· resolve application difficulties that require multiplication of fountain or blended numbers.

You are watching: Write the product as a mixed number


Just as you add, subtract, multiply, and divide as soon as working with totality numbers, you also use this operations once working through fractions. Over there are numerous times when it is crucial to main point fractions and also An expression in which a totality number is combined with a proper fraction. For instance 5

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is a mixed number.


")">mixed numbers
. Because that example, this recipe will make 4 crumb piecrusts:

5 cup graham crackers 8 T. Sugar

 cups melted butter  tsp. Vanilla

Suppose you only want to do 2 crumb piecrusts. You can multiply all the ingredient by , due to the fact that only fifty percent of the variety of piecrusts room needed. After ~ learning exactly how to multiply a portion by another fraction, a entirety number or a combined number, friend should have the ability to calculate the ingredients essential for 2 piecrusts.


When you main point a portion by a fraction, you room finding a “fraction of a fraction.” suppose you have actually  of a candy bar and you want to discover  of the :

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 By splitting each fourth in half, you can divide the candy bar right into eighths.

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Then, choose half of those to acquire

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.

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In both of the over cases, to discover the answer, you deserve to multiply the molecule together and also the platform together.

Multiplying two Fractions

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Example:

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Multiplying much more Than two Fractions

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Example:

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Example

Problem

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Multiply.

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Multiply the numerators and also multiply the denominators.

Simplify, if possible. This fraction is currently in shortest terms.

Answer


If the result The an outcome when two numbers are multiplied. Because that example, the product the 4 • 5 is 20.


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requirements to be simplified to shortest terms, divide the numerator and also denominator by usual factors.


Example

Problem

Multiply. Leveling the answer.

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Multiply the numerators and multiply the denominators.

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Simplify, if possible.

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Simplify by dividing the numerator and also denominator by the typical factor 2.

Answer

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Example

Problem

Multiply. Leveling the answer.

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Reorder the molecule so that you can see a fraction that has a common factor.

Simplify.

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Answer

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You perform not need to use the “simplify first” shortcut, however it might make your work easier since it keeps the number in the numerator and also denominator smaller while you room working through them.

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 Multiply. Simplify the answer.

A)

B)

C)

D)


A)

Incorrect.  is one equivalent portion to the exactly answer , however it is not in shortest terms. You have to divide numerator and also denominator through the common factor 3. The exactly answer is .

B)

Incorrect. You may have added numerators (3 + 1) and added denominators (4 + 3) instead of multiplying. The exactly answer is .

C)

Correct. One means to find this prize is to multiply numerators and also denominators

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, climate simplify:
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.

D)

Incorrect. You probably found a typical denominator, multiplied correctly, yet then forgot to simplify. Recognize a common denominator is no necessary and makes the multiplication harder due to the fact that you space working with better than essential numbers. The correct answer is .

Multiplying a fraction by a whole Number


When working through both fractions and whole numbers, the is advantageous to create the totality number as an improper fraction (a fraction where the molecule is higher than or same to the denominator). All totality numbers deserve to be written v a “1” in the denominator. Because that example:

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,
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, and
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. Remember the the denominator speak how many parts there space in one whole, and the molecule tells how many parts girlfriend have.

Multiplying a portion and a totality Number

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Example:

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Often when multiplying a whole number and also a fraction the result product will certainly be an not correct fraction. The is often preferable to compose improper fractions together a mixed number because that the last answer. You deserve to simplify the portion before or after rewriting together a blended number. See the instances below.


Example

Problem

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Multiply. Simplify the answer and write together a blended number.

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Rewrite 7 as the improper fraction

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.

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Multiply the numerators and also multiply the denominators.

Rewrite together a combined number.

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.

Answer

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Example

Problem

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Multiply. Leveling the answer and write as a combined number.

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Rewrite 4 as the improper fraction

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.

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Multiply the numerators and also multiply the denominators.

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Simplify.

Answer

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 3


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Multiply. Simplify the answer and also write it as a blended number.

