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# How to divide an improper fraction by a whole number

### How to turn improper fractions into whole numbers

• ator. Divide 402 by 11, which equals 36 with a remainder of 6. Find the whole number
• Dividing Fractions By Whole Numbers Multiply the bottom number of the fraction by the whole number. To Divide a Fraction by a Whole Number: Step 1
• This video will show you how to convert an improper fraction into a mixed number. Please check our website for more videos and articlesThanks for learning!!w..
• This video explains how to divide a whole number by a fraction. It contains plenty of examples and practice problems.My Website: https://www.video-tutor.ne..
• ators of each fraction by each other (the numbers on the bottom). The result is the deno

Multiply the whole number by the denominator, an add the result to the fraction's numerator to get the new numerator. 4 + 5/3 is 4*3 = 12, 12 + 5 = 17, so 17/3. Do the same thing on a calculator if you want the answer as a decimal. 158 view Dividing Mixed Fraction with a Whole Number To divide the given mixed fractions with a whole number initially, we need to convert the given mixed fraction to a normal fraction (improper fraction), by doing this we can solve the given problem with the same method we used for solving division problems on fraction with the whole number The standard way of dividing a whole number by a fraction is to multiply the whole number by the reciprocal of the fraction. You can also draw a diagram to help you visualize the process. Method 1 Multiplying by the Reciproca Proper and Improper Fractions: A fraction is a number representing a part of a whole.The whole may be a single object or a group of objects. The fraction representing four parts out of $$9$$ equal parts in which the whole is divided can be denoted by $$\frac{4}{9}$$

### Dividing Fractions By Whole Numbers - Math is Fu

1. ator. Then take that value and add it to your numerator. 2 ½ changes to ⁵⁄₂. Example 1
2. ator. If there is no remainder, then your answer is a whole number rather than a mixed number, and you need not do anything further. Likely, though, you will have a remainder. Set this aside for now
3. ator goes into the numerator. 437 61428571428571 6. 7 quotient — 539 35 — 4 re
4. Dividing Fraction by a Fraction Refer to the Procedure of dividing fractions by converting them into a multiplication of fractions. The procedure is as follows Write the Reciprocal of Second Fraction and then multiply with the first fraction number

Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6 by 3, 6 ÷3 = 2 Also, how do you convert an improper fraction into a mixed number? Example: replace the incorrect fraction 402/11 with a mixed number. Divide the numerator by the denominator. Divide 402 by 11, which gives 36 with the remainder of 6. Find the whole number. The integer is the number of times the denominator is divided by the numerator. Make the.

### How to divide an improper fraction? - YouTub

• ator. The rest of the steps will be the same. Welcome to Kate's Math Lessons! Teachers,make sure to check out the study guides and activities. Boom Cards
• You can divide a whole number by a fraction simply by inverting (turning upside down) the divisor, in this case, the fraction, and then multiplying as you would if you were dividing two fractions such as 2/3 divided by 1/3. EXAMPLE: Divide the who..
• How to change a mixed number to an improper fraction. Sometimes we need to change a mixed number to an improper fraction (for example, before we do multiplying or dividing of fractions. Let's start with 3 and 4/5 - now we have 3 whole cakes, and 4 slices of the cake, divided into fifths
• ator (bottom part). The quotient is the whole number, and the remainder is the numerator. Let's go through some examples to understand the concept better
• ator into the numerator. Identify the quotient, remainder, and divisor. Write the mixed number as quotient remainder divisor remainder divisor

Step 1: Divide the numerator (39) by the denominator (5): 7 ← quotient -- 5)39 35 -- 4 ← reminder. Step 2: Build your answer using the quotient (7) as the whole number and the remainder (4) as the numerator, keeping the same denominator (5). Thus, The improper fraction 39 5 is equivalent to 7 4 5 as a mixed number in its simplest form First step: Write the whole number and the mixed number as improper fractions. Second step: Write the reciprocal of the divisor, 2/5, and multiply. Third step: Simplify, if possible. Notice that we can simplify our problem at this step, to make our calculations easier. Five goes evenly into 30, so we can divide both 5 and 30 by 5, to give 1 and 6 Answers to Dividing Mixed Numbers 1 31 45 2 4 5 81 3 1 19 33 4 5 32 5 3. Convert the mixed number to an improper fraction. Divide Mixed Number Fractions 1 Math Fractions Worksheets Fractions Mixed Numbers Dividing mixed numbers by fractions whole number quotients Below are six versions of our grade [

