — Start Using Them Early

    Math Words — Start Using Them Early

    Every parent is concerned that their children will not get what they need to be successful. Especially in math.

    Instead of worrying, you can take action. And it’s not hard.

    Use “big” math words.

    Don’t refrain from teaching your child math words just because they’re big or seem complicated to you.

    This sentence, “May I have milk, please,” has five simple words. To a grown-up.

    But to a child, a five word sentence is no different than a five syllable word. Like, “parallelogram.”

    In fact, if you teach your child to count to 10, it’s the same as teaching your child an eleven syllable word. (Seven has two syllables.)

    To put this in perspective, the word overintellectualization has only ten syllables!

    O – ver – in – tel – lec – tu – a – li – za – tion

    One – two – three – four – five – six – seven – eight – nine – ten

    In fact, overintellectualization is easier to say when you look at it like this.

    Try some words!

    Give these math words a shot with your little ones:

    Parallelogram (pear-uh-lell-uh-gram)

    A parallelogram is a shape. It has four sides. The sides that are across from each other are parallel to each other. Which means a square is a type of parallelogram. And so is a rectangle.

    So the next time you see a square or a rectangle, say to your child, “Hey, there’s a rectangle. It’s also a parallelogram. Can you say parallelogram?”

    Hypotenuse (hi-pot-uh-news)

    The hypotenuse is any diagonal that you take instead of walking first to the left and then to the right (or vice versa). So the next time you walk across the street at a diagonal, say to your child, “Were walking the hypotenuse. Can you say hypotenuse?”

    Coplanar (co-plane-er)

    Any two things that are on the same flat surface are coplanar. Like two people standing on the floor together.

    When you’re around stairs, stand on a different step than your child. Say, “Look, we are not coplanar.”

    Then move to the same step as your child and say, “Now we are coplanar. We are on the same flat surface. Can you say coplanar?”

    Go do it. Have fun!

    You don’t have to know the formal definitions of your math words. Just know a place or two where you can demonstrate them in your own world.

    Remember, getting your child familiar with math words will make a big difference.

    So pull out some big words, and try them on for size. Your little ones can handle it!

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