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FRACTIONS Basic Fractions Comparing Fractions Adding Fractions Subtracting Fractions Fraction Fun! What are fractions?

What are fractions? Fractions are for counting PART of something The denominator tells us how many pieces something is cut into. The numerator tells how many fractional pieces there are

Basic Fractions A fraction is part of an entire object. 1/4 is pink 1/2 is pink 3/4 is pink 4/4 or one whole is pink

Comparing Fractions If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction. For example: 5/8 is larger than 3/8 all of the pieces are the same and five pieces are more than three pieces. If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction. For example: 5/8 is larger than 3/8 all of the pieces are the same and five pieces are more than three pieces. Comparing, cont.

Comparing Fractions, cont. If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction. For example: 5/8 is larger than 5/16 Each fraction says there are five pieces. If an object is divided into 8 pieces, each piece will be larger than if the object were split into 16 pieces. Therefore five larger pieces are more than five smaller pieces. If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction. For example: 5/8 is larger than 5/16 Each fraction says there are five pieces. If an object is divided into 8 pieces, each piece will be larger than if the object were split into 16 pieces. Therefore five larger pieces are more than five smaller pieces.

Adding Fractions Adding fractions with COMMON denominators is simple. Just add the numerators together, and place the resulting answer in the top of a fraction and use the existing denominator for the bottom number. Then reduce the fraction, if possible For example: 3/8 + 2/8 = 5/8 Adding fractions with COMMON denominators is simple. Just add the numerators together, and place the resulting answer in the top of a fraction and use the existing denominator for the bottom number. Then reduce the fraction, if possible For example: 3/8 + 2/8 = 5/8 Adding, cont.

Adding Fractions You can only add together fractions that have the same denominator, so you must first change one or both of the fractions so that you end up with two fractions having a common denominator. The easiest way to do this, is to simply select the opposite fraction's denominator to use as a top and bottom multiplier. Please look at the example on the next page… You can only add together fractions that have the same denominator, so you must first change one or both of the fractions so that you end up with two fractions having a common denominator. The easiest way to do this, is to simply select the opposite fraction's denominator to use as a top and bottom multiplier. Please look at the example on the next page… Adding, cont.

Adding Fractions Example: You have the fractions 2/3 and 1/4 Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number: 4/4 x 2/3 = 8/12 Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number: 3/3 x 1/4 = 3/12 These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction. Add these two new fractions together: 8/12 + 3/12 = 11/12 Example: You have the fractions 2/3 and 1/4 Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number: 4/4 x 2/3 = 8/12 Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number: 3/3 x 1/4 = 3/12 These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction. Add these two new fractions together: 8/12 + 3/12 = 11/12

Subtracting Fractions To subtract two fractions with the same denominator, subtract the numerators and place that difference over the common denominator. Look at a pizza cut into 8 pieces. Each piece is 1/8 of the pizza. Here we have 7 pieces or 7/8 of the pizza. Now take away 3/8 or 3 pieces. We’re left with 4 pieces! We just subtracted the numerators! Subtracting, cont.

Subtracting Fractions To Subtract Fractions with different denominators: Find the Lowest Common Denominator (LCD) of the fractions Rename the fractions to have the LCD Subtract the numerators of the fractions The difference will be the numerator and the LCD will be the denominator of the answer. Simplify the Fraction Click here to learn more about the LCD

LCD To find the least common denominator, list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows... First list the multiples of each denominator. Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,... Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list. Therefore, the least common denominator of 1/5 and 1/6 is 30. To find the least common denominator, list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows... First list the multiples of each denominator. Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,... Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list. Therefore, the least common denominator of 1/5 and 1/6 is 30. LCD, cont.

LCD For more LCD help click here!

Fraction Fun! If you eat 1/4 of this pizza how much will be left? If you eat 2 pieces of this pizza and your friend eats 1 how many 10ths did you eat altogether? Answer

Fraction Fun! All the children are going to share the pizza. We will cut enough pieces so each child can have one, and the pieces should all be the same size. If 7 children shared the pizza equally, what fraction of the pizza did each child get? Answer

Fraction Fun! Answers 1. What fraction of the circle is shaded green? 2. What fraction of the circle is shaded red? 3.What fraction would you write for the color RED? 4.What fraction would you write for the color green?

3/4 left 3/10 eaten More Fun! Back to Question

1/7 More Fun! Back to Question

Back to Question 1.4/6 or 2/3 2.2/3 3.3/8 4.1/8

Concept Map

2005 Connecticut Mathematics Curriculum Framework Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies. How are quantitative relationships represented by numbers? Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies. How are quantitative relationships represented by numbers? Standards 2.1 and 2.2

2.1 Students should understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent numbers in expanded and regrouped forms in the base ten place value system. b. Recognize that a fraction with the same numerator and denominator represents the whole object or an entire set. c. Use fractions to measure and to represent points on a ruler or number line. 2.2 Students should use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities a. Use strategies that involve place value patterns and algebraic properties to estimate, add and subtract. b. Approximate solutions to problems involving computation through the use of efficient methods. c. Solve multiplication and division problems using rectangular arrays, number patterns, skip counting and repeated addends. d. Compare fractions, identify equivalent fractions, add and subtract fractions with like and unlike denominators using models and pictures. 2.1 Students should understand that a variety of numerical representations can be used to describe quantitative relationships. a. Represent numbers in expanded and regrouped forms in the base ten place value system. b. Recognize that a fraction with the same numerator and denominator represents the whole object or an entire set. c. Use fractions to measure and to represent points on a ruler or number line. 2.2 Students should use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities a. Use strategies that involve place value patterns and algebraic properties to estimate, add and subtract. b. Approximate solutions to problems involving computation through the use of efficient methods. c. Solve multiplication and division problems using rectangular arrays, number patterns, skip counting and repeated addends. d. Compare fractions, identify equivalent fractions, add and subtract fractions with like and unlike denominators using models and pictures. Grade 3

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