Example: Convert the following mixed number to an improper fraction. 3 5 9. Step 1: Multiply the denominator (the bottom number in the fraction) and the whole number. 9 × 3 = 27. Step 2: Add the answer from Step 1 to the numerator (the top number in the fraction) 27 + 5 = 32. Step 3: Write answer from Step 2 over the denominator To do this, just multiply both parts of the fraction by 2, getting 6/10. Now we want to get the denominator to equal 1 to get rid of the fraction so we divide each part of the fraction by 10. That gives us .6/1, which is also equal to just .6. Combine that with the whole number (1) from the answer, and your final answer in decimal form is 1.6

### How To Divide a Whole Number by a Fraction - YouTub

Another way to convert an improper fraction is to find how many whole numbers you get, by using a division. For example let's convert $$\frac{17}{5}$$ to a mixed number again. We start by dividing. Adding and subtracting mixed numbers. 7. Multiplying fractions and whole numbers. 8. Dividing fractions with whole numbers. 9. Multiplying proper fractions. 10. Multiplying improper fractions and mixed numbers. 11. Dividing fractions and mixed numbers. 12. Applications of fraction operations. Back to Course Inde To divide improper fractions, we use the same rule as we do to divide any fractions, and that is as follows: which is used to show part of a whole number. While having fun with some real-life.

### How do you multiply and divide improper fractions

Improper Fractions to Mixed Fractions. To convert an improper fraction to a mixed fraction divide the denominator by the numerator. The quotient becomes the whole number, the remainder will be the numerator, and the divisor becomes the denominator. Let us consider an example. Convert $$\frac{17}{4}$$ to a mixed fraction - 2 - DIVIDING A FRACTION BY A WHOLE NUMBER Step 1: Write the whole number as a fraction with 1 as the denominator. y 5 2 4 1 4 5 2 y Step 2: Re-write as a multiplication problem by inverting the second fraction. 4 1 5 2 u Step 3: Cross cancel if you can. 1 4 1 5 2 u 2 Step 4: Multiply the numerators. Multiply the denominators. 2 1 5 1 u = 10 1 Step 5: Write the answer in simplest form Simplify Fraction 1: Our first fraction is a mixed number, so we'll convert it to an improper fraction. If you're not sure how, check out this guide. 3 5 2 = ( 3 + 5 2 ) = 5 1 5 + 5 2 = 5 1 7 Simplify Fraction 2: Our second fraction doesn't have whole numbers, but we can reduce it a little by dividing the top and bottom by the same number. 6 2. To divide fractions, you need to invert the divisor and multiply. To invert a fraction, reverse the numerator and denominator. The special name given to an inverted fraction is reciprocal. Recall that a whole number has a understood denominator of 1. Read this lesson on dividing fractions if you need help on how to divide fractions Frazer says To divide a whole numbers (integers) by a fraction follow these 4 easy steps. Step 1 • Change the integer, or whole number, into a fraction by putting it over a denominator of 1. • Convert any mixed fractions into improper fractions. Step 2 • Swap the numerator and denominator the the dividend fraction, and then change th

### How to convert improper fractions into a whole number - Quor

number to an improper fraction is to multiply the bottom number by the regular number, add in the top number, and then put this on top of the original bottom number as a new fraction. For instance, to convert 11/2 to an improper fraction, you do the following: I multiplied the bottom 2 by the regular 1, and then added in the 1 from on top Math. When you divide a proper fraction by an improper fraction, is the quotient less than 1,greater than 1,or equal to 1? I think it is less than one but I'm not sure . math. write each mixed number as an improper fraction 1 7/8 . Business Math. Convert the following mixed number to an improper fraction: 12 3/ Description. This calculator divides two fractions. It accepts proper, improper, mixed fractions and whole number inputs. If they exist, the solutions and answers are provided in simplified, mixed and whole formats. There general steps to divide fractions are described below. If the inputs are mixed fractions or whole numbers, convert them to. Division of the fractions is converted into a multiplication operation by multiplying the improper fraction with the reciprocal of the whole number. The resulting fraction, if required, is written as a mixed number in simplest form Take the reciprocal of the unit fraction and multiply the whole number you've got with the given whole number for the quotient. Switch up a gear with this bunch of printable worksheets on dividing fractions and whole numbers for grade 5 and grade 6 and interpret dividing proper fractions and improper fractions by whole numbers

