CHAPTER 7 VOCABULARY Least Common Multiple (LCM) – the smallest number that is a multiple of two or more numbers Least Common Denominator (LCD) – is the LCM of two or more denominators
BRAIN POP VIDEO Adding & Subtracting Fractions
InvestigateMaterials needed: fractions stripsDraw Conclusions1. Describe how you would determine what fraction strips, all with the same denominator, would fit ½ + 1/32. Explain how finding strips with the same denominator for ½ + 1/3 and ½ + ¼ are different.7.1 ADDITION WITH UNLIKE DENOMINATORS
7.1 MATH JOURNAL QUESTIONHow can you use models to add fractions that do not have the same denominator?
InvestigateMaterials: Fraction stripsDraw Conclusion:1. Describe how you determined what fraction strips , all with the same denominator, would fit exactly under the difference?2. Explain whether you could have used fraction strips of any other denominator to find the difference, if so, what is the denominator?7.2 SUBTRACTION WITH UNLIKE DENOMINATORS
CONNECT PG. 292Sometimes you can use different sets of same-denominator fraction stripsto find the difference. All of the answers will be correct.
7.4 LEAST COMMON MULTIPLE One way: make a list Start by making a list of the first 5 multiples of each number (you may have to find more than the first 5 depending on the numbers). Underline the common multiples of the numbers. Circle the LCM of the numbers.Example: 6: 6, 12, 18, 24, 30, 36, 42, 48 8: 8, 16, 24, 32, 40, 48, 56, 64LCM of 6 & 8 is 24.
ANOTHER WAY – USE PRIME FACTORIZATION What numbers are prime factors of either 6 or 8? The prime factor 2 occurs most often in the prime factorization of ___. Write each prime factor the greatest number of times it appears in one factor tree. Multiply. 2 x 2 x 2 x 3 = 24 LCM is 24.
LEAST COMMON DENOMINATOR PG. 300 Step 1: find the least common multiple of both denominators. Step 2: use the LCM as the LCD and create equivalent fractions.***important information*** Whatever you do to the denominator you must do the same to the numerator!
SHARE & SHOW (EXTRA PRACTICE) FIND THE LCM 3&53&9 9 & 15Find the LCD & then write an equivalent fraction3&1 5&1 1&15 4 8 5 12 2
7.5 MATH JOURNAL QUESTIONWhat are some helpful strategies for finding the LCD of pairs of fractions?
ONE WAY – USE A COMMONDENOMINATOR ANOTHER WAY – USE THE LCD7.6 USE COMMON DENOMINATORS
Explain how you knowwhether your answer isreasonable. EXAMPLE PG. 308
26. Sara is making a key chain, using the bead design shown. What fraction of the beads in her design are either blue or red?Use the picture for 26 – 27. 27. In making the key chains, Sara uses the pattern of beads 3 times. After the key chain is complete, what fraction of the total beads are either white or blue.PROBLEM SOLVING PG. 310
Step 1: Estimate the sumStep 2: Find a common denominator.Use the common denominator towrite equivalent fractions with likedenominators.Step 3: Add the fractions. Then addthe whole numbers. Write the answerin simplest form.Explain how you know whether youranswer is reasonable.What other common denominatorcould you have used?7.8 ADD & SUBTRACT MIXED NUMBERS
Step 1: Estimate the difference.Step 2: Find a common denominator.Use the common denominator towrite equivalent fractions with likedenominators.Step 3: Subtract the fractions.Subtract the whole numbers. Writethe answer in simplest form.Explain how you know whether youranswer is reasonable.SUBTRACTING MIXED NUMBERS
Use the table to solve 25 – 28.PROBLEM SOLVING PG. 320
Use the table to solve. Gavin needs to make 2 batches of purple paint. Explain how you could find the total amount of paint Gavin mixed.7.8 MATH JOURNAL QUESTION
ONE WAY – RENAME THE FIRST MIXED EXPLAIN WHY IT IS IMPORTANT TO WRITENUMBER EQUIVALENT FRACTIONS BEFORE RENAMING. Step 1: Estimate the difference. Step 2: Write equivalent fractions, using the LCD. Step 3: Rename 2 3/6 as a mixed number with a fraction greater than 1. Step 4: Find the difference of the fractions. Then find the difference of the whole numbers. Write the answer in simplest form. Check to make sure your answer is reasonable.7.9 SUBTRACTION WITH RENAMING
ANOTHER WAY – RENAME BOTH MIXEDNUMBERS AS FRACTIONS GREATER THAN 1. Step 1: Write equivalent fractions, using the LCD. Step 2: Rename both mixed numbers as fractions greater than 1. Step 3: Find the difference of the fractions. Then write the answer in simplest form.SUBTRACTION WITH RENAMING
Use the map to solve 10 – 12. 10. In the morning, Julie rides her bike from the sports complex to the school. In the afternoon, she rides from the school to the mall and then to Kyle’s house. How far does Julie ride her bike? 11. Saturday afternoon, Mario walks from his house to the library. That evening, Mario walks from the library to the mall and then to Kyle’s house. Describe how you use the properties to find how far Mario walks. 12. Pose a Problem Write and solve a new problem that uses the distance between three locations.PROBLEM SOLVING PG. 328
7.10 MATH JOURNAL QUESTIONHow can properties help you add fractions with unlike denominators?