// Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction bar means to divide the numerator by the denominator One Way To Remember Numerator North # of parts in whole Denominator Down Page # you have Divided by What Fraction is Shaded? ⅝ Page / ¾ Page Identifying Forms of Fractions There are three forms of fractions:! Proper fraction: The numerator (top number) is always less than the denominator. The value of a proper fraction is less than whole.! Improper fraction: The numerator is equal to or greater than the denominator. When the numerator is equal to the denominator, an improper fraction is equal to whole.! Mixed Number: A whole number & a proper fraction are written next to each other. A mixed number always has a value of more than whole. Page Tell whether each of the following is a proper fraction (P), an improper fraction (I) or a mixed number (M). 0 0 0
// Page Tell whether each of the following is a proper fraction (P), an improper fraction (I) or a mixed number (M). Page Thinking About the Size of Fractions! The size of the numerator compared to the size of the denominator tells you: A fraction is equal to ½ when the numerator is exactly half of the denominator A fraction is less then ½ when the numerator is less than half of the denominator A fraction is greater than ½ when the numerator is more than half of the denominator! The symbol means is equal to! The symbol < means is less than! The symbol > means is greater than Page In the box between each pair of fractions, write a symbol that makes the statement true. Page In the box between each pair of fractions, write a symbol that makes the statement true. 0 Pages Reducing Fractions! Reducing a fraction means dividing both the numerator & the denominator (top & bottom) by a number that goes into each evenly.! Reducing changes the numbers in a fraction, but reducing does not change the value of a fraction.! When both the numerator & the denominator of a fraction end with zeros, you can cancel the zeros one-for-one. This is a shortcut for reducing ten. Always check to see if you can continue to reduce.! Sometimes a fraction can be reduced more than once to reach the lowest terms Pages Questions When Reducing! Are the numerator & denominator both even? Divide by! Add the digits of the numerator separate from the digits of the denominator. Do they add up to a number that is divisible by? Divide by! Do the numerator & the denominator end in a 0 or? Divide by! If no to all previous questions: You just have to try,, & so on
//! Reduce each fraction to lowest terms 0 Pages! Reduce each fraction to lowest terms 0 0 Pages Page Raising Fractions to Higher Terms! An important skill in the addition & subtraction of fractions is raising a fraction to higher terms.! Raising to higher terms is the opposite of reducing.! To reduce a fraction, you must divide both the numerator & denominator by the same number.! To raise a fraction to higher terms, multiply both the numerator & the denominator by the same number. Page Raise each fraction to higher terms by filling in the missing numerator. 0 Page Raise each fraction to higher terms by filling in the missing numerator. Pages 0 Changing Improper Fractions to Whole or Mixed Numbers! The answers to many fraction problems are improper fractions. These answers are easier to read if you change them to whole numbers or mixed numbers.! To change an improper fraction, divide the denominator into the numerator.
// Pages 0 Change each fraction to a whole number or a mixed number. Reducing any remaining fractions. Pages 0 Change each fraction to a whole number or a mixed number. Reducing any remaining fractions. 0 Page Changing Mixed Numbers to Improper Fractions! When you multiply & divide fractions, you will have to change mixed numbers to improper fractions. To change a mixed number to an improper fraction, follow these steps:. Multiply the denominator (bottom number) by the whole number.. Add that product to the numerator (top number). Write the sum over the denominator. Page Change each mixed number to an improper fraction Page Change each mixed number to an improper fraction 0 Pages Addition of Fractions with the Same Denominators! To add fractions with the same denominators (bottom numbers), first add the numerators.! Then write the total (or sum) over the denominator.! Don t forget to check to see if you can reduce your answer.
// Add + Pages + 0 Page Addition of Fractions with Different Denominators! If the fractions in an addition problem do not have the same denominators, you must find a common denominator.! common denominator a number that can be divided evenly by every denominator in the problem.! lowest common denominator or LCD The lowest denominator that can be divided evenly by every denominator in the problem. Pages Finding a Common Denominator! Method : Multiply the denominators together.! Brute force method: List the multiples of the larger number until you find a multiple of the smaller number! Prime factorization method: find prime factors of both numbers. Circle the numbers they have in common. Write those once then write in the rest of the numbers and multiply to find the LCM Add + 0 Pages + + Pages + Page Subtracting Fractions with the Same Denominators! To subtract fractions, subtract the numerators & put the difference (the answer) over the denominator.
// Page Pages Subtracting Fractions with Different Denominators! When fractions do not have the same denominators, first find a common denominator.! Change each fraction to a new fraction with the common denominator.! Then subtract. Pages Subtract & Reduce Pages Subtract & Reduce 0 0 Pages Borrowing & Subtracting Fractions! Sometimes there is no top fraction to subtract the bottom fraction from. Other times the top fraction is not big enough to subtract the bottom fraction from. To get something in the position of the top fraction, you must borrow. To borrow means to write the whole number on top as a whole number & an improper fraction.! For example,. The numerator & denominator of the improper fraction should be the same as the denominator of the other fraction in the problem. Pages Subtract & Reduce
// Pages Subtract & Reduce 0 0 Page Multiplication of Fractions! When you multiply whole numbers (except & 0), the answer is bigger than the two numbers you multiply.! When you multiply two proper fractions, the answer is smaller than either of the two fractions. When you multiply two fractions, you find a fraction of a fraction or a part of a part.! To multiply fractions, multiply the numerators together & the denominators. Then reduce. Page x x x Page x x x Pages 0 Canceling & Multiplying Fractions! Canceling is a way of making multiplication of fractions problems easier.! Canceling is similar to reducing.! To cancel, divide a numerator & denominator by a number that goes evenly into both of them.! You don t have to cancel to get the right answer, but it makes the multiplication easier. Pages 0 x x x x
// Pages 0 x 0 x x x 0 Page Multiplying Fractions & Whole Numbers! To multiply a whole number & a fraction, first write the whole number as a fraction.! Write the whole number as the numerator & a the denominator. Page x 0 x Page x x 0 Multiplying Mixed Numbers! To multiply mixed numbers, first change the mixed numbers to improper fractions.! Then multiply the improper fractions.! Reduce the answer. Page Page x x x x
// Page x x x Pages Dividing Fractions by Fractions! To divide fractions, take the reciprocal (or inverse) of the divisor (the number at the right of the sign) & follow the rules for multiplying fractions.! To make a reciprocal means to write the numerator on the bottom & the denominator on the top. Pages Divide & Reduce Pages Divide & Reduce 0 Pages Dividing Whole Numbers by Fractions & Dividing Fractions by Whole numbers & Dividing with Mixed Numbers! In fraction division problems, change whole numbers & mixed numbers to improper fractions.! Then take the reciprocal of the fraction you are dividing by & follow the rules for multiplying fractions. Pages Divide & Reduce 0
// Pages Divide & Reduce Page Finding a Number When a Fraction of It Is Given! There is a kind of division problem that is sometimes hard to recognize. Think about the question ½ of what number is? Without using pencil & paper, you can probably come up with the answer. You know that ½ of is.! To solve the problem, you find a solution to the statement ½ x?. The statement asks you to find the missing number in a multiplication problem. To find the missing number, divide by ½. Solve Page of what number is? of what number is? 0 Solve Page of what number is? of what number is 0? 0