Adding Three Fractions Problem Solving: Choosing the Best Graph Adding Three Fractions How do we use good number sense with fractions? Let s review least common multiples. Look at the following set of numbers. What do you think the colors represent? 9 7 0 0 0 0 0 The colors surrounding each number show multiples of (blue), (red), and (yellow). The number surrounded by all three colors is the least common multiple of,, and. It is important to have good number sense when we do any kind of calculation. Look at the problem below. It does not make sense to use paper and a pencil to subtract. We just count backward in our heads and get 99.,000 Good number sense is also important when we work with fractions. The problem requires that we add three fractions. Look at the denominators carefully. Unit
How do we find the least common multiple for three fractions? To solve this problem, we need to find the least common multiple of all three denominators. + 0 If we think about least common multiples, we can use one of two strategies to find a smaller common denominator. Use a Number Line We might think it easiest to multiply all three denominators together to get a common denominator. If we multiply 0, we get 00. The number 00 is a multiple of,, and 0. However, 00 is so large that the fractions would be hard to understand. Multiples of : 0 0 0 0 0 0 Multiples of : 0 0 0 Multiples of 0: 0 0 0 0 0 0 0 70 0 90 00 0 Count by Multiples s 0 0 0 0 0 0 s 0 0 0 0s 0 0 0 0 0 0 70 0 90 00 0 In all three numbers, 0 is the first, or least, common multiple. Unit
Now that we know that 0 is the least common multiple of,, and 0, we can solve the problem in two steps. Add: + 0 Step Find the common denominator. Step Solve the problem. = 0 = 0 0 0 = 0 0 0 0 + 0 0 0 The answer is 0 0, or. In this problem, the numerator and the denominator are the same. So we know that this fraction equals. Let s see how this works with three other fractions. Unit
Example Find the least common multiple to make common denominators. Count on a number line, or count by multiples. + Multiples of : 0 9 7 0 9 Multiples of : 0 0 Multiples of : 0 0 0 s 9 7 0 9 s 0 s 0 0 0 Solve the problem. The answer is 9. Unit Apply Skills Turn to Interactive Text, page. = = = 9 + 9 9 Reinforce Understanding Use the mbook Study Guide to review lesson concepts.
Problem Solving: Choosing the Best Graph Which graph displays our data in the best way? Each graph below shows data in a different way. Study each graph to see why one type is better than another for showing different sets of data. Vertical Bar Graph 0,000 Decline in Newspaper Subscribers,000 Number of Subscribers 0,000,000 0,000,000 0,000,000 0,000 99 99 997 99 999 000 00 00 Years Horizontal Bar Graph Speed of Race Cars for One Lap Olsen Racing Team 7 Formula Harmon Brothers 0 0 7 00 0 7 00 Seconds Bar graphs are good for showing relationships between numbers over time. Unit
Pictograph Tons of Flour Sold (in millions) Flour Sold FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR FLOUR Pictographs are good when we want to communicate a general idea. 0 99 999 000 00 00 Year Line Graph 9: PM Sunsets in Seattle and San Diego Line graphs are good for showing trends. Time of Day : PM 7: PM :00 PM : PM : PM San Diego Seattle : PM : PM 0:00 PM Jan. Feb. Mar. Apr. May June Month July Aug. Sept. Oct. Nov. Dec. Problem-Solving Activity Turn to Interactive Text, page 7. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Unit
Homework Activity Tell which fraction goes in the blank on each number line.... Is the missing fraction,, or? Is the missing fraction,, or? Is the missing fraction,, or? Activity Add the fractions. Find the least common multiple to help you find a common denominator.. + + 0 0 0 0 0 0 0 0 0. + + 0. + +. + 9 + 7 9 Activity Solve.... 7 + + 9 0 0 0 7 Activity Distributed Practice Solve..,79 +,0 0,0??. 7,90 apple,097,0 9.... 70 0,00 + 0. 700,00? 7. q7 Copyright 00 by Cambium Learning Sopris West. All rights reserved. Permission is granted to reproduce this page for student use. Unit 7