Download LCM and Comparing/Ordering Fractions

LCM and Comparing/Ordering Fractions Page: Name: Class: Date: Warm-­‐up Problem Multiples A MULTIPLE of a number is the PRODUCT of that number and a nonzero whole number. Ex. List the first 5 multiples of 25: 25, 50, 75, 100, 125 Least Common A COMMON MULTIPLE is a multiple that two numbers have in Multiple (LCM) common. The LEAST common multiple of two numbers is the smallest multiple that is common to both of them. Ex. Circle the common multiples of 4 and 6. Then, find the LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24… Multiples of 6: 6, 12, 18, 24, 30, 36… LCM: (Circle 12, 24; LCM is 12) Is there such a thing as greatest common multiple? NO! Find LCM: One way to find the LCM is to LIST the multiples of each Method 1 number, then look for the SMALLEST multiple. List the Multiples Find LCM: A VENN DIAGRAM is helpful for finding LCM. Method 2 Use Prime STEP 1: Write the PRIME factorizations of each number. Factorizations and STEP 2: Put the prime factors into a VENN diagram. a Venn Diagram STEP 3: Multiply EVERYTHING together. Practice: Find the LCM by listing multiples: 1.) 12 and 10 (LCM: 60) 2.) 20 and 25 (LCM: 100) Find the LCM using Prime Factorizations and a Venn Diagram: 3.) 24 and 36 (LCM: 72) 4.) 6𝑎! 𝑎𝑛𝑑 18𝑎! (LCM: 18a^3) 5.) 12𝑥 𝑎𝑛𝑑 15𝑥𝑦 (LCM: 60xy) 6.) 8𝑚! 𝑎𝑛𝑑 14𝑚! (LCM: 56m^4) 7.) 25𝑦 ! 𝑎𝑛𝑑 15𝑥 (LCM: 75xy^2) More resources can be found on our class website: www.elliottsttims.weebly.com/resources LCM and Comparing/Ordering Fractions Page: Name: Class: Date: LCM vs. LCD LCD means Least Common DENOMINATOR. The LCD of two fractions is the LCM of the denominators. Comparing and Before comparing or ordering fractions, write each fraction Ordering Fractions with a COMMON DENOMINATOR. Then, compare NUMERATORS. Ex. Compare these fractions, using <, >, or =. 5 7
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ANSWER: ! < !"; LCD is 40 Practice: Put the following fractions in order from least to greatest. ! ! !
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The swimming team won ! of its meets, and the !
soccer team won ! of its games. Which team won the greatest fraction of its competitions? More resources can be found on our class website: www.elliottsttims.weebly.com/resources LCM and Comparing/Ordering Fractions Page: Name: Class: Date: Warm-­‐up Problem Multiples A ____________________ of a number is the ____________________ of that number and a nonzero whole number. Ex. List the first 5 multiples of 25: Least Common A __________________ _________________ is a multiple that two Multiple (LCM) numbers have in common. The ___________________ common multiple of two numbers is the smallest multiple that is common to both of them. Ex. List the multiples of 4 and 6. Circle the common multiples. Then, find the LCM of 4 and 6. Multiples of 4: Multiples of 6: LCM: Is there such a thing as greatest common multiple? ___________ Find LCM: One way to find the LCM is to _______________ the multiples of Method 1 each number, then look for the ______________________ multiple. List the Multiples Find LCM: A ____________ ____________________ is helpful for finding LCM. Method 2 Use Prime STEP 1: Write the _______________ factorizations of each number. Factorizations and STEP 2: Put the prime factors into a _______________ diagram. a Venn Diagram STEP 3: Multiply _____________________ together. Practice: Find the LCM by listing multiples: 1.) 12 and 10 2.) 20 and 25 Find the LCM using Prime Factorizations and a Venn Diagram: 3.) 24 and 36 4.) 6𝑎! 𝑎𝑛𝑑 18𝑎! 5.) 12𝑥 𝑎𝑛𝑑 15𝑥𝑦 6.) 8𝑚! 𝑎𝑛𝑑 14𝑚! 7.) 25𝑦 ! 𝑎𝑛𝑑 15𝑥 More resources can be found on our class website: www.elliottsttims.weebly.com/resources LCM and Comparing/Ordering Fractions Page: Name: Class: Date: LCM vs. LCD LCD means Least Common _________________________. The LCD of two fractions is the ___________ of the denominators. Comparing and Before comparing or ordering fractions, write each fraction Ordering Fractions with a __________________ _______________________. Then, compare ______________________. Ex. Compare these fractions, using <, >, or =. 5 7
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Practice: Put the following fractions in order from least to greatest. ! ! !
8.) ! , ! , !" ! ! !
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9.) !" , ! , ! , !" !
10.)
The swimming team won ! of its meets, and the !
soccer team won of its games. Which team won the !
greatest fraction of its competitions? More resources can be found on our class website: www.elliottsttims.weebly.com/resources