@@ -151,13 +151,13 @@ <h3 style="margin:7px">Key Points</h3>
151151< summary > < h2 itemprop ="name " style ="margin:7px "> Mathematics</ h2 >
152152</ summary >
153153< br >
154- < section id ="numbers ">
154+ < section style =" margin:12px " itemprop =" about " itemscope itemtype =" http://schema.org/LearningResource " id ="numbers ">
155155< details >
156- < summary > < h3 itemprop ="about " itemscope itemtype =" http://schema.org/LearningResource "> 1. Numbers</ h3 > </ summary >
156+ < summary > < h3 itemprop ="name "> 1. Numbers</ h3 > </ summary >
157157< br >
158158< br >
159- < section id ="numerals ">
160- < h3 itemprop ="name " itemscope itemtype =" http://schema.org/LearningResource " > Numerals</ h3 >
159+ < section itemprop =" about " itemscope itemtype =" http://schema.org/LearningResource " id ="numerals ">
160+ < h3 itemprop ="name "> Numerals</ h3 >
161161< br >
162162< p itemprop ="description "> Notations of numeric Values</ p >
163163< br >
@@ -202,12 +202,12 @@ <h3 itemprop="name" itemscope itemtype="http://schema.org/LearningResource" >Num
202202< br >
203203< br >
204204< br >
205- < section itemscope itemtype ="http://schema.org/LearningResource " id ="systems ">
205+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource " id ="systems ">
206206< h3 itemprop ="name "> Numeric Systems</ h3 >
207207< br >
208208< p itemprop ="description "> The Values of Numbers.</ p >
209209< br >
210- < p itemprop =" description " > Example #1 - The year 2025 in the decimal system with Arab numerals</ p >
210+ < p > Example #1 - The year 2025 in the decimal system with Arab numerals</ p >
211211< br >
212212< div >
213213< table >
@@ -242,7 +242,7 @@ <h3 itemprop="name">Numeric Systems</h3>
242242</ table >
243243</ div >
244244< br >
245- < p itemprop =" description " > (2 × 10³) + (0 × 10²) + (2 × 10¹) + (5 × 10⁰) = 2025</ p >
245+ < p > (2 × 10³) + (0 × 10²) + (2 × 10¹) + (5 × 10⁰) = 2025</ p >
246246< br >
247247< br >
248248< p itemprop ="usageInfo "> Basic Geometry uses Arab numbers and the decimal system, but there are other numbers and numeral systems in use.</ p >
@@ -319,18 +319,18 @@ <h3 itemprop="name">Numeric Systems</h3>
319319</ details >
320320</ section >
321321< br >
322- < section style ="margin:12px " id ="equation ">
322+ < section itemprop =" about " itemscope itemtype =" http://schema.org/LearningResource " style ="margin:12px " id ="equation ">
323323< details >
324- < summary > < h3 itemprop ="about " itemscope itemtype =" http://schema.org/LearningResource " > 2. Equations</ h3 > </ summary >
324+ < summary > < h3 itemprop ="name " > 2. Equations</ h3 > </ summary >
325325< br >
326326< br >
327- < section itemscope itemtype ="http://schema.org/LearningResource ">
327+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource ">
328328< h4 itemprop ="name "> = Equation</ h4 >
329329< br >
330- < p itemprop ="about "> The numbers or expressions of one side equal in value to the other side.
330+ < p itemprop ="description "> The numbers or expressions of one side equal in value to the other side.
