Name Date. Find the LCM of the numbers using the two methods shown above.

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1 Lest Common Multiple Multiples tht re shred by two or more numbers re clled common multiples. The lest of the common multiples is clled the lest common multiple (LCM). There re severl different wys to find the LCM of two or more numbers. Exmple Find the lest common multiple (LCM) of nd 0. Method List the multiples of ech number. Then circle the common multiples. Multiples of :,,,, 0, 0,,,, 0 Multiples of 0: 0, 0, 0,, 0, 0, Some common multiples of nd 0 re 0 nd 0. The lest of these common multiples is 0. So, the LCM of nd 0 is 0. Method Mke fctor tree for ech number. 0 Write the prime fctoriztion of ech number. Circle ech different fctor where it ppers the gretest number of times. = ppers once in both fctoriztions, so circle it here. ppers more often here, so circle ll s. 0 = ppers once. Do not circle the s or s gin. = 0 Find the product of the circled fctors. So, the LCM of is 0 is 0. Find the LCM of the numbers using the two methods shown bove.., 0.,.,., 0.,. 0,.,.,.,, 0 0.,,. 0.,.,, 0. SPOTLIGHTS A spotlight t dnce club flshes every seconds. Another spotlight flshes every 0 seconds. Both lights just flshed. After how mny minutes will both lights flsh t the sme time gin?. CLOCKS A clock chimes every minutes. Another clock chimes every hlf hour. Both clocks just chimed t midnight. How mny times will both clocks chime t the sme time over the next hours?. SUBWAYS Three subwy lines rrive t sttion t the sme time. Line A rrives t the sttion every minutes, Line B rrives every minutes, nd Line C rrives every minutes. How long must you wit until ll three lines rrive t the sttion t the sme time gin? Copyright Big Ides Lerning, LLC Topic.

2 Equivlent Frctions nd Simplifying Frctions The number lines show the grphs of two frctions, nd. These frctions represent the sme number. Two frctions tht represent the sme number re clled equivlent frctions. To write equivlent frctions, you cn multiply or divide the numertor nd the denomintor by the sme nonzero number. Exmple Write two frctions tht re equivlent to. Multiply the numertor nd denomintor by. Divide the number nd denomintor by. = = Two equivlent frctions re nd. = = A frction is in simplest form when its numertor nd its denomintor hve no common fctors besides. Exmple Write the frction in simplest form. Divide the numertor nd denomintor by, the gretest common fctor of nd. = = in simplest form is. 0 0 Write two frctions tht re equivlent to the given frction Write the frction in simplest form Is the frction in simplest form? Explin.. Write five frctions tht ech simplify to one-ninth.. SLEEP It is recommended tht 0- to -yer old students should sleep bout hours ech night. Wht frction of the dy is this? Write your nswer in simplest form. Copyright Big Ides Lerning, LLC Topic.

3 Mixed Numbers nd Improper Frctions A mixed number is the sum of whole number nd frction. An improper frction is frction with numertor tht is greter thn or equl to the denomintor. The shded prt of the model represents the mixed number nd the improper frction. or Exmple Write s n improper frction. = + Definition of mixed number = + = whole =. So, wholes =. Add. written s n improper frction is. Exmple Write s mixed number. ) Divide the numertor,, by the denomintor,. The quotient is. The reminder is. Write the reminder s frction, reminder. divisor written s mixed number is. Write the mixed number s n improper frction Write the improper frction s mixed number Find the improper frction with denomintor of tht is equivlent to.. Find the improper frction with denomintor of tht is equivlent to. Copyright Big Ides Lerning, LLC Topic.

4 Adding nd Subtrcting Frctions To dd or subtrct two frctions with like denomintors, write the sum or difference of the numertors over the denomintor. Adding or Subtrcting Frctions with Like Denomintors c + b c = + b, where c 0 c c b c = b, where c 0 c Exmple Find +. Exmple Find. + = + Add the numertors. = Subtrct the numertors. =, or = To dd or subtrct two frctions with unlike denomintors, first write equivlent frctions with common denomintor. There re two methods you cn use. Exmple Find + Method : Adding or Subtrcting Frctions with Unlike Denomintors Method Multiply the numertor nd the denomintor of ech frction by the denomintor of the other frction. Method Use the lest common denomintor (LCD). The LCD of two or more frctions is the lest common multiple (LCM) of the denomintors. + =. Exmple Find 0. Rewrite using common denomintor Method : Rewrite the difference s of =. + = + 0 =, or Multiply. 0. The LCM of nd 0 is. So, the LCD is. 0 = 0 = Rewrite using the LCD,. Multiply. =, or Evlute Copyright Big Ides Lerning, LLC Topic.

5 Multiplying nd Dividing Frctions To multiply two frctions, multiply the numertors nd multiply the denomintors. Exmple Find. Exmple Find = = = Multiply the numertors. Multiply the denomintors. b c Multiplying Frctions d = c, where b, d 0 b d = Divide out common fctors. = =, or. Rewrite s. Multiply the numertors. Multiply the denomintors. Two numbers whose product is re reciprocls. To write the reciprocl of number, write the number s frction. Then invert the frction. Every number except 0 hs reciprocl. To divide number by frction, multiply the number by the reciprocl of the frction. b c d = b d Dividing Frctions c = d, where b, c, d 0 b c Exmple Find. Exmple Find. = = = Write the reciprocl of the number. Multiply by the reciprocl of, which is. = Multiply. = = =, or Rewrite s. Multiply by the reciprocl of, which is. Multiply.. Evlute AREA Find the re of rectngulr court tht is meters long nd meters wide.. CARPENTRY How mny -foot pieces cn you cut from piece of wood tht is feet long? Copyright Big Ides Lerning, LLC Topic.

6 Writing Frctions, Decimls, nd Percents A percent is prt-to-whole rtio where the whole is 00. The symbol for percent is %. In the model, of the 00 squres re shded. You cn write the shded prt of the model s frction, deciml, or percent. Frction: forty-seven out of one hundred, or 00 Deciml: forty-seven hundredths, or 0. Percent: forty-seven percent, or % Exmple Write the percent or deciml s frction.. % = 00 = 0 b. % = 00 =, or c. 0. = 0 = Exmple Write the percent or frction s deciml.. % =. = 0. b. = = 0. c. = = 00 = 0. Exmple Write the deciml or frction s percent.. 0. = 0. = % b. 0. = 0. =.% c. = 0 0 = 0 00 = 0% Write the percent or deciml s frction %. %. % 0. %. %. 0.% Write the percent or frction s deciml %. %. %. 00%. 0.%. 0% Write the deciml or frction s percent Which is greter, or %?. Which is greter,.% or 0.? Copyright Big Ides Lerning, LLC Topic.