| Multiply. Simplify the answer and also write it as a blended number. A) B) C) D)
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A) Incorrect. You might have added numerators and added denominators, to gain , 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 | | Problem |
| Multiply. Leveling the answer and also write together a combined number. | |
| | Change to an not correct fraction. 5 • 2 + 1 = 11, and also the denominator is 5. | | | | Change to an not correct fraction. 2 • 4 + 1 = 9, and also the denominator is 2. | | | | Rewrite the multiplication problem, using the not correct fractions. | | | | Multiply numerators and also multiply denominators. | | | | Write together a blended number. | | Answer | | |
| Example | | Problem |
| Multiply. Leveling the answer and also write as a mixed number. | |
| | Change to an not correct fraction. 3 • 3 + 1 = 10, and also the denominator is 3. | | | | Rewrite the multiplication problem, using the improper fraction in ar of the mixed number. | | | | Multiply numerators and multiply denominators. | | | | Rewrite together a mixed number. with a remainder that 4. | | | | 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 |
| Multiply. Simplify the answer and write together a blended number. | |
| | Change to an improper fraction. 5 • 1 + 3 = 8, and also the denominator is 5. | | | | Change to an not correct fraction. 4 • 2 + 1 = 9, and also the denominator is 4. | | | | 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. | | | | Multiply. | | | | 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  | Multiply. Simplify the answer and also write together a combined number. A) B) C) D)
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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. 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 . | | | 4 T. Sugar is needed. | 8 T. Sugar: This is an additional example of a totality number multiply by a fraction. | | | 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 : 2 • 1 + 1, and the denominator is 2. Then, rewrite the multiplication problem, using the improper portion in place of the blended number. Multiply. | | | 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 “ of.”
| Example | | Problem | The expense of a holidays is $4,500 and you are forced to salary 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? | |
| | You require to uncover of 4,500. “Of” speak you to multiply. | | | | Change 4,500 come an improper portion by rewriting it with 1 as the denominator. | | | | Divide. | | | 900 | Simplify. | | Answer | You will need to pay $900 when you reserve the trip. |
| Example | | Problem |
| 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. | |
| | Sleeping is of the pie, so the variety of hours spent resting is of 24. | | | | Rewrite 24 as an improper portion with a denominator of 1. | | | 8 hrs sleeping | Multiply numerators and also multiply denominators. Leveling to 8. | | | | Attending institution is of the pie, for this reason the variety of hours spent attending school is of 24. | | | | Rewrite 24 as an improper fraction with a denominator that 1. | | | 4 hrs attending school | Multiply numerators and also multiply denominators. Simplify to 4. | | | | Eating is of the pie, therefore the number of hours invested eating is of 24. | | | | Rewrite 24 as an improper fraction with a denominator the 1. | | | 2 hrs spent eating | Multiply numerators and multiply denominators. Leveling 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
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A) 8 Correct. of 12 is 4 ( ), 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.
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