### Division of Fraction by a Whole Number - Definition

Then, divide each improper fraction by 2 to find the center of the plate. Finally, convert each improper fraction to a mixed number: Therefore, the distance to the center of the hole from each of the plate edges is 2 23/32 inches and 113/16 inches. Reducing Fractions A fraction needs to be reduced when it is not in lowest terms Examples of Converting Improper Fractions to Mixed Numbers. To write an improper fraction as a mixed number, divide the numerator by the denominator. Write the whole number part down and write any remainders as the numerator of the fraction. The denominator is the same as the denominator of the improper fraction. For example, here is 5 / 2 You can always turn an improper fraction into a mixed number. ������. ������ To turn an improper fraction into a mixed numbe r, divide the numerator by the denominator. 11 ÷ 4 = mixed number. ������ The whole number quotient is the whole number. ������ The remainder is the numerator for the fraction. ������ Then, just copy the denominator of the. Before you tackle this, you need to know about multiplying fractions. Frazer says To divide a fraction by an integer, or whole number, follow these 4 easy steps. Step 1 • Change the integer, or whole number, into a fraction by putting it over a denominator of 1. • Convert any mixed fractions into improper fractions. Step To divide fractions with mixed numbers, the following steps are used: Step 1: Keep the fraction as it is. Step 2: Convert the mixed number into a proper or improper fraction and flip the second fraction. Step 3: Change the sign into multiplication between the fractions, multiply and simplify them

### 3 Ways to Divide a Whole Number by a Fraction - wikiHo

Decompose Fractions, Fractional division Improper Fraction: the numerator is larger than the denominator Mixed number: a combination of a whole number and a fraction Designed for fourth through sixth grade, but can be used with third graders Using: Bar Models Decomposition/ Recomposition Fractional Division/ Common Denominator Traditional. When converting from a Mixed Number to an Improper Fraction: Multiply the integer by the denominator and add the numerator to get the new numerator. Keep the denominator the same. Example: 2 1 3 = ( 2 1 × 3 3) + 1 3 = 2 × 3 3 + 1 3 = 6 3 + 1 3 = 7 3. When converting from an improper Fraction to a Mixed Number: Divide the numerator by the. What about division with fractions and whole numbers? Make the whole number a fraction, by putting it over 1. Example: 5 is also 5 1. Then continue as before. Example: 2 3 ÷ 5. Make 5 into 5 1: 2 3 ÷ 5 1. Then continue as before. Step 1. Turn the second fraction upside down (the reciprocal)

### Proper and Improper Fractions: Definition, Properties

1. ator into the numerator. Step 2: The quotient is the whole number part of the mixed number. Step 3: The remainder is the numerator of the fractional part of the mixed number. Step 4: The divisor is the deno
2. Now you can watch worked examples of how to convert an improper fraction to a mixed number in the following video. In an earlier example, we changed $1{\Large\frac{4}{5}}$ to an improper fraction by first seeing that the whole is a set of five fifths
3. ator. Like. So, let's see what this means. Let's looks at a hexagon... That's 7 pieces... Hey, this is just
4. ator of 1; for example, 2 = 2 1 . Zero can be written as a fraction using zero as the numerator and any whole number as the deno
5. It is initially an improper fraction, which then broken down into a mixed number form. Division of mixed numbers is very similar to the multiplication of the mixed numbers. Here are the steps followed when dividing mixed numbers: Begin by converting each mixed fraction to an improper. Invert or flip upside down the improper fraction that is the.
6. ator by 2
7. ator. Write down the whole number result. Use the remainder as the new numerator over the deno Fraction worksheets: completing a whole number. Below are six versions of our grade 3 math worksheet on completing a whole number with an improper fractions; students must find the improper fraction missing from the addition equation with whole number sum. These worksheets are pdf files Convert $28 %$ into a decimal number. To divide fractions by fractions, start by replacing the division sign with a multiplication sign. Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros); Write 7/8 as a decimal. It does go into 63 The easiest way to change a whole number, other than zero (0), into an improper fraction is to place the nonzero whole number over 1, i.e., the nonzero whole number is the numerator and one (1) is the denominator, as follows: a = a/1, where a is a.. When dividing, you simply flip the second fraction over and multiply straight across like normal. When multiplying a whole number and mixed number, simply put the whole number over one. Then, convert the mixed number into an improper fraction. Then, multiply the mixed number with the numerator and add in the denominator

