Article: We use cross multiplication for math problems where we know the fractions are equivalent, but one of the numbers has been replaced with a variable (typically x) for which we must solve. In cases like this, we know these fractions are equivalent because they're the sole terms on opposite sides of an equal sign, but it's often not obvious how to solve for the variable. Luckily, with cross multiplication, solving these types of problems is easy. In other words, you multiply the numerator of one fraction by the denominator of the other and vice versa, then set these two answers equal to each other and solve. Take our two examples of 4/8 and 8/16. These two don't contain a variable, but we can prove the concept since we already know they're equivalent. By cross multiplying, we get 4 x 16 = 8 x 8, or 64 = 64, which is obviously true. If the two numbers are not the same, then the fractions are not equivalent. Since cross multiplication is the easiest way to determine equivalent fractions when you must solve for a variable, let's add a variable. For example, let's consider the equation 2/x = 10/13. To cross multiply, we multiply 2 by 13 and 10 by x, then set our answers equal to each other: 2 13 = 26 10 x = 10x 10x = 26. From here, getting an answer for our variable is a matter of simple algebra. x = 26/10 = 2.6, making the initial equivalent fractions 2/2.6 = 10/13. One of the best things about cross multiplication is that it works in essentially the same way whether you're dealing with two simple fractions (as above) or with more complex fractions. For instance, if both fractions contain variables, you just have to eliminate these variables at the end during the solving process. Similarly, if the numerators or denominators of your fractions contain variable expressions (such as x + 1), simply "multiply through"by using the distributive property and solve as you normally would. For instance, let's consider the equation ((x + 3)/2) = ((x + 1)/4). In this case, as above, we'll solve by cross multiplying: (x + 3) 4 = 4x + 12 (x + 1) 2 = 2x + 2 2x + 2 = 4x + 12, then we can simplify the equation by subtracting 2x from both sides 2 = 2x + 12, then we should isolate the variable by subtracting 12 from both sides -10 = 2x, and divide by 2 to solve for x -5 = x
Question: What is a summary of what this article is about?
Set the two fractions equal to one another. Take the two equivalent fractions and multiply across the equals sign in an "X" shape. Introduce a variable. Use cross multiplication for equations with multiple variables or variable expressions.

The sheep should have run out by now,so you can start to explore the other places including the enemy and your allies. You should now have at least 4 people on wood by now. Blacksmiths cost 150 wood each, and markets cost 175 wood each. The thing is that markets are slower to build, and blacksmiths has a lot of upgrades for the military later on that you can use. They are good upgrades for the economy. Build a farm after you build the market. Farms cost 60 wood and cost 60 wood to reseed. It is better once you hunt deer somewhere farther away from the town center. Each deer stocks up to 140 food, and there should be at least 4 of 'em there. You don't need stone in the Feudal Age, so get gold. Have 2 villagers go on gold. You need 100 more gold to advance to the Castle Age. The Feudal Age should only take about 7 or 8 minutes. You need 800 food, 200 gold, and a blacksmith and a market to advance to the Castle Age. If you have extra wood, build a barracks farther to the enemy. On top of a cliff is best because infantry can't get up there by climbing. Then you can advance to the Castle Age. Keep exploring with your scout. By now, you should have at least 50% of the map explored (unless you are playing with a normal, large, or giant map).
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Create more villagers and add 2 to wood and 1 or 2 to forage bushes. Build a blacksmith and/or market. Research Horse Collar (in the mill) and Double-Bit Axe (in the lumber camp). Create 2 more villagers. Build a mining camp near gold, not stone. By now, you should haveAt least 15 villagersA scoutAt least 650 foodMillLumber campMining campAt least 100 woodAt least 200 gold200 stoneBlacksmithMarketLoom, Horse Collar, and Double-bit Axe researched Wait until you have 800 food.