Dividing Whole Numbers And Fractions

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Need to larn how to multiply fractions with whole numbers? Or how to divide fractions by whole numbers? The process is probably easier than you call up! We break downwardly the 4 simple steps to follow for multiplying fractions by whole numbers, too as the one extra step to divide fractions and whole numbers. Acquire this of import math skill, then test your knowledge by taking our quiz at the cease of this guide.

How to Multiply Fractions With Whole Numbers: 4 Steps

Multiplying fractions past whole numbers can seem intimidating, but the process is actually quite elementary: but four steps to follow. Nosotros walk you through each of the steps with our starting time sample question, and so provide 2 additional examples so you'll accept a solid grasp on how to multiply fractions with whole numbers.

Sample Question 1: ⅜ x half dozen

Step one: Turn the Whole Number Into a Fraction

Your first step is turning the whole number into its own fraction. This is easy: yous just requite it a denominator of i. And so, from our example, six becomes ⁶ /₁ . This is true because 6 divided into i group withal equals 6. This is true for any whole number: three = ⁱⁱⁱ /₁ , 17 =¹⁷ /₁ , etc.

At present we have ⅜ x ^{half dozen} /_i

Step 2: Multiply the Numerators

Next, we multiply the two numerators (the top number in a fraction).

3 10 6 = 18, so now we accept the numerator for our respond: ¹⁸ /__

Step iii: Multiply the Denominators

Now multiply the two denominators (the bottom number in a fraction). When you lot're multiplying a fraction with a whole number, this volition exist easy because you're just multiplying by 1.

8 x 1 = 8.

Add it to our reply to become: ^eighteen /8. There we get!

Step 4: Simplify

But we're non done even so. It might exist possible to simplify the fraction. The simplest course of the fraction is when the top and bottom of the fraction are the smallest whole numbers they can be. For example, the fraction ¹⁸ /8 isn't in its simplest class because it can withal be reduced downwards to ⁹ /four by dividing both the top and bottom of the fraction by 2.

⁹ /4 is the fraction in its simplest class, but you lot may prefer to change information technology into a mixed number since ⁹ /four is greater than 1.

4 goes into ix twice, with a remainder of i, and then the reply can also be written as two ¼.

You might as well want to give the answer equally a decimal. Nosotros have an unabridged guide on converting fractions to decimals (besides as the other style around), but here's how to do this 1 simply. The 2 remains the same, since it's a whole number. You probably already know that ¼ is equal to 0.25, so that becomes the value on the right side of the decimal, for a final answer of 2.25.

Sample Question ii: iv ten ⅖

Step 1: ⁴ /one x ⅖

Step 2: iv x 2 = 8

Step 3: 5 ten i = five

Step iv: Our answer, ⁸ /five , tin't be simplified any farther as an improper fraction (where the numerator is larger than the denominator), simply it can exist converted into a mixed number. 5 goes into eight once, with 3 remaining, so the mixed number answer is 1 ⅗.

To convert ⅗ into a decimal, first we want to get the denominator to a value of ten. To do this, just multiply both parts of the fraction by 2, getting ⁶ /10. Now we want to become the denominator to equal 1 to get rid of the fraction so we divide each part of the fraction by ten. That gives the states ^.6 /1, which is also equal to just .6. Combine that with the whole number (i) from the answer, and your final answer in decimal form is one.vi.

Sample Question 3: 5 ten ii ³ /seven

Step i: The fraction is in the grade of a mixed number, so showtime nosotros demand to catechumen it to an improper fraction. Call up, when adding or subtracting fractions, the denominators must be the aforementioned. To get the whole number ii to have the same denominator, make it into a fraction, ² /1, then multiply the superlative and bottom by seven. You lot'll go ^xiv /7 which, when added to ³ /7, is ¹⁷ /7. Make the 5 a fraction, too. Now nosotros accept: ⁵ /1 x¹⁷ /7

Footstep 2: 5 x 17 = 85

Step iii: 7 x 1 = 7

Step 4: Now we take ⁸⁵ /7. Information technology can't be simplified, but it tin exist made into a mixed number. 7 goes into 85 twelve times, with a remainder of 1. Our final answer is 12 ⁱ /seven, or 12.fourteen in decimal grade.

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5 Steps to Dividing Fractions by Whole Numbers (and Vice Versa)

Dividing ii fractions is the aforementioned as multiplying by the second fraction's reciprocal. This means that, in one case y'all've mastered multiplying fractions by whole numbers, you pretty much know how to carve up fractions by whole numbers!

Below we walk you through the steps and explicate two examples, one where y'all separate a fraction by a whole number (using the same values as case #i above), and another where you divide a whole number by a fraction.

