Being able to efficiently and correctly manipulate fractions is essential to doing well on the Math IC test. A fraction describes a part of a whole. It is composed of two expressions, a numerator and a denominator. The numerator of a fraction is the quantity above the fraction bar, and the denominator is the quantity below the fraction bar. For example, in the fraction 1 /2, 1 is the numerator and 2 is the denominator. Equivalent Fractions Two fractions are equivalent if they describe equal parts of the same whole. To determine if two fractions are equivalent, multiply the denominator and numerator of one fraction so that the denominators of the two fractions are equal. For example, 1/2 = 3/6 because if you multiply the numerator and denominator of 1 /2 by 3, you get:
As long as you multiply or divide both the numerator and denominator of a fraction by the same nonzero number, you will not change the overall value of the fraction. Fractions represent a part of a whole, so if you increase both the part and whole by the same multiple, you will not change their fundamental relationship. Reducing Fractions Reducing fractions makes life with fractions a lot simpler. It takes unwieldy fractions such as 450 /600 and makes them into smaller, easier-to-work-with fractions. To reduce a fraction to its lowest terms, divide the numerator and denominator by their GCF. For example, for 450 /600, the GCF of 450 and 600 is 150. So the fraction reduces down to 3 4. A fraction is in reduced form if its numerator and denominator are relatively prime (their GCF is 1). Thus, it makes sense that the equivalent fractions we studied in the previous section all reduce to the same fraction. For example, the equivalent fractions 4/6 and 8/12 both reduce to 2/3. Comparing Fractions When dealing with integers, large positive numbers with a lot of digits, like 5,000,000, are 美国GREater than numbers with fewer digits, such as 5. But fractions do not work the same way. For example, 200/20,000 might seem like a big, impressive fraction, but 2 /3 is actually larger, because 2 is a much bigger part of 3 than 200 is of 20,000. In certain cases, comparing two fractions can be very simple. If the denominators of two fractions are the same, then the fraction with the larger numerator is bigger. If the numerators of the two fractions are the same, the fraction with the smaller denominator is bigger. However, you’ll most likely be dealing with two fractions that have different numerators and denominators, such as 200/20,000 and 2/3. When faced with this situation, an easy way to compare these two fractions is to utilize cross-multiplication. All you have to do is multiply the numerator of each fraction by the denominator of the other, then write the product of each multiplication next to the numerator you used to get it. We’ll cross-multiply 200/20,000 and 2/3:英语作文
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