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. You might have added numerators and added denominators, to gain

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, i m sorry is the mixed number . Make sure you multiply numerators and also multiply denominators. Multiplying the two numbers offers , and also since 15 ÷ 6 = 2R3, the mixed number is . The fractional part simplifies come . The exactly answer is .

B)

Correct. Multiply the 2 numbers provides , and also since 15 ÷ 6 = 2R3, the combined number is . The fractional component simplifies to .

C)

Incorrect. Multiplying the numerators and also multiplying the denominators outcomes in the improper portion , but you should express this together a blended number. The correct answer is .

D)

Incorrect. You might have added numerators and placed it end the denominator the 6. Make certain you multiply numerators and multiply denominators. Multiply the two numbers provides , and since 15 ÷ 6 = 2R3, the blended number is . The fractional component simplifies to . The exactly answer is .

Multiplying combined Numbers


If you desire to main point two combined numbers, or a fraction and a mixed number, you have the right to again rewrite any type of mixed number as an not correct fraction.

So, to multiply two mixed numbers, rewrite each as an improper fraction and climate multiply as usual. Main point numerators and also multiply denominators and simplify. And, as before, once simplifying, if the answer come out together an not correct fraction, then transform the answer to a combined number.


Example

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Problem

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Multiply. Leveling the answer and also write together a combined number.

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Change

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 to an not correct fraction. 5 • 2 + 1 = 11, and also the denominator is 5.

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Change

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 to an not correct fraction. 2 • 4 + 1 = 9, and also the denominator is 2.

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Rewrite the multiplication problem, using the not correct fractions.

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Multiply numerators and also multiply denominators.

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Write together a blended number.

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Answer

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Example

Problem

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Multiply. Leveling the answer and also write as a mixed number.

Change

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 to an not correct fraction. 3 • 3 + 1 = 10, and also the denominator is 3.

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Rewrite the multiplication problem, using the improper fraction in ar of the mixed number.

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Multiply numerators and multiply denominators.

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Rewrite together a mixed number.

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with a remainder that 4.

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Simplify the fractional part to lowest state by dividing the numerator and denominator through the typical factor 2.

Answer

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As you witnessed earlier, periodically it’s useful to look for common factors in the numerator and also denominator before you leveling the products.


Example

Problem

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Multiply. Simplify the answer and write together a blended number.

Change

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 to an improper fraction. 5 • 1 + 3 = 8, and also the denominator is 5.

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Change

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 to an not correct fraction. 4 • 2 + 1 = 9, and also the denominator is 4.

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*

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Rewrite the multiplication trouble using the wrong fractions.

Reorder the molecule so that you deserve to see a fraction that has a usual factor.

Simplify.

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Multiply.

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Write together a mixed fraction.

Answer

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In the critical example, the very same answer would certainly be found if you multiplied numerators and multiplied denominators without removing the common factor. However, girlfriend would obtain

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, and then friend would need to simplify an ext to get your last answer.

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 Multiply. Simplify the answer and also write together a combined number.

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. You more than likely wrote both combined numbers together improper fractions correctly. Girlfriend probably also correctly multiply numerators and also denominators. However, this improper portion still needs to be rewritten as a combined number and also simplified. Splitting 80 ÷15 = 5 v a remainder that 5 or , climate simplifying the fractional part, the exactly answer is .

B)

Incorrect. You most likely wrote both mixed numbers together improper fractions correctly. You probably likewise correctly multiplied numerators and denominators, and wrote the answer together a combined number. However, the blended number is no in lowest terms.

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 can be streamlined to  by separating numerator and denominator by the common factor 5. The exactly answer is .

C)

Incorrect. This is the an outcome of adding the two numbers. To multiply, rewrite each mixed number together an wrong fraction:  and . Next, multiply numerators and also multiply denominators: . Then, write the result improper fraction as a combined number: . Finally, leveling the fractional component by separating both numerator and denominator through the common factor, 5. The exactly answer is .

D)

Correct. First, rewrite each combined number as an not correct fraction:  and . Next, multiply numerators and multiply denominators: . Then compose as a mixed fraction . Finally, leveling the fractional part by separating both numerator and also denominator by the typical factor 5.