331331< br >
332332< br >
333- < p itemprop =" description " > Example:
333+ < p > Example:
334334< br >
335335< br >
3363361 + 2 = 3
@@ -339,21 +339,21 @@ <h4 itemprop="name">= Equation</h4>
339339< br >
340340< br >
341341< br >
342- < section itemscope itemtype ="http://schema.org/LearningResource " id ="operations ">
342+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource " id ="operations ">
343343< h3 itemprop ="name "> Basic Operations</ h3 >
344344< br >
345345< br >
346- < section itemscope itemtype ="https ://schema.org/LearningResource id= "addition ">
346+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="addition ">
347347< h3 itemprop ="name "> + Addition</ h3 >
348348< br >
349- < p itemprop =" description " >
349+ < p >
350350Example #1:
351351< br >
352352< br >
3533531 + 1 = 2
354354</ p >
355355< br >
356- < p itemprop =" abstract " >
356+ < p >
357357🌻+🌻=🌻🌻
358358</ p >
359359< br >
@@ -368,19 +368,19 @@ <h3 itemprop="name">+ Addition</h3>
368368< br >
369369< br >
370370< br >
371- < section itemscope itemtype ="https ://schema.org/LearningResource id= "subtraction " itemref="addition ">
371+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="subtraction " itemref ="addition ">
372372< h3 itemprop ="name "> - Subtraction</ h3 >
373373< br >
374374< p itemprop ="description "> The opposite of addition</ p >
375375< br >
376- < p itemprop =" description " >
376+ < p >
377377Example #1:
378378< br >
379379< br >
3803802 - 1 = 1
381381</ p >
382382< br >
383- < p itemprop =" abstract " >
383+ < p >
384384🌻🌻-🌻=🌻
385385</ p >
386386< br >
@@ -395,20 +395,19 @@ <h3 itemprop="name">- Subtraction</h3>
395395< br >
396396< br >
397397< br >
398- < section itemscope itemtype ="https ://schema.org/LearningResource id= "multiplication " itemref="addition ">
398+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="multiplication " itemref ="addition ">
399399< h3 itemprop ="name "> × Multiplication *</ h3 >
400- < meta itemprop ="url " content ="https://basic-geometry.github.io ">
401400< br >
402401< p itemprop ="description "> An advanced form of addition</ p >
403402< br >
404- < p itemprop =" description " >
403+ < p >
405404Example #1:
406405< br >
407406< br >
4084072 × 3 = 6
409408</ p >
410409< br >
411- < p itemprop =" abstract " > 🌻🌻🌻+🌻🌻🌻=🌻🌻+🌻🌻+🌻🌻=🌻🌻🌻🌻🌻🌻</ p >
410+ < p > 🌻🌻🌻+🌻🌻🌻=🌻🌻+🌻🌻+🌻🌻=🌻🌻🌻🌻🌻🌻</ p >
412411< br >
413412< br >
414413< p itemprop ="usageInfo "> Important notice: 2×🌻🌻🌻=🌻🌻🌻🌻🌻🌻 ,
@@ -426,18 +425,18 @@ <h3 itemprop="name">× Multiplication *</h3>
426425< br >
427426< br >
428427< br >
429- < section itemscope itemtype ="https ://schema.org/LearningResource id= "division " itemref="multiplication ">
428+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="division " itemref ="multiplication ">
430429< h3 itemprop ="name "> ÷ Division /</ h3 >
431430< br >
432431< p itemprop ="description "> The opposite of multiplication</ p >
433432< br >
434- < p itemprop =" description " > Example #1:
433+ < p > Example #1:
435434< br >
436435< br >
4374366 / 3 = 2
438437</ p >
439438< br >
440- < p itemprop =" abstract " > 🌻🌻🌻🌻🌻🌻/🌻🌻🌻 = 2</ p >
439+ < p > 🌻🌻🌻🌻🌻🌻/🌻🌻🌻 = 2</ p >
441440< br >
442441< br >
443442< p itemprop ="usageInfo "> Important notice: 🌻🌻🌻🌻🌻🌻 over 3 equals 🌻🌻 .</ p >
@@ -449,11 +448,11 @@ <h3 itemprop="name">÷ Division /</h3>
449448</ details >
450449</ section >
451450< br >
452- < section style =" margin:12px " itemscope itemtype ="http://schema.org/LearningResource " id ="fractions ">
451+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource " style =" margin:12px " id ="fractions ">
453452< details >
454453< summary > < h3 itemprop ="name "> 3. Fractions</ h3 > </ summary >
455454< br >
456- < p itemprop ="about "> Fractions are the results of division, some are non-whole numbers.</ p >
455+ < p itemprop ="description "> Fractions are the results of division, some are non-whole numbers.</ p >
457456< p itemprop ="description "> E.g. the results of breaking a branch in half are 2 half branches.