Changing Improper Fractions to Mixed Numbers. The worksheet has 12 questions with improper fractions needing to be converted into mixed numerals. Working out space is provided for students to write the division number sentence associated with changing the improper fraction to the mixed numeral. An answer sheet is included in the download The fraction cannot be reduced (simplified): irreducible fraction. Fraction 13/5 is a positive improper fraction (numerator > denominator). Rewrite the fraction: As a mixed number (also called a mixed fraction): Mixed number = a whole number and a proper fraction, of the same sign We call the line that separates 13 and 6 the division line. It is also known as the fraction bar or vinculum. 13/6 is an improper fraction because the numerator is greater than the denominator. A mixed number is an integer (whole number) and a proper fraction In an improper fraction, the numerator is greater than the denominator. They are called improper because if we illustrate the fraction on model, the number of shaded parts will be more than the total parts which is not practically possible. We can not distribute something in 13 parts if there are only 10 total parts. Example An improper fraction is a fraction that has a larger numerator than denominator. The numerator is the number on top in a fraction. The denominator is the number on bottom. To convert the improper fraction to a mixed number, you will take the numerator and divide it by denominator. In this example you will take 13 and divide it by 4

### How to divide fractions: 3 easy steps to solve hard

• To divide mixed fractions, you could first convert each to an improper fraction. Then, switch to a multiplication problem by multiply by the reciprocal of the divisor. Simplify and convert your answer back to a mixed fraction to get your answer! This tutorial will show you how
• ator of the mixed fraction and writes it beside and keeps adding it self to the latest number and he keeps on doing that way generating a series until he reaches the value of the numerator. Now he counts the number of occurrences of the numbers in the series.
• Mixed Numbers Calculator (also referred to as Mixed Fractions): This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists
• ator of 1. Step 2 Swap the numerator and deno
• ator of the given fraction by the same number. Example: Find the two fractions equivalent to 5/7. Solution: Equivalent Fraction 1: 5/7= 5/7 x 2/2 = 10/14. Equivalent Fraction 2: 5/7 = 5/7 x 3/3 = 15/21

### How to Divide Mixed Fractions: 12 Steps (with Pictures

• ator. 4 ÷ 2 = 2. So the answer is 2/7
• ator.The notation means that we break an object into b equal pieces and we have a of those pieces
• An improper fraction and a mixed number will represent the same amount, but simply be written in a different form. Let's try a few more examples. Let's write the following improper fractions as mixed numbers: 4/3 3/2 7/4. 4/3 can be visualized as 1⁄3 + 1⁄3 + 1⁄3 + 1⁄3. We know that 3/3 is equal to 1, so....

An improper fraction is defined as a fraction whose numerator (top number) is greater than or equal to the denominator (bottom number). This is also called being top-heavy. An improper fraction is most often turned into a mixed number with a remainder, but some fractions can be turned into whole numbers An improper fraction has the top number ( numerator ) equal to or larger than the bottom number ( denominator ) such as 100 / 50 . So divide the bottom number into the top number to get a whole. Divide 3 1/2 by 8 = (7/2) / 8 = 7/ (2×8) = 7/16. For dividing a whole number by a fraction, (If we are dividing by a mixed number, first convert it into improper fraction) multiply the denominator of the fraction by the whole number. This will give the numerator of the answer. Numerator of the fraction becomes denominator Dividing Fractions with Whole and Mixed Numbers 2 - Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too Then write this sum over the denominator. * = 2 x 2 + 1 2 = 2 2 2 * 2 * To express an improper fraction as a mixed number, divide the denominator into the numerator. * = 2 -6 2 2 3 3 2 3 * Express the mixed number as an improper fraction. = 3 x 5 + 1 5 = * Express the mixed number as an improper fraction. = 5 x 9 + 8 9 = * Express the improper.

