Rational Numbers---Adding Fractions With Like Denominators.

Transcription

1 Rtionl Numbers---Adding Frctions With Like Denomintors. A. In Words: To dd frctions with like denomintors, dd the numertors nd write the sum over the sme denomintor. B. In Symbols: For frctions c nd b c, where c 0, c + b c = + b c. C. Exmple: becomes + 5 which produces the result 5. Rtionl Numbers---Subtrcting Frctions With Like Denomintors. A. In Words: To subtrct frctions with like denomintors, subtrct the numertors nd write the difference over the sme denomintor. B. In Symbols: For frctions c nd b c, where c 0, c - b c = - b c.. Exmple: 5-5 becomes - 5 which produces the result 5. Rtionl Numbers---Adding nd Subtrcting Unlike Frctions (When Denomintors re NOT the Sme). the A. To dd or subtrct frctions with unlike denomintors:. Find the Lest Common Denomintor (LCD).. Renme the frctions with common denomintor.. Add or subtrct the numertors. 4. Plce the sum or difference over the common denomintor. 5. Simplify.

2 Rtionl Numbers---The Lest Common Denomintor (LCD) Defined. A. You find the LCD between two or more frctions by finding the Lest Common Multiple (LCM) of the denomintors of the frctions. B. The Lest Common Multiple.. A multiple of number is product of tht number nd ny whole number.. Multiples tht re shred by two or more numbers re clled common multiples.. The lest of the common non-zero multiples of two or more numbers is clled the Lest Common Multiple (LCM). Rtionl Numbers---Finding The Lest Common Denomintor (LCD). A. You cn find the LCM by mking chrt:. Exmple: Find the Lest Common Denomintor for,,, & 6 x *x *x *x 4*x 5*x 6*x The LCM of,,, & 6 is 6. I. IMPORTANT REVIEW: Prime Numbers A. A prime number is whole number greter thn one tht hs exctly two fctors, nd itself. B. Prime Fctoriztion.. When positive integer (other thn one) is expressed s product of fctors tht re ll prime, the expression is clled the prime fctoriztion.

3 Rtionl Numbers---Finding The Lest Common Denomintor (LCD). A. You cn find the LCM by finding the Prime Fctoriztion of ech Number.. Find the common denomintors nd dd: Find the prime fctors of ech denomintor. Express these fctors s powers. Number Prime Fctors Powers 8 = = b.. List ll the powers in incresing order of their exponents, using ech only once. The Lest Common Multiple (LCD) will be. c. Multiply the numertor nd the denomintor by the fctor needed to chnge the denomintor into the LCD (). For the frction 8 find how mny times 8 goes into. Multiply this number by both the numertor nd the denomintor:. 8 so 8 = 6. For the frction 5 find how mny times goes into. Multiply this number by both the numertor nd the denomintor:. 8 so 58 8 = 40. So = = = 76 = 9 4

4 . A short-cut wy to find common denomintor is to multiply the numertor & denomintor of the first frction by the denomintor of the second frction. Then multiply the numertor & denomintor of the second frction by the denomintor of first frction.. Exmple 5 + becomes which becomes which becomes Divisibility Rules: A number is divisible by:. if the ones digit is divisible by b. if the sum of its digits is divisible by c. 4 if the lst two digits re divisible by 4 d. 5 if the ones digit is 0 or 5 e. 6 if the number is divisible by nd f. 8 if the lst three digits re divisible by 8 g. 9 if the sum of ll the digits is divisible by 9 h. 0 if the ones digit is 0 Simplifying Frctions---Using Prime Fctors. A. A frction cn be simplified two wys:. Brek ech number into it's prime fctors.. Exmple : 6 9 becomes.. Next, cncel out the common fctors.. We cncel out the, leving only in the numertor nd in the denomintor. b. The remining frction is in it's simplest form: 4

5 Simplifying Frctions---Using the Gretest Common Fctor. A. A frction cn be simplified two wys:. Brek ech number into it's prime fctor (s in XI bove). Using the Gretest Common Fctor.. Exmple: Write 40 in simplest form.. Find the prime fctoriztion of the numertor nd the denomintor = 9. 9 hs two fctors in common,.. The product 4, is the gretest common fctor of the numertor nd the denomintor. 4. By cnceling out the common fctors, you re in ffect dividing both the numertor nd denomintor by the gretest common fctor. b. The product of the remining fctors, 5 0, is the simplified form of the frctionl rtionl number 40. 5