Solving difficulties by multiplying Fractions and Mixed Numbers


Now the you know how to main point a fraction by another fraction, by a whole number, or by a combined number, you can use this understanding to solve problems that involve multiplication and fractional amounts. For example, you can now calculate the ingredients essential for the 2 crumb piecrusts.


Example

Problem

5 cup graham crackers 8 T. Sugar

 cups melted butter  tsp. Vanilla

The recipe at left makes 4 piecrusts. Discover the ingredients needed to make only 2 piecrusts.

Since the recipe is for 4 piecrusts, you can multiply every of the ingredient by  to find the measurements for simply 2 piecrusts.

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 cups the graham crackers space needed.

5 cups graham crackers: due to the fact that the an outcome is an improper fraction, rewrite  as the improper portion .

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4 T. Sugar is needed.

8 T. Sugar:  This is an additional example of a totality number multiply by a fraction.

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 cup melted butter is needed.

 cups melted butter: You need to multiply a blended number through a fraction. So, an initial rewrite as the improper fraction

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: 2 • 1 + 1, and the denominator is 2. Then, rewrite the multiplication problem, using the improper portion in place of the blended number. Multiply.

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 tsp. Vanilla is needed.

 tsp. Vanilla: Here, you multiply a fraction by a fraction.

Answer

The ingredients essential for 2 pie crusts are: cups graham crackers

4 T. Sugar

 cup melted butter

 tsp. Vanilla


Often, a difficulty indicates the multiplication by a fraction is necessary by using phrases prefer “half of,” “a 3rd of,” or “

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 of.”


Example

Problem

The expense of a holidays is $4,500 and you are forced to salary

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 of that amount as soon as you make reservation the trip. Just how much will certainly you need to pay as soon as you reserve the trip?

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You require to uncover

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 of 4,500. “Of” speak you to multiply.

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Change 4,500 come an improper portion by rewriting it with 1 as the denominator.

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Divide.

900

Simplify.

Answer

You will need to pay $900 when you reserve the trip.


Example

Problem

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The pie graph at left represents the fractional component of daily activities.

Given a 24-hour day, how many hours space spent sleeping? Attending school? Eating? usage the pie chart to determine your answers.

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Sleeping is  of the pie, so the variety of hours spent resting is  of 24.

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Rewrite 24 as an improper portion with a denominator of 1.

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8 hrs sleeping

Multiply numerators and also multiply denominators. Leveling

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 to 8.

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Attending institution is  of the pie, for this reason the variety of hours spent attending school is  of 24.

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Rewrite 24 as an improper fraction with a denominator that 1.

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4 hrs attending school

Multiply numerators and also multiply denominators. Simplify

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 to 4.

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Eating is  of the pie, therefore the number of hours invested eating is  of 24.

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Rewrite 24 as an improper fraction with a denominator the 1.

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2 hrs spent eating

Multiply numerators and multiply denominators. Leveling

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 to 2.

Answer

Hours spent:

sleeping: 8 hours

attending school: 4 hours

eating: 2 hours


Neil purchase a dozen (12) eggs. He used  of the eggs for breakfast. How many eggs space left?

A) 8

B) 4

C) 9

D) 3


Show/Hide Answer

A) 8

Correct.  of 12 is 4 (

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), for this reason he supplied 4 of the eggs. Since 12 – 4 = 8, there space 8 eggs left.

B) 4

Incorrect.  of 12 is 4, but that gives how many eggs Neil used, not how numerous he had left. You must subtract 4 from 12 to uncover the variety of remaining eggs. The exactly answer is 8.

C) 9

Incorrect. Girlfriend may have actually incorrectly found  of 12 to be 3.  of 12 is 4, and then 12 – 4 is 8. The exactly answer is 8.

D) 3

Incorrect. You require to discover  of 12, which is 4. Then subtract 4 indigenous 12 to get 8 remaining eggs.

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Summary


You multiply 2 fractions by multiply the numerators and multiplying the denominators. Frequently the result product will not be in shortest terms, so girlfriend must likewise simplify. If one or both fractions are entirety numbers or combined numbers, first rewrite each together an improper fraction. Then multiply together usual, and simplify.