1. Change the mixed number into an improper fraction by multiplying the denominator by the whole number. Then add the numerator in. Your denominator stays the same. 2. Find a common denominator. 3. Whatever you do to the bottom, you do to the top. (or cross multiply to find the new numerators) 4 Converting improper fractions to mixed numbers • While improper fractions are good for calculations, they are rarely used in everyday situations. For example, people do not wear a size . 23 2. shoe. • To convert to an improper fraction we need to work out how many whole numbers we have. • Let's use the example from the previous section

An improper fraction is a fraction where the numerator is greater than the denominator.. A mixed number is a number that consists of a whole number and proper fraction.For example, $1\frac{1}{2}$ is a mixed number. Rules to write an improper fraction as a mixed number. To write an improper fraction as a mixed number, we rewrite it as a division problem and divide In this video tutorial the instructor shows how to convert mixed numbers to improper fractions. The instructor gives a two step approach where in the first step he tells you to multiply the denominator with the whole number and add this result to the numerator. Now in the second and final step the previously obtained result is placed in the numerator with the original denominator giving you. divide simplify the answer and write as a mixed number and we have two and one-fourth divided by one and three-fourths so the first thing we want to do since both of these are mixed numbers is to convert them both into improper fractions so let's start with two and one-fourth so we're still going to have four in the denominator but instead of two and one-fourth remember two is the same thing.

A mixed number is composed of a whole number and a fraction. 6 2/3, 18 5/4, and 2 2/5 are all mixed numbers. Converting Improper Fractions Into Mixed Numbers Improper fractions can also be represented as a mixed number. To convert an improper fraction into a mixed number, divide the numerator by the denominator. The resultant becomes the whole. Mixed numbers and improper fractions in Year 5. When you have a whole number and a fraction side by side, like 1 ½ , it's called a mixed number. You can convert this into a fraction, but the numerator will be bigger than the denominator. In this case 3 / 2. This is called an improper fraction (you may also hear it being called a top-heavy. as an improper fraction. The numerator is . 4 • 5 + 1 = 21. Answer. 4 21. Find the reciprocal by interchanging (flipping) the numerator and denominator. Self Check A What is the reciprocal of 2 3 5? Dividing a Fraction or a Mixed Number by a Whole Number Objective . When you divide by a whole number, you multiply by the reciprocal of. As an improper fraction (numerator larger than denominator): 28,717 / 32 = 28,717 / 32 As a mixed number (mixed fraction) (a whole number and a proper fraction, of the same sign): 28,717 / 32 = 897 13 / 32 As a decimal number: 28,717 / 32 = 897.40625 ≈ 897.41 As a percentage: 28,717 / 32 ≈ 89,740.63% More operations of this kind

Whole Numbers Estimating Sums, Differences, Products, and Quotients Quiz: Multiplying and Dividing Fractions and Mixed Numbers; Simplifying Fractions and Complex Fractions; Quiz: Proper and Improper Fractions, Mixed Numbers, and Renaming Fractions Previous Renaming Fractions Multiply the whole number part by the fraction's denominator. Add that to the numerator. Then write the result on top of the denominator. Accordingly, the question is what is 1 and 2/3 as an improper fraction? The mixed number 1 2/3 is 5/3 as an improper fraction. In the same vein people ask what is 2 and 3/4 as an improper fraction

