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Fractions By Jamie Ireland Fraction Parts There are two parts to every fraction. – The numerator is the number on the top of the fraction. Example: ¾; 3 is the numerator. – The denominator is the number on bottom of the fraction. Example: ¾; 4 is the denominator. How to say the Fractions To say the fraction you must first name it. Take ¾. This is pronounced three fourths. If you have 5/6, you would pronounce it five sixths. You have units, which are numbers like 1,2,3… Then you have half (halves if plural) and then thirds. After thirds you add a th to the denominator when you name the fractions. THE THREE QUESTIONS There are three questions which you should ask yourself when dealing with fractions. – 1. What is the unit? If you have a candy bar the whole candy bar is the unit. Same if you have a piece of paper. – 2. How many pieces are in the unit? If the candy bar is in three pieces then there are three pieces in the unit. If the paper is in four pieces then there is four pieces in the unit. – 3. Are the pieces the same size? The pieces must be the of equal size. Halves If you cut an object into two equal parts, then each part is a half of the object. Half can be written like this: ½. Fourths An object can be split into fourths if you split the object into four equal parts. Take a piece of paper and fold it in half. Then fold it in half again and the paper will be in fourths. Naming Fractions The three questions help you to name the fractions. You count how many parts there are all together and that number is your denominator. – The number of equal parts of the unit leads to the name half, third, or whatever the number is. In this case it is fourths. ?/4 Then you count how many parts are shaded or colored. That is your numerator. ¼ For more information: http://www.aaamath.com/B/fra16_x2.htm More Facts Now that you know how to name fractions, you should know the different types of fractions. A fraction with a bigger number in the numerator is called an improper fraction. – Example 4/3 A fraction that has a whole number in front of it is called a mixed number. – Example 1 ½ How do you say fractions greater than one and mixed numbers. For fractions greater than one you say it like a regular fractions. – Example: 5/3 say it five thirds For mixed numbers you say the whole number and say an “and” and then say the fraction. – Example 2 ½ you say it two and a half. Adding Fractions When adding fraction the denominator stays the same. So if you add 1/3 + 1/3, the denominator will stay at 3. Then you add the top numbers together to get the numerator. 1+1=2 So the answer is 2/3. Another Practice Problem CLICK HERE: Adding Fractions Adding mixed numbers and fractions greater than one. You add fractions greater than one just like you add any other fractions – Example 4/3 + 1/3 = 5/3 To add mixed numbers you can add the whole numbers first and then the fractions. – 1 1/4 + 1 ¼ you can add the ones together 1+1 = 2 then the fractions ¼ + ¼ = 2/4. The answer would be 2 2/4. Equivalent Fractions Any fraction that has the same number in the denominator and the numerator equals one. – Example: 2/2=1 To get an equivalent fraction for any fraction, you can multiple the denominator and the numerator by the same number. – Example: ½*2/2=2/4 Converting whole numbers to fractions REMEMBER THAT ANY WHOLE NUMBER IS A FRACTION. The whole number is on top of the fractions while one is on the bottom. – Examples 1 = 1/1 4 = 4/1 Equivalent fractions for whole numbers Remember to multiply the top and bottom numbers by the same number. – Example 4 = 4/1 4/1 *2/2 =8/2 Converting Mixed Numbers to Fractions Greater Than One IF you have 1 ½ then to convert it to a fraction greater than one, you have to multiply the whole number to a fraction with the same denominator as the fraction in the problem so that you can add them together. – Example 1 ½ 1 * 2/2=2/2 2/2 + ½ = 3/2 1 ½ = 3/2 Converting fractions greater than one to a mixed number If you have 4/3 and you want to convert it to a mixed number, then you can draw a picture like this. As you can see the mixed number would be 1 1/3. Another way to convert fractions greater than one to a mixed number. You could also do this by figuring out how many times the denominator goes into the numerator. That would be the whole number and what was left would be the fraction. – Example 6/4 – Four goes into 6 once, with two left. That two left goes over the four. The fraction is 1 ¼. Also if you have a fraction like 2 6/5, you can make that into a fraction like 3 1/5. – You simply add the whole numbers from the fractions to the whole number in front of the fraction. 2 6/5 ; 6/5 = 1 1/5; 1+2=3; 2 6/5 =3 1/5 Adding Fractions with Unlike Denominators First you have to make the fractions have the same denominator. To make ½ into fourths you have to multiply both the top and bottom numbers by 2. ½*2/2=2/4 Now that both fractions have the same denominator you can add them. 2/4 + 2/4 = 4/4 And you know that 4/4=1. Subtracting Fractions To subtract two fractions, the denominator of both fractions have to be the same. The denominator will have the same number as it did before you subtracted. In this case it is 4. The numerator is the first numerator minus the second numerator. – Example: 2-1=1 The answer would be ¼. Another example Subtracting mixed numbers To subtract a mixed number you must first convert it to a fraction greater than one. – Example 2 ½ - 2/2 Remember that 2 is 2/1. 2/1 * 2/2 =4/2 Then you add that to the fraction 4/2+1/2=5/2 Then you subtract 5/2-2/2 = 3/2 You can also convert it to 1 3/2, by only converting one of the whole numbers. When you are subtracting two mixed numbers you should subtract the fraction part first then subtract the whole numbers. – Example 1 2/3 – 1 1/3; 2/3 – 1/3 = 1/3; 1 – 1 = 0 so 1 2/3 – 1 1/3 = 1/3 For More Information This website uses circles and number lines to teach fractions. http://www.visualfractions.com/ This site provides help in finding the least common multiple for renaming fractions. http://www.mathleague.com A Good Source Mathematics learning in early childhood- There is a chapter in there that talks about fractions which was written by Arthur F. Coxford and Lawrence W. Ellerbruch. This book is sometimes referred to as the thirty-seventh yearbook.