6th Grade - Explain How To Divide Fractions

Fractions, Decimals and Percentages
Explain How to Divide Fractions
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).
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.

Sample Problems


3/7 x 5/8



9/12 4/5



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?



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)


5-7/8 x 6-1/2

(3- 3/16)

Learning Tips


To multiply fractions you have two choices. First, you can multiply both numerators and both denominators and then simplify your answer. However, sometimes this will leave you with very large fractions to simplify. You can take a shortcut and cross cancel before multiplying across the numerators and denominators. In order to cross cancel, you’ll need to find the greatest common divisor of opposite numerators and denominators. If there is no common divisor, you cannot cross multiply. Let’s look at the problem 3/8 x 4/5. The opposite terms to compare across the diagonals are 3 with 5 (1st numerator with 2nd denominator) and 8 with 4 (1st denominator with 2nd numerator). When we look at 3 and 5 we can see that there is no common divisor because these are both prime numbers and 3 does not go into 5 evenly. However, when we look at 8 and 4 we know that there is a common devisor because 4 x 2 = 8. This means the greatest common divisor will be 4. Now, to cross cancel we simply divide both terms by 4 (8 4 = 2 and 4 4 = 1). You would show this work by going to the original problem, crossing off the old terms and writing in the new terms. So, the new problem becomes: 3/2 x 1/5. Now, you simply need to solve. Your answer will already be in simplest form.


To divide fractions you need to always multiply by the reciprocal of the second fraction. The reciprocal has the same terms, but in opposite places on the fraction. Let’s say we’re looking to find the reciprocal of ¾. Three is in the numerator, but when written as the reciprocal it will become the denominator and the four in the denominator becomes the number in the numerator. Hence, the reciprocal of ¾ is 4/3. Basically, the numbers trade places. Now, you’ll need to use this concept every time you divide fractions because dividing fractions is the same as multiplying by the reciprocal. So, ½ ¾ becomes ½ x 4/3. To complete the computation you now follow the steps to complete multiplication of fractions.


To multiply or divide mixed numbers you must convert them into improper fractions. You can convert a mixed number like 1-2/5 into an improper fraction by multiplying the denominator by the whole number, then adding the numerator to that product. The sum becomes your new numerator. So, 5x1=5 and 5+2=7, keep the denominator and the improper fraction is 7/5.


If you’re multiplying or dividing a whole number by a fraction, you need to write the whole number as a fraction. You do this by making the whole number your numerator and one your denominator. For example, the whole number 5 written in fraction form is 5/1. So, the problem 4/5 x 5 should be rewritten as 5/4 x 5/1.


It is important to always check that you’ve written your answer in simplest form. Remember, if both the numerator and denominator have a common devisor, your fraction is not in lowest terms. To reduce the fraction, you’ll need to divide both terms by the greatest common divisor. For example, in the fraction 4/16, both terms are divisible by 4. So, the reduced form of the fraction is ¼. Also, if the numerator is larger than the denominator, you have an improper fraction. Improper fractions must be made into mixed numbers to be considered simplified. To simplify any improper fraction, such as 10/3, you divide the numerator by the denominator (103) and write the answer showing the remainder (3 r 1). The first number is the whole number, the remainder is the numerator and the denominator stays the same. So, 10/3 = 3-1/3 in simplest form.


Here are a few tips for solving word problems. If you know how many parts and how much in each, multiply. Also, if the problem used the word “of”, multiply. If you know the total and the number of parts, or you know the total and the amount in each, divide.

Extra Help Problems


11/12 x 4/5



6-2/3 x 4/9



3 x 4-1/2



16 x 7/10



11-1/5 x 4-3/5



9/16 11/8



4/15 2/3



14 1/3



9 2-1/4



6-1/3 9/10



7-1/5 1-1/2



1/3 11/6



2-2/4 x ½

(5/4 = 1-1/4)


16 9/12 6 1/3

(201/76 = 2-49/76)


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)


There are 8 puppies in a litter. Each puppy weighs 1 ¾ pounds. How much do all the puppies weigh together?

(14 lbs)


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?



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)


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)


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.)


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.)


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.)


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.)


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.)


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)


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