# 6th Grade - Explain How To Divide Fractions

 Grade Level: 6th Skill: Fractions, Decimals and Percentages Topic: Explain How to Divide Fractions Goal: Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5 - 8 anddivide; 15 - 16 = 5 - 8 x 16 - 15 = 2 - 3). Skill Description: Solve multiplication and division problems involving positive fractions and mixed numbers. Determine which operation to use to problem solve and follow through using appropriate steps to perform calculations. Explain how to perform multiplication and division of positive fractions calculations.

## Building Blocks/Prerequisites

### Sample Problems

 (1) 3/7 x 5/8 (15/56) (2) 9/12  4/5 (45/48) (3) Half of the children at Westmont School watch television every night. One-Third of those children watch for more than an hour. What fraction of the total children watch for more than an hour a night? (1/6) (4) A bottle holds 7 ½ ounces of liquid. Tom wants to fill the bottle up using its cap. The cap hold 1/3 an ounce of liquid. How many capfuls will fill the bottle? (22 ½) (5) 5-7/8 x 6-1/2 (3- 3/16)

### Online Resources

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### Extra Help Problems

 (1) 11/12 x 4/5 (11/15) (2) 6-2/3 x 4/9 (2-26/27) (3) 3 x 4-1/2 (13-1/2) (4) 16 x 7/10 (11-1/5) (5) 11-1/5 x 4-3/5 (51-13/25) (6) 9/16  11/8 (9/22) (7) 4/15  2/3 (2/5) (8) 14  1/3 (42) (9) 9  2-1/4 (4) (10) 6-1/3  9/10 (7-1/27) (11) 7-1/5  1-1/2 (4-4/5) (12) 1/3  11/6 (2/11) (13) 2-2/4 x ½ (5/4 = 1-1/4) (14) 16 9/12  6 1/3 (201/76 = 2-49/76) (15) A ribbon is 40 inches long. Stacy wants to cut the ribbon into pieces. Each piece will be ¾ of an inch. How many pieces can she get out of the ribbon? (53 pieces) (16) There are 8 puppies in a litter. Each puppy weighs 1 ¾ pounds. How much do all the puppies weigh together? (14 lbs) (17) During the 6th grade field day, Bryan’s long jump was measured at 12-1/2 feet. Jasmine’s jump was 1 1/3 times as far as Bryan’s. How far did Jasmin jump? (16-2/3) (18) Belen spent 1-1/2 hours doing her chores. Will spent 2-1/3 as many hours as Belen. How many hours did Will spend doing his chores? (3 ½ hours) (19) Evan has a plank that is 16- 1/2 feet long. He wants to cut it into pieces that measure ¾ of a foot. How many pieces will he get from the plank? (22 pieces) (20) Amy needs to solve the following problem: 3-1/8 x 12. Explain the steps she needs to use to rewrite and solve the problem. (First, Amy needs to make 3-1/8 an improper fraction by 8 x 3 +1 and then placing it over 8. The improper fraction will be 25/8. Then, she needs to write the fraction version of 12, 12/1. Lastly, she will multiply 25/8 x 12/1. She can cross cancel the 8 and 12 by dividing both by the GCF of 4. Her new fractions will be 25/2 x 3/1. Now, 25 x 3 = 75 and 2 x 1 = 2. So her final answer would be 75/2 or 37 1/2.) (21) Ty is working on the following problem: 8-3/4  11/12. Rewrite the problem and explain the steps he needs to use to solve it. (35/4 x 12/11. After changing the problem, Ty should cross cancel, using the 4 and 12, using the GCF of 4. 4 will become 1 and 12 will become 3. Next, he will multiply 35 x 3 and 1 x 11to get 105/11. He will then change the improper fraction into a mixed number by dividing. He will get 9-6/11.) (22) Lili worked out the problem 12  1/5. She got the answer 12/5 and simplified it. Her final answer is 2-2/5. Is she correct? If not, what does she need to do to fix the problem? (Her answer is not correct. She needed to multiply 12 by the reciprocal of 1/5.) (23) If a/b satisfies the equation 12  a/b = 6, then 6 x a/b = 12. Explain why this is true. (To solve a division equation, you can use the multiplicative inverse.) (24) If a/b satisfies the equation a/b x 2/3 = 115/230, then 115/230  a/b = 2/3. Explain why this is true. (The second problem is using the rule of the multiplicative inverse.) (25) If m/n satisfies the equation, m/n  30/40 = 12/16. Write a number sentence to solve this problem. (It is not necessary to solve for m/n.) (12/16 x 30/40 = m/n)