458457< br >
459458< br >
@@ -481,16 +480,15 @@ <h3 itemprop="name">÷ Division /</h3>
481480< br >
482481< br >
483482< br >
484- < section itemscope itemtype ="http://schema.org/LearningResource " id =operations_with_fractions >
483+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource " id =operations_with_fractions >
485484< h3 itemprop ="name "> Operations with Fractions</ h3 >
486485< br >
487486< br >
488- < section itemscope itemtype ="https ://schema.org/LearningResource id= "adding_fractions " itemref="addition ">
487+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="adding_fractions " itemref ="addition ">
489488< h3 itemprop ="name "> Adding Fractions</ h3 >
490489< br >
491- < p itemprop ="description "> Adding the counters if the denominators are the same.</ p >
490+ < p itemprop ="abstract "> Adding the counters if the denominators are the same.</ p >
492491< br >
493- < div itemprop ="abstract ">
494492< p > Example #1:</ p >
495493< br >
496494< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -509,15 +507,13 @@ <h3 itemprop="name">Adding Fractions</h3>
509507 < mn > 1</ mn >
510508 </ mrow >
511509</ math >
512- </ div >
513510< br >
514511< br >
515512< p itemprop ="usageInfo "> If the denominators are not the same, both the counter and the denominator of at least one of the fractions shall be multiplied or divided by the same number to match the other denominator.
516513< br >
517514< br >
518515The denominators can be multiplied by each other to get a common denominator. In this case the counters need to be multiplied respectively.</ p >
519516< br >
520- < div itemprop ="abstract ">
521517< p > Example #2:</ p >
522518< br >
523519< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -538,17 +534,15 @@ <h3 itemprop="name">Adding Fractions</h3>
538534 < mfrac > < mn > 11</ mn > < mn > 15</ mn > </ mfrac >
539535 </ mrow >
540536</ math >
541- </ div >
542537</ section >
543538< br >
544539< br >
545540< br >
546- < section itemscope itemtype ="https ://schema.org/LearningResource id= "subtracting_fractions " itemref="adding_fractions ">
541+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="subtracting_fractions " itemref ="adding_fractions ">
547542< h3 itemprop ="name "> Subtracting Fractions</ h3 >
548543< br >
549544< p itemprop ="description "> Subtracting the counters if the denominators are the same.</ p >
550545< br >
551- < div itemprop ="abstract ">
552546< p > Example #1:</ p >
553547< br >
554548< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -567,7 +561,6 @@ <h3 itemprop="name">Subtracting Fractions</h3>
567561 < mn > 1</ mn >
568562 </ mrow >
569563 </ math >
570- </ div >
571564< br >
572565< br >
573566< p itemprop ="usageInfo "> If the denominators are not the same, both the counter and the denominator of a fraction shall be multiplied or divided by the same number to match the other counter.
@@ -599,15 +592,14 @@ <h3 itemprop="name">Subtracting Fractions</h3>
599592< br >
600593< br >
601594< br >
602- < section itemscope itemtype ="https ://schema.org/LearningResource id= "multiplying_fractions " itemref="multiplication ">
595+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource" id ="multiplying_fractions " itemref ="multiplication ">
603596< h3 itemprop ="name "> Multiplying Fractions</ h3 >
604597< br >
605- < p itemprop ="description "> A fraction can be multiplied by multiplying its counter, or dividing its denominator.
598+ < p itemprop ="abstract "> A fraction can be multiplied by multiplying its counter, or dividing its denominator.
606599< br >
607600< br >
608601Multiplying by a fraction means multiplying counter by counter and denominator by denominator.</ p >
609602< br >
610- < div itemprop ="abstract ">
611603< p > Example:</ p >
612604< br >
613605< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -624,20 +616,18 @@ <h3 itemprop="name">Multiplying Fractions</h3>
624616 < mfrac > < mn > 8</ mn > < mn > 15</ mn > </ mfrac >
625617 </ mrow >
626618</ math >
627- </ div >
628619</ section >
629620< br >
630621< br >
631622< br >
632- < section itemscope itemtype ="https ://schema.org/LearningResource https://schema.org/MathSolver " id =" dividing_fractions " itemref ="division ">
623+ < section id =" dividing_fractions " itemscope itemtype ="http ://schema.org/LearningResource " itemref ="division ">
633624< h3 itemprop ="name "> Dividing Fractions</ h3 >
634625< br >
635- < p itemprop ="description "> A fraction can be divided by dividing its counter, or multiplying its denominator.
626+ < p itemprop ="abstract "> A fraction can be divided by dividing its counter, or multiplying its denominator.
