# how to simplify improper fractions

This brings us to the topic of this article of simplifying fractions. In math, these fractions are referred to as equivalent fractions. Improper fractions $$\frac{5}{3}$$ is called an improper fraction, because the top number is bigger than the bottom number. Improper fractions are simply top-heavy fractions whose numerators (the numbers on top) are bigger than their denominators. It's better to use the GCD because if you don't use the GCD first, more than one division step will be necessary. This math worksheet was created on 2020-01-20 and has been viewed 142 times this week and 395 times this month. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons You can simplify a negative fraction by simplifying its positive equivalent and then adding a negative sign. Examples of improper fractions are 16/3, 81/9, 525/71. All rights reserved. What portion of the whole pie did you end up eating? This type of fraction is said to be in simplest form. The fractions, $$\frac{3}{9}$$ and $$\frac{1}{3}$$, are equivalent, so the simplified mixed number is $$4\frac{1}{3}$$. just create an account. Divide the numerator by the denominator, as shown: Write the result as a mixed numeral: $$2\frac{1}{3}$$. This fraction is simpler because I now have 4 parts to make one whole instead of 12. The fraction, $$\frac{12}{51}$$ has a numerator of 12 and denominator of 51. So, 2/3 means that a whole contains 3 equal-sized parts, and only 2 of the 3 are being counted. Since you only need 3 parts to make 1 whole and 4 parts are being counted, the fraction 4/3 actually represents a number greater than 1 whole, and this is true for all improper fractions. study , represents the “part” that you will eat divided by the total number of parts, or the “whole”. Below are six versions of our grade 6 math worksheet on simplifying fractions; some of the fractions will be larger than 1 (improper fractions). Divide […] Why say four-eighths (48 ) when we really mean half (12) ? Remember is the same as . However, we know from working with this same fraction above that it can be simplified further to 3/2. We’ll get into mixed numbers a little later. - Definition & Examples, What is a Compound Sentence? What Is the Rest Cure in The Yellow Wallpaper? Add that to the numerator Then write the result on top of the denominator. Worksheets > Math > Grade 6 > Fractions - simplify > Simplify improper fractions. Commonly, we have four types of fractions. has a numerator of 5 and a denominator of 25. The process of simplifying fractions means to reduce the numerator and the denominator by their greatest common factor, or their GCF. When you reduce a fraction, it becomes simpler because the number of parts in the whole is made small as possible, without changing the value of the fraction. Select a subject to preview related courses: To reduce a fraction to lowest terms, try to find the largest number that divides into both numerator and denominator. A fraction can also be reduced by factoring both numerator and denominator into prime factors, then cancelling all common factors. Visualizing equivalent fractions review. This image is helpful to illustrate just how much pie you ate: By eating your brother’s piece of pie and your own, you actually ate one half of the pie. Adding these together results in a fraction of $$\frac{1}{4}$$+$$\frac{1}{4}$$=$$\frac{1+1}{4}$$, or $$\frac{2}{4}$$. Not sure what college you want to attend yet? lessons in math, English, science, history, and more. © copyright 2003-2020 Study.com. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. Visit the High School Algebra I: Help and Review page to learn more. To review, the correct terminology for the “part” of a fraction is the numerator, and the “whole” is called the denominator. Practice: Simplify fractions. The fraction 4/3 is an example of this, and these types of fractions are called improper fractions. But most of the times, when you cannot solve the fraction problem, you think it … In math, these fractions are referred to as. How to convert 66/35 into a mixed number. This is because both 2 and 4 can be divided by 2 to equal the fraction ½. Need additional help, video reviews, or practice questions? Now that you have a visual reference for fractions, let’s move on to some practice to familiarize yourself with the terminology and the step-by-step process of simplifying fractions: The fraction, $$\frac{5}{25}$$, has a numerator of 5 and a denominator of 25. For example, consider the fraction 6/4. , share the GCF of 3. You can simplify a fraction if the numerator (top number) and denominator (bottom number) can both be divided by the same number. Equivalent fractions review. The fraction, $$\frac{1}{4}$$. Notice that in all of the examples we have looked at so far, the numerator is smaller than the denominator. The terms 'simplifying' or 'reducing' means the same thing when referring to fractions, so these terms can be used interchangeably. What is an Improper Fraction? Simplifying (or reducing) fractions means to make the fraction as simple as possible. Although a topic of elementary mathematics, fractions are important and occur in everyday calculations. Simplify the improper fraction, $$\frac{24}{9}$$. 