At the end of the lesson, students explain how to convert mixed numbers to improper fractions. I listen for terms like numerator, denominator, whole, part, improper fraction, and mixed number. Note: Many students, by the end of this lesson, have discovered shortcuts for converting mixed numbers to improper fractions Example 2: change an improper fraction to a mixed number. Write the following improper fraction as a mixed number: 17 5 17 5. Work out how many times the denominator divides into the numerator. Show step. The denominator of the fraction is 5 and the numerator of the fraction is 17. 5 divides into 17 three times 3) Divide both the numerator and the denominator of the fraction by the greatest common factor, GCF (GCD). In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms. A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction DIVIDING FRACTIONS BY WHOLE NUMBERS SHEET 1 To divide a fraction by a whole number, follow these 3 simple steps: • Change the whole number into a fraction by putting it over a denominator of 1. • Invert this divisor fraction (swap the numerator and denominator of the second fraction) and change the division operator to a multiplication. For converting mixed numbers to improper fractions, multiply the whole number and denominator and add it to the numerator. This will be the numerator of the improper fraction. For eg. 5 3/4 = (5 x 4 + 3)/4 = 23/4. For converting improper fraction to mixed number (or mixed fraction), divide the numerator by denominator ### How To Turn A Mixed Number Into An Improper Fractio

1. ator is not necessary) First multiply the numerators. Then multiply the deno
2. An online mixed number calculator is a free and best tool that allows you to add, subtract, multiply, and divide the mixed number fraction. In simple terms, this fraction and whole number calculator allows you to solve fraction problems with whole numbers and fractions form
3. ator, 5. ������ Mixed Number - has a mix of a whole number and a fraction. For example, 3 2/7 is a mixed number because it has a whole number, 3, and a fraction 2/7
4. ator. The whole number is 5. The deno
5. ator. Such fractions are called improper fractions
6. Learners will apply previous understanding of finding equivalent fractions, and converting between fractions and mixed numbers to work with fractions in more complex ways. Students will continue to use visual models to learn and practice adding, subtracting, multiplying and dividing fractions

### Dividing Fractions Definition, Examples How to Divide

1. PROPER FRACTIONS, MIXED NUMBERS, IMPROPER FRACTIONS. PROBLEMS. Return to the Lesson. Change each improper fraction to a mixed number or a whole 13. number. Do not write the division box. Divide mentally. 12. a) 7 5 = 1: 2 5 : b) 24 3 = 8 : c) 23 9 = 2: 5 9 : d) 31 8 = 3: 7 8
2. ator to get the Quotient. 8 ÷ 4 = 2. Step 2 : Multiply the Quotient by the Numerator. 2 x 5 = 10. Hence, 5/4 of 8 = 10 . Question 2. Find : 7/6 of 24. Explanation. Step 1 : Divide the Whole Number by the deno
3. ators and..
4. 5th Grade's Dividing With Whole Numbers & Unit Fractions. Mixed Operations with Fractions. Dividing Whole Numbers by Fractions. Dividing Fractions by Whole Numbers. Word Problems. Mystery Questions. 100. 2/5 x 1/4 = Write your answer in its simplest form. What is 1/10
5. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS 4.NF.A.1 Explain why a fraction ������/������ is equivalent to a fraction (������ × ������)/(������ × ������) by using visual fraction models, with attention to how the number and size of the parts differ even though.
6. ator. 2. Note the whole number remainder. 3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original deno
7. ator with the whole number. Numerator = 2 *4. = 8. Place this numerator over the original deno

### Dividing Fractions and Mixed Number

1. The main step is convert the mixed numbers to the improper fraction. Write the improper fractions in the form of a/b / c/d. The algebraic formula says that a/b / c/d is (a * d) / (b * c) that means ad/bc. Use above formula and multiply those relevant terms to get the answer in improper fraction format
2. ators 3. if numerator on upper number is smaller than numerator on bottom number, borrow from the whole number and add to the numerator 4. subtract numerators 5. subtract whole numbers 6.
3. ator with the whole and add it with the numerator. For example, if we have 6 1/2 and 2 1/4 , you will multiply 6 x 2 + 1 = 13 and 2 x 4 +1 = 9. The obtained fraction will be 13/2 and 9/4. These two fractions are improper fractions.
4. ator are 1, 3, 5, and 15. We can see that 3 is the highest common factor, so we divide the numerator and the deno    