636627< br >
637628< br >
638629Dividing by a fraction means multiplying by the reciprocal of that fraction.</ p >
639630< br >
640- < div itemprop ="abstract ">
641631< p > Example:</ p >
642632< br >
643633< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -662,7 +652,6 @@ <h3 itemprop="name">Dividing Fractions</h3>
662652 < mfrac > < mn > 5</ mn > < mn > 6</ mn > </ mfrac >
663653 </ mrow >
664654</ math >
665- </ div >
666655</ section >
667656</ section >
668657< br >
@@ -671,13 +660,13 @@ <h3 itemprop="name">Dividing Fractions</h3>
671660</ details >
672661</ section >
673662< br >
674- < section itemscope itemtype ="http://schema.org/LearningResource " id ="powers ">
663+ < section itemprop =" about " itemscope itemtype ="http://schema.org/LearningResource " style =" margin:12px " itemref =" multiplication " id ="powers ">
675664< details >
676- < summary > < h3 style =" margin:12px " itemprop ="name "> 4. Powers</ h3 > </ summary >
665+ < summary > < h3 itemprop ="name "> 4. Powers</ h3 > </ summary >
677666< br >
678- < p style =" margin:12px " itemprop ="description "> Raising a number or unit of measurement to a power means multiplying it by itself.</ p >
667+ < p itemprop ="abstract "> Raising a number or unit of measurement to a power means multiplying it by itself.</ p >
679668< br >
680- < p style =" margin:12px " itemprop =" description " > Raising a value to the 3rd power means multiplying it by itself twice.
669+ < p > Raising a value to the 3rd power means multiplying it by itself twice.
681670< br >
682671< br >
683672Example #1:
@@ -687,7 +676,7 @@ <h3 itemprop="name">Dividing Fractions</h3>
687676</ p >
688677< br >
689678< br >
690- < p style =" margin:12px " > Raising a value to the -4th power means the reciprocal of the 4th power.
679+ < p > Raising a value to the -4th power means the reciprocal of the 4th power.
691680< br >
692681< br >
693682Example #2:
@@ -697,7 +686,7 @@ <h3 itemprop="name">Dividing Fractions</h3>
697686</ p >
698687< br >
699688< br >
700- < p style =" margin:12px " itemprop =" description " > The result of raising a value to a fraction is a root.
689+ < p > The result of raising a value to a fraction is a root.
701690< br >
702691< br >
703692Example #3:
@@ -708,23 +697,23 @@ <h3 itemprop="name">Dividing Fractions</h3>
708697< br >
709698< br >
710699< br >
711- < section id ="geometry ">
712- < h3 style =" margin:7px " itemprop ="about " > The 2nd and the 3rd Powers manifesting in Geometry</ h3 >
700+ < section id ="geometry " itemprop =" about " itemscope itemtype =" http://schema.org/LearningResource " itemref =" powers " >
701+ < h3 itemprop ="name " > The 2nd and the 3rd Powers manifesting in Geometry</ h3 >
713702< br >
714- < section itemscope itemtype ="https ://schema.org/LearningResource " id ="square " itemref =" subtraction ">
715- < h3 style =" margin:7px " itemprop ="name "> Area of a Square</ h3 >
703+ < section itemprop =" about " itemscope itemtype ="http ://schema.org/LearningResource " id ="square ">
704+ < h3 itemprop ="name "> Area of a Square</ h3 >
716705< br >
717706< figure itemprop ="image " itemscope itemtype ="http://schema.org/ImageObject ">
718707 < img class ="center-fit " src ="square.png " alt ="A square is a 2 dimensional plane shape with 2 perpendicular pairs of parallel straight sides. Area = side × side = side² ">
719708</ figure >
720709< br >
721- < p style =" margin:12px " itemprop ="usageInfo "> The square is the foundational shape for area calculations. All area formulas relate to this instance.</ p >
710+ < p itemprop ="usageInfo "> The square is the foundational shape for area calculations. All area formulas relate to this instance.</ p >
722711< br >
723- < p style =" margin:12px " itemprop ="abstract "> A rectangle is a 2 dimensional plane shape with 2 perpendicular pairs of parallel straight sides.
712+ < p itemprop ="abstract "> A rectangle is a 2 dimensional plane shape with 2 perpendicular pairs of parallel straight sides.
724713< br >
725714< br >
726715The area of a rectangle is the product of its width and length.</ p >
727- < p style =" margin:12px " itemprop ="description "> A square is a rectangle with equal sides.</ p >
716+ < p itemprop ="description "> A square is a rectangle with equal sides.</ p >
728717< br >
729718< div itemprop ="description ">
730719< math display ="block " xmlns ="http://www.w3.org/1998/Math/MathML " >
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