's' : ''}}. While both represent the same amount, 3/2 has 2 parts to make one whole and 2 is smaller than the 4 parts to make one whole in the fraction 6/4. To simplify improper fractions you just have to simplify as you would with a regular fraction. If you have 3 siblings, the pie will be divided into 4 equal pieces, and you will each get one piece to eat. Well, half of the six pieces is three, so the fraction, $$\frac{3}{6}$$, means to reduce the numerator and the denominator by their greatest common factor, or their GCF. The denominator tells how many equal-sized parts make one whole and the numerator tells how many of those parts are being counted. You can see from the picture below that these fractions are the same, but ½ is the simpler of the two fractions … I converted the improper fractions to mixed numerals (e.g. Determine whether your fraction is improper. Note: Simplifying an improper fraction will always result in an improper fraction. Mixed numbers contain both a whole number and a fraction. instead of 5/4, I answered 1 1/4). Plus, get practice tests, quizzes, and personalized coaching to help you I can also make an equivalent fraction by dividing the numerator and denominator by the same number. improper fractions: fractions that have a numerator with a higher value than the denominator . And mixed numbers have a whole number sitting next to a proper fraction -- for example, 4 3/6 or 1 1/2. For […] Enrolling in a course lets you earn progress by passing quizzes and exams. succeed. Obviously, if each of the four children eat their piece, then the whole pie will be gone! Completing this lesson should help you do the following: To unlock this lesson you must be a Study.com Member. For thisfollow a set of rules stated below to reduce fraction manually: In the first step simply divide the numerator or top number by the denominator or the bottom number of fraction. As you can imagine, the structure of an improper fraction is different, in that the numerator is greater than the denominator. One way is to multiply the numerator and denominator by the same number. Although mixed numbers are great for everyday use, it is often easier to work with improper fractions when you want to solve math problems. Although they are divided differently, the two rectangles can be seen to represent the same amount. - Definition & Overview, How to Estimate in Math: Definition & Concept, What is PEMDAS? It’s fun playing with integers. Because the greatest common factor of 3 and 9 is 3, divide both the numerator and denominator of the fraction by 3, resulting in $$\frac{1}{3}$$, , are equivalent, so the simplified mixed number is $$4\frac{1}{3}$$. Also remember that our fraction calculator is always available for you to use. Already registered? credit by exam that is accepted by over 1,500 colleges and universities. Write the prime factors of both numerator and denominator: Multiply the common factors identified in Step 2 for the GCF: Divide both the numerator and denominator by the GCF to get the simplified fraction: $$\frac{12\div 6}{18\div 6}=\frac{2}{3}$$. Example: Change the improper fraction 402/11 to a mixed number. Betty has a master's degree in mathematics and 10 years experience teaching college mathematics. Write 7/4 as a mixed number. Simplifying fractions in this way makes our work with more complex problems easier. Improper Fractions. The first step is to determine the largest number that evenly divides the numerator and the denominator (also called the Greatest Common Factor of these numbers). Welcome to The Simplifying Improper Fractions to Lowest Terms (Easier Questions) (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. They must be divided by the same number or the new fraction will not equivalent to the original one. - Definition & Examples, Quiz & Worksheet - Reducing & Simplifying Improper Fractions, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Addition, Subtraction, Multiplication, and Division with Decimal Notation, Adding and Subtracting Decimals: Examples & Word Problems, Multiplying and Dividing Decimals: Examples & Word Problems, How to Estimate with Decimals to Solve Math Problems, Changing Between Improper Fraction and Mixed Number Form, How to Add and Subtract Like Fractions and Mixed Numbers, How to Add and Subtract Unlike Fractions and Mixed Numbers, Practice with Fraction and Mixed Number Arithmetic, Solving Problems using Fractions and Mixed Numbers, Using the Number Line to Compare Decimals, Fractions, and Whole Numbers, How to Simplify Word Problems with Fractions Using Whole Numbers, How to Solve Algebra Problems with Fractions, What is an Improper Fraction? 3/6 or 1 1/2 their GCF ' means the same thing when referring to fractions how to simplify improper fractions... 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