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Academic Academic-Clinic.com Clinic.com Clinic.com The achiever’s guide to academic life and beyond… Website: http://academic-clinic.com Facebook: http://www.facebook.com/academic.clinic Twitter: http://twitter.com/acadclinic College entrance exam and science high school entrance test tips. Conquer UPCAT, ACET, USTET, DLSUCET, PSHS-NCE, and other entrance tests . Math I - 1 - Feel free to pass this on to your friends, but please don’t post it online. Discuss UPCAT and other college entrance exam questions and answers at Academic-Clinic’s Facebook Page . We encourage you to answer the questions we post there and actively participate in the discussions on our wall . For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam information, visit the Academic-Clinic website . Tell your friends and classmates to come find and join us. The more, the merrier. Good luck! BASIC ARITHMETIC AND ALGEBRA POINTERS Whole (natural) numbers Natural numbers numbers, which appear as a result of calculus of single subjects: peoples, animals, birds, trees, different wares and so on. Series of natural numbers: 1, 2, 3, 4, 5, is continued endlessly and is called natural series . Arithmetical operations Addition – an operation of finding a sum of some numbers: 11 + 6 = 17. Here 11 and 6 – addends , 17 – the sum . If addends are changed by places, a sum is saved the same: 11 + 6 = 17 and 6 + 11 = 17. Subtraction – an operation of finding an addend by a sum and another addend: 17 – 6 = 11. Here 17 is a minuend , 6 – a subtrahend , 11 – the difference . Multiplication. To multiply one number n (a multiplicand ) by another m ( a multiplier ) means to repeat a multiplicand n as an addend m times. The result of multiplying is called a product. The operation of multiplication is written as: n x m or n · m. For example, 12 x 4 = 12 + 12 + 12 + 12 = 48. In our case 12 x 4 = 48 or 12 · 4 = 48. Here 12 is a multiplicand, 4 – a multiplier, 48 – a product. If a multiplicand n and a multiplier m are changed by places, their product is saved the same: 12 · 4 = 12 + 12 + 12 + 12 = = 48 and 4 ·12 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 48. Therefore, a multiplicand and a multiplier are called usually factors or multipliers. Division – an operation of finding one of factors by a product and another factor: 48 : 4 = 12. Here 48 is a dividend , 4 – a divisor , 12 – the quotient . At dividing integers a quotient can be not a whole number. Then this quotient can be present as a fraction . If a quotient is a whole number, then it is called that numbers are divisible , i.e. one number is divided without remainder by another. Otherwise, we have a division with remainder . For example, 23 isn’t divided by 4 ; this case can be written as: 23 = 5 · 4 + 3. Here 3 is a remainder . Raising to a power. To raise a number to a whole (second, third, forth, fifth etc.) power means to repeat it as a factor two, three, four, five and so on. The number, repeated as a factor, is called a base of a power ; the quantity of factors is called an index or an exponent of a power ; the result is called a value of a power . A raising to a power is written as:
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