Sample Question four: ⅜ / vi

Step 1: Turn the Whole Number Into a Fraction

Only equally we did when nosotros went over multiplying fractions past whole numbers, turn 6 into a fraction past adding a 1 to the denominator: ⁶ /1

Step 2: Flip the 2d Number

This is the actress step that's needed for dividing fractions. Right now we have ⅜ / ⁶ /one. Flip the second number, and change the division sign to a multiplication sign: ⅜ x ⅙

Once you practise that, you work through the problem only every bit you did with the examples above.

Stride 3: Multiply Numerators

3 10 1 = 3

Step 4: Multiply Denominators

8 ten half-dozen = 48

That gives u.s. ³ /48

Step 5: Simplify

Don't forget to simplify! We can divide both the numerator and denominator by 3, which gives us a final answer of ^ane /xvi or 0.0625.

Sample Question 5: 4 / ⅖

Step 1: ⁴ /1 / ⅖

Step 2: ⁴ /1 10 ⁵ /2

Step 3: 4 x v = xx

Step four: i x 2 = 2

Step 5: ²⁰ /ii simplifies to 10!

3 Tips for Avoiding Mistakes

Now y'all know the basic steps for how to multiply fractions with whole numbers as well as how to divide fractions with whole numbers, only it's withal possible to make devil-may-care errors when working through these problems, fifty-fifty if you understand the concepts well. Reduce your chances of making a mistake past following these three tips.

#one: Know Whether to Expect a Big or Small Number

1 of the all-time means to check for and avoid silly mistakes is to quickly know if your answer is mode off from what you expected. When you split up or multiply fractions and whole numbers, there are sure patterns you can look.

Answer will likely exist > 1

Fraction multiplied by a whole number
Whole number multiplied by a fraction
Whole number divided by a fraction

Reply volition likely be < 1

Fraction divided by a whole number

At present, evidently, knowing this fox won't just requite you the right answer, but if you're working through a problem similar ⅖ / four and you lot get a number greater than 1, yous can be pretty certain you should become back and recheck your work.

#2: Keep Numerators and Denominators Organized

Information technology can exist easy to get numerators and denominators dislocated, specially when division is involved and y'all're flipping fractions. Most mistakes are made when people multiply the wrong numbers or put a numerator answer in the denominator spot (or vice versa).

Avoid this by keeping your work neat and ever making it clear what are numerators and what are denominators. For example, after yous multiply the numerators, add a dash under your respond (like ⁴ /___)so yous remember what you just solved for and that the next value you solve for volition exist the denominator.

#three: E'er Make Certain to Simplify

As before long as you finish the multiplication and write your answer downwards, you might be tempted to move correct on to the adjacent question. Spend an actress few seconds seeing if your answer can be simplified though. Some teachers volition take points off for right, but non-simplified answers, and yous definitely don't want to get deductions after yous've washed all the work right! Simplify as far equally y'all tin can and, if your fraction's value is greater than 1, convert it to a mixed number if that's what your instructor prefers (some take different preferences, and so ask to make sure you're doing all the steps you lot need to).

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Quiz: Dividing and Multiplying Fractions by Whole Numbers

Fix to test your noesis of how to multiply fractions with whole numbers? In this section are ten questions. For each, you'll be multiplying fractions past whole numbers or dividing fractions by whole numbers. Give them a try, so check your answers with the key beneath.

#1: 5 x ⁴ /3

#ii: ⁱⁱ /9 x xi

#3: 12 x ⅕

#iv: ½ / 3

#5: ⁴ /ix x vii

#half-dozen: ⅞ x 2

#7: 8 / ⅔

#eight: ^five /12 ten 5

#ix: 5 / ^four /vii

#x: ⁴ /xv x 9

Answer Central

#1: 6 ⅔
#ii: 2 ⁴ /9
#3: 2 ⅖
#iv: ⅙
#5: 3 ¹ /nine
#6: 1 ¾
#7: 12
#eight: 2 ^ane /12
#9: eight ¾
#10: 2 ^{half dozen} /15

What'southward Side by side?

Desire to acquire more about decimals, fractions, and percentages? Check out The iii Steps to Catechumen Decimals to Fractions (and Back)

f you're unsure what high school math classes y'all should be taking, this guide volition aid you figure out your schedule to exist certain yous're prepare for college!

Now that you're an skillful in multiplying and dividing fractions, challenge yourself by learning how to catechumen Celsius to Fahrenheit!

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About the Author

Christine graduated from Michigan State University with degrees in Environmental Biological science and Geography and received her Master'south from Duke Academy. In loftier school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.