ADD & SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS

Chapter 7

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

7.1 ADDITION WITH UNLIKE DENOMINATORS

InvestigateMaterials needed: fractions strips

Draw Conclusions1. Describe how you would

determine what fraction strips, all with the same denominator, would fit ½ + 1/3

2. Explain how finding strips with the same denominator for ½ + 1/3 and ½ + ¼ are different.

CONNECT PG. 288

PROBLEM SOLVING PG. 290

7.1 MATH JOURNAL QUESTION

How can you use models to add fractions that do not have the same denominator?

7.2 SUBTRACTION WITH UNLIKE DENOMINATORS

InvestigateMaterials: Fraction strips

Draw 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?

CONNECT PG. 292Sometimes you can use different sets of same-denominator fraction strips to find the difference. All of the answers will be correct.

SHARE & SHOW (EXTRA PRACTICE)

UNLOCK THE PROBLEM (TEST PREP) PG. 294

7.2 MATH JOURNAL QUESTION

7.3 ESTIMATE FRACTION SUMS & DIFFERENCES

One way – benchmark numbers 0, ½, 1

Use benchmark numbers to estimate the following fractions: 4/6 1/8 3/5 7/8

UNLOCK THE PROBLEM PG. 295

ANOTHER WAY PG. 296 (MENTAL MATH)

TRY THIS! ESTIMATE (PG.296)

PROBLEM SOLVING PG. 298 (17-19 & 21)

7.3 MATH JOURNAL QUESTION

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, 64

LCM 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 & 5 3 & 9 9 & 15

Find the LCD & then write an equivalent fraction3 & 1 5 & 1 1 & 15 4 8 5 12 2

UNLOCK THE PROBLEM & WORD PROBLEMS PG. 302

7.4 MATH JOURNAL QUESTION

How can you find the least common multiples and least common denominators?

7.5 STRATEGIES TO FIND THE LCD

ACTIVITY PG. 304

TRY THIS! PG. 304

PROBLEM SOLVING PG. 306

7.5 MATH JOURNAL QUESTION

What are some helpful strategies for finding the LCD of pairs of fractions?

7.6 USE COMMON DENOMINATORS

ONE WAY – USE A COMMON DENOMINATOR

ANOTHER WAY – USE THE LCD

EXAMPLE PG. 308

Explain how you know whether your answer is reasonable.

PROBLEM SOLVING PG. 310

Use the picture for 26 – 27.

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?

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.

7.6 MATH JOURNAL QUESTION

MID – CHAPTER REVIEW

7.8 ADD & SUBTRACT MIXED NUMBERS

Step 1: Estimate the sum

Step 2: Find a common denominator. Use the common denominator to write equivalent fractions with like denominators.

Step 3: Add the fractions. Then add the whole numbers. Write the answer in simplest form.

Explain how you know whether your answer is reasonable.

What other common denominator could you have used?

SUBTRACTING MIXED NUMBERS

Step 1: Estimate the difference.

Step 2: Find a common denominator. Use the common denominator to write equivalent fractions with like denominators.

Step 3: Subtract the fractions. Subtract the whole numbers. Write the answer in simplest form.

Explain how you know whether your answer is reasonable.

PROBLEM SOLVING PG. 320

Use the table to solve 25 – 28.

7.8 MATH JOURNAL QUESTION

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.

7.9 SUBTRACTION WITH RENAMING

ONE WAY – RENAME THE FIRST MIXED NUMBER

EXPLAIN WHY IT IS IMPORTANT TO WRITE 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.

SUBTRACTION WITH RENAMING

ANOTHER WAY – RENAME BOTH MIXED NUMBERS 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.

ON YOUR OWN PG. 323

CONNECT TO READING PG. 324

7.9 MATH JOURNAL QUESTION

How can you rename to find the difference of two mixed numbers?

7.10 USE PROPERTIES OF ADDITION

Remember () tell you which operation to do first.

Unlock the Problem

EXAMPLE PG. 326

TRY THIS! PG. 326

PROBLEM SOLVING PG. 328

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.

7.10 MATH JOURNAL QUESTION

How can properties help you add fractions with unlike denominators?

CHAPTER 7 REVIEW

CHAPTER REVIEW