COMMON FRACTIONS. or a / b = a b. , a is called the numerator, and b is called the denominator.

Transcription

1 COMMON FRACTIONS BASIC DEFINITIONS * A frtion is n inite ivision. or / * In the frtion is lle the numertor n is lle the enomintor. * The whole is seprte into "" equl prts n we re onsiering "" of those prts. * The enomintor n never equl zero (ie. 0). * A proper frtion is frtion whose numertor is less thn its enomintor (ie. < ). * An improper frtion is frtion whose numertor is greter thn or equl to its enomintor (ie. ). * If the reminer is 0 when the enomintor of n improper frtion is ivie into the numertor the improper frtion n e rewritten s whole numer. * We n write ny whole numer s frtion y writing it s the numertor of frtion whose enomintor is. INTRO TO MULTIPLYING FRACTIONS EQUIVALENT FRACTIONS * Equivlent frtions re two or more frtions tht represent the sme quntity or hve the sme vlue. BUILDING FRACTIONS * Rell the multiplitive ientity. ( n ) * We get n equivlent frtion to the one we strte with if we multiply tht frtion y ; the n e written s et. * In other wors we get frtion equivlent to the one we strte with if we multiply oth numertor n enomintor y the sme nonzero numer.

2 REDUCING FRACTIONS * We n reue frtion to lower (or lowest) terms y using the ft tht if is the gretest ommon ftor (the GCF) of numertor n enomintor the resulting frtion will e in lowest terms. * We get n equivlent frtion to the one we strte with if we ivie oth numertor n enomintor y the sme nonzero numer. * If we ivie oth numertor n enomintor y ny ftor ommon to oth the resulting frtion will e in lower terms ut not neessrily in lowest terms. * If the GCF of the numertor n enomintor is then the frtion is reue to lowest terms. LEAST COMMON MULTIPLE (LCM) * The lest ommon multiple (LCM) of two or more numers is the smllest (lest) numer tht is multiple of ll the numers. * Fining The LCM By Inspetion * Fining The LCM By Prime Ftoriztion. Write own the prime ftoriztion of eh numer writing repete ftors in eponentil form. 2. Write own eh ifferent se tht ppers in ny of the ftoriztions. 3. Rise eh se to the highest power to whih it ours in ny of the ftoriztions. 4. The LCM is the prout of ll the ftors foun in Step 3. * Note: The LCM will lwys e greter thn or equl to your lrgest numer. * Note: The GCF will lwys e less thn or equl to your smllest numer. LEAST COMMON DENOMINATOR (LCD) * The lest ommon enomintor (LCD) of two or more frtions is the LCM of the enomintors; tht is the LCD is the smllest numer tht is multiple of ll the enomintors. To fin the LCD we use the sme metho tht we use for fining the LCM.

3 COMPARING FRACTIONS * If two frtions reue to the sme frtion they re equivlent. * In n eqution tht is of the form we ll n the ross prouts. Two frtions re equivlent if their ross prouts re equl. Tht is if. * If two frtions hve the sme enomintor ut ifferent numertors then the frtion with the lrger numertor is the lrger frtion. If neessry we n rewrite the frtions s frtions with the sme enomintor (y uiling frtions) so tht we n then ompre them. * The ross prouts re only use to etermine whether or not two frtions re equivlent. They o not tell you whih frtion is lrger. ADDING AND SUBTRACTING FRACTIONS W/ SAME DENOMINATORS * Before we n (or sutrt) ny two or more frtions they first must hve the sme (ommon) enomintors * If the sum (or ifferene) is not in lowest terms it must e reue to lowest terms. ADDING AND SUBTRACTING FRACTIONS W/ DIFFERENT DENOMINATORS. Fin the LCD of ll the enomintors. 2. Rewrite eh frtion s n equivlent frtion tht hs the LCD s its enomintor. 3. A (or sutrt) the resulting frtions. 4. Reue the sum (or ifferene) to lowest terms if possile. * When ing (or sutrting) frtion n whole numer first write the whole numer s frtion y iviing it y. Then follow the ove 4 steps. SHORTCUTS IN MULTIPLYING FRACTIONS * We n ivie the numertor of one frtion n the enomintor of ny of the frtions y ny ftor ommon to oth. It is never neessry to fin the LCD when we multiply frtions.

4 FINDING A FRACTIONAL PART OF A NUMBER * We fin frtionl prt of numer y multiplying the frtion n the numer together. MULTIPLICATIVE INVERSE (RECIPROCAL) * The multiplitive inverse (or reiprol) of numer is foun y writing the numer s frtion if neessry n then interhnging the numertor n enomintor of the frtion. * Zero hs no reiprol. Why not? * The prout of numer n its reiprol is lwys. DIVIDING FRACTIONS -OR- * To ivie one frtion y nother we multiply the ivien y the multiplitive inverse (or reiprol) of the ivisor. It is never neessry to fin the LCD when we multiply frtions. MIXED NUMBERS * A mie numer is the sum of whole numer n proper frtion lthough the plus sign is omitte when we write mie numers. * Every mie numer n e rewritten s n improper frtion n every improper frtion n e rewritten s whole numer or s mie numer. * Two Methos To Convert Mie Numer To An Improper Frtion Metho A. Emple: Metho B. Emple: 4 4 4

5 * Metho To Convert Improper Frtion To A Mie Numer. Divie the numertor of the improper frtion y its enomintor. 2. The quotient eomes the whole numer prt of the mie numer. 3. The reminer eomes the numertor of the frtion prt of the mie numer. 4. The enomintor of the improper frtion eomes the enomintor of the frtion prt of the mie numer. ADDING AND SUBTRACTING MIXED NUMBERS * An improper mie numer is mie numer where the frtion prt itself is n improper frtion. * Two Methos To A (Or Sutrt) Mie Numers Metho A. Convert ll mie numers to improper frtions n then perform the ition (or sutrtion). The finl nswer n e written s n improper frtion or s mie numer. Metho B. A (or sutrt) the whole numer prts. A (or sutrt) the frtion prts. Simplify if the sum (or ifferene) is n improper mie numer. MULTIPLYING AND DIVIDING MIXED NUMBERS * Mie numers must e onverte to improper frtions efore they n e multiplie or ivie. Do not multiply (or ivie) the whole numer prts n multiply (or ivie) the frtion prts. COMPLEX FRACTIONS * A simple frtion ontins only one frtion r. The numertor n enomintors re oth whole numers. * A omple frtion is frtion in whih the numertor n/or enomintor is not whole numer. It my ontin ition n/or sutrtion symols. Comple frtions ontin more thn one frtion r. * Simplifying Comple Frtions. Use orer of opertions to simplify epressions ove n elow the "min" frtion r seprtely. 2. Divie the frtion ove the "min" frtion r y the frtion elow the "min" frtion r. ORDER OF OPERATIONS * When evluting epressions tht involve whole numers frtions n/or mie numers we use the sme orer of opertions tht we use with whole numers.