# 6th Grade - Use Common Multiples With Fractions

 Grade Level: 6th Skill: Fractions, Decimals and Percentages Topic: Use Common Multiples with Fractions Goal: Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Skill Description: Find the LCM, least common multiple, of two or more numbers. Use common multiples to find equivalent fractions. This is necessary to find common denominators to create like fractions for the purpose of adding or subtracting. Find the greatest common divisor of the two terms of a fraction and use them to reduce fractions to simplest form.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Reduce to lowest common terms: 12/96 (1/8) (2) What is the least common multiple (LCM) of 8,6? (24) (3) Find the greatest common factor (GCF) of 12 and 36. (12) (4) Jillian was solving the math problem, 2 7/8 + 1 ½. She began by changing 1 ½ to 1 4/8. What steps did she take to make this conversion? Why was this step necessary? (She found the LCM and used it as the denominator for both fractions. The LCM of 2 and 8 is 8. To change 1 ½ to 1 4/8 she changed the denominator to an 8 by multiplying 2 x 4 = 8. Then, she multiplied the numerator by the same number (1 x 4 = 4). Her new fraction is 4/8. She needed to do this, because in adding fractions or mixed numbers, you must have a common denominator.) (5) Stella solved the problem: Solve 2/3 x 4/6 and write your answer in simplest form. Her answer was 8/18. Is this the correct answer? Explain. (Stella’s answer is incorrect, because it is not in simplest form. Both 8 and 18 are divisible by 2.)

### Online Resources

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### Extra Help Problems

 (1) List the first five multiples of 12. (12, 24, 36, 48, 60) (2) Find the GCF of 12 and 15. (3) (3) What is the greatest common factor of 4, 10, and 20? (2) (4) Find the LCM of 12 and 15. (60) (5) What is the least common multiple of 4, 10, and 20? (20) (6) What is the greatest common divisor (GCD) of the terms of the fraction 12/22? (2) (7) What is the GCD of the terms of the fraction 20/140? (20) (8) Explain how to use the GCD of 32/48 to put the fraction in lowest terms. (divide both terms (numerator and denominator) by 16 to get 2/3) (9) One multiple of the number 4 is 20. knowing this, how can you write an equivalent fraction for ¾, using 20 as the denominator? (3/4 = 15/20, since 4 x 5 = 20, you need to multiply the numerator by 5. 3 x 5 = 15. (10) Choose a multiple of 6 to write an equivalent fraction for 4/6. (ex. 8/12) (11) What is the greatest common divisor of the fraction 24/96? (24) (12) Find the greatest common factor of 40 and 50. (10) (13) Find the greatest common factor of 8 and 42. (8) (14) Find the greatest common factor of 11 and 13. (1) (15) Find the greatest common factor of 123 and 18. (3) (16) Find the least common multiple of 32 and 16. (16) (17) If Juan is solving the math problem, 6/5 – 1/10, what does he need to do before he can begin subtracting? (He needs to make the denominators like. Since 10 is the LCM of 5 and 10, this will be the new denominator. He will need to change 6/5 into 12/10.) (18) Aidan needs to solve the addition problem 2-1/3 + 4/5. He knows that the LCM of 3 and 5 is 15. How will he use 15 to rewrite the problem before it can be solved? (He will make both denominators 15 and change the numerators of each fraction to match what he did on the bottom. The new fractions will be 2-5/15 + 12/15.) (19) Explain how to rewrite the subtraction problem to make like terms for the problem 1-9/12 – 4/8 and then solve. (Use the LCM of 24 to rewrite the denominators as like terms; 1-18/24 – 12/24.) (20) Kelly solved the multiplication 5/8 x 1/5. She found the answer 5/40. What is the GCD of these terms and how can Kelly use it to put the answer in simplest form? (Divide both the numerator and denominator by 5 to rewrite the fraction in simplest form as 1/8.) (21) Mr. Garcia wants to purchase packs of juice and snack cakes for the 6th grade social. The juices come in packs of 4 and the snack cakes come in packs of 8. He wants to buy equal amounts of juices and snack packs. What is the least number of packages of each that Mr. Garcia can buy. (8) (22) Water balloons come in packages of 50 and water guns come in packages of 4. Mrs. Jones Bill wants to have the same number of balloons and water guns for the end-of-year water fight. What is the least number of packages of balloons and water guns she needs to buy so that she has equal amounts of each? (100) (23) Enrique has to play soccer on August 7th and every seventh day after that. How many days will he play soccer in August? (4) (24) Hotdogs are sold in packages of 8 and buns are sold in packages of 12. What is the least number of hot dogs and buns that Luis can buy so that he has the same number of each? (24) (25) Stephanie has to baby-sit on June 1st and every 5th day after that. How many days will she baby-sit in June? (7)