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How to Divide Fractions

How to Divide Fractions

How to Divide Fractions

Fractions are not found only in school math books. Many careers use fractions on a daily basis. Food service professionals use fractions to help increase or decrease recipes to match larger or smaller groups. In the medical field, nurses, medical assistants and pharmacists use fractions especially when dealing with blood pressure and medications. Those who have careers in finance such as cashiers, counter clerks, accountants, and bookkeepers also use fractions in their daily lives. Architects, builders and construction workers depend on fractions for proper measurements and sizes. These and over one hundred other jobs according to xpmath.com, use fractions in their careers.

Yes, teachers try to convince students that the knowledge they are providing will be useful in life, but students still question that validity and always ask “How do I divide fractions?”. With fractions, the facts are there and learning how to divide fractions is also helpful.

Parts of Fractions

An understanding of the parts of fractions will help you when you are learning how to divide fractions. A fraction is a portion of a whole number. It is represented by a number over top of another number with a line separating the two. For example, ¼ is a fraction that can be spoken as “one over four”, “one-fourth” or “a quarter”. For division purposes, think of fractions simply in terms of their numbers. In this case, “one over four”.

The top number in a fraction is known as the numerator. The bottom number of a fraction is the denominator. The line itself is a representation of division. For example, ¼ is dividing one into four equal parts. If you think of this in terms of a dollar, you divide one dollar into four quarters, or into four equal parts of 25 cents.

Reciprocal

Also a help in dividing fractions is to understand the reciprocal of a fraction. A fraction’s reciprocal is the fraction written upside down. For example, the reciprocal of 2/3 is 3/2. You can double-check a number’s reciprocal by multiplying the fractions by each other. If you multiply 2/3 X 3/2 the answer is 6/6. 6/6 equals one. Reciprocal’s have a product of one. Another example, is 5/6 and 6/5. The product of these two fractions is 30/30 which is equal to one.

Dividing Fractions

The process of division is splitting a number into equal parts. If you use whole numbers, for example, 8 divided by 4 equals 2. You can split the number 8 into 4 equal groups of two parts. The same is true for fractions, but the process is different and can be simplified by remembering a few key phrases.

How Do You Divide Fractions

“Keep, Change, Flip” is one way to remember how to divide fractions.

  • Keep the first fraction the same
  • Change the division sign to a multiplication sign
  • Flip the second fraction into its reciprocal

For example, ½ divided by 1/6 becomes ½ times 6/1 (the reciprocal). Now, multiply the numerators by each other for an answer of 6. Then, multiply the denominators by each other for an answer of 2. Your fraction is now 6/2. Since, you can’t leave a larger number on the top of the fraction, simplify the answer by dividing 6 by 2 for an answer of 3.

Try another example. 1/3 divided by ¾ becomes 1/3 times 4/3. Multiply 1 and 4 for an answer of 4. Multiply 3 and 3 for an answer of 9. Your answer is 4/9. 4/9 cannot be simplified.

Mathisfun.com suggests a song to remember how to divide fractions.  If music helps you remember, try singing this song-

“Dividing fractions. As easy as Pie. Flip the second fraction. Then, multiply. And, don’t forget to simplify before it’s time to say goodbye.”

If “Keep. Change. Flip.” Doesn’t work for you. Maybe the words “Leave me. Change me. Turn me over.” Will help. Find whatever works for you to help you remember how to multiply and divide fractions.

Word Problems

A fraction division problem may not always be represented by a mathematical equation. You will find fraction division problems in word, story problems. For example, you have a piece of string that is ¾ yard long. You want to make kites that each have a 3/8 of a yard string tail. How many kites are you able to make from the string you have?

You need to divide your ¾ yard string by 3/8 yard pieces. To solve the problem keep the first fraction the same: ¾. Change the symbol X and flip the last 8/3. Your new mathematical problem now reads ¾ x 8/3. Multiply the numerators for an answer of 24. Multiply the denominators for an answer of 12. 24/12 is your fraction. Divide 24 by 12 for an answer of 2. You can make 2 kites with a 3/8 yard string tail from the string that you have available.

Remember the fraction that gets flipped, also known as inverted, or using the reciprocal is the one to the right of the division sign, or the second fraction.

How to Divide Fractions With Whole Numbers

The process for dividing fractions with whole numbers is the same as with mixed fractions. The only difference is you have to change the whole number into a fraction. You do this by placing the whole number over a number one in the denominator. For example, 5 becomes 5/1. This does not matter if the five is the first or second number in the problem.

  • For example 2/3 divided by 5 becomes 2/3 divided by 5/1.
  • Keep 2/3, change to multiplication and flip 1/5
  • Multiply the numerators- 2 x1= 2
  • Multiply the denominators- 3 x5= 15
  • The fraction is 2/15
  • It cannot be simplified

Try it with the whole number as the first number.

  • For example, 6 divided by 1/3.
  • Change the 6 into a fraction by placing it over 1- 6/1
  • Keep 6/1, change to multiplication and flip- 3/1
  • Multiply the numerators- 6 x3= 18
  • Multiply the denominators- 1×1=1
  • The fraction is 18/1
  • Simplified into 18

How to Divide Mixed Fractions

A mixed fraction is one that has a whole number and a fraction. For example 2 ¼ . If a math problems asks you to divide a mixed fraction- 2 ¼ divided by ¾, you must first change the mixed fraction into an improper fraction. An improper fraction has a larger numerator than denominator. You do this by multiplying the denominator by the whole number and adding the numerator to the result for the new numerator. You keep the original denominator. For example, 2 ¼ equals 4 times 2 (8), plus 1 for an answer of 9/4.

Then, you proceed with the “Keep. Change. Flip.” Process. 9/4 divided by ¾–

  • Keep 9/4, change to multiplication, flip 4/3
  • Multiply the numerators- 9 x4= 36
  • Multiply the denominators- 4 x 3= 12
  • The fraction is 36/12
  • Simplify the fraction by dividing 36 by 12 for a final answer of 3

Another example, with the mixed fraction as the second number is 4/5 divided by 1 2/8.

  • Change the mixed fraction into an improper fraction by multiplying 8 x1 and adding 2 for a result of 10/8
  • Keep 4/5, change to multiplication, flip 8/10
  • Multiply the numerators- 4 x8= 32
  • Multiply the denominators- 5 x10= 50
  • The fraction is 32/50
  • Reduce the fraction by dividing each number by 2 for a result of 16/25

Multiplication is the opposite of division and it is easier to multiply than it is to divide. When you change the second fraction into the reciprocal, you change the problem into multiplication to get the same result.

Dividing fractions requires memorization of your multiplication tables and a solid grasp of addition. Whether you are solving numerical problems or word problems, fraction division uses the same formula and with practice, you may find yourself pursuing a career that uses fraction division on a daily basis.

This is an important skill for school, college tests and even household tasks such as recipes and measurements for carpeting, wood, tile, etc. Once you learn how to divide a fraction, it is a skill you’ll keep forever and one that you’ll be proud you took the time to master.

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