3-5 Adding and Subtracting Fractions. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Transcription

1 Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2 Warm Up Find the LCM for each set of numbers and 2. and and 4. and

3 Learn to add and subtract fractions.

4 From January 1 to March 14 of any given year, Earth completes approximately 1 of 5 its orbit around the Sun, while Venus completes 1 approximately its orbit. 3 The illustration shows what the positions of the planets would be on March 14 if they started at the same place on January 1 and their orbits were circular. To find out how much more of its orbit Venus completes than Earth, you need to subtract fractions.

5 Example 1: Adding or Subtracting Fractions with Like Denominators A. Add. Write the answer in simplest form = = 6 8 = 3 4 Add the numerators and keep the denominator. Simplify.

6 Example 1: Adding or Subtracting Fractions with Like Denominators B. Subtract. Write the answer in simplest form = 9 4 Subtract the numerators and 11 keep the denominator. = 5 11 The answer is in the simplest form.

7 Check It Out: C. Add. Write the answer in simplest form = = 6 6 = 1 Simplify. Add the numerators and keep the denominator.

8 Check It Out D. Subtract. Write the answer in simplest form = 7 4 Subtract the numerators and 10 keep the denominator. = 3 10 The answer is in the simplest form.

9 To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator. Two Ways to Find a Common Denominator Find the LCM (least common multiple) of the denominators. Multiply the denominators. Helpful Hint The LCM of two denominators is the lowest common denominator (LCD) of the fractions.

10 Example 2: Adding and Subtracting Fractions with Unlike Denominators A. Add. Write the answer in simplest form = = = = The LCM of the denominator is 24. Write equivalent fractions. Add Estimate = is a reasonable answer. 24

11 Example 2: Adding and Subtracting Fractions with Unlike Denominators B. Subtract. Write the answer in simplest form = = 8 9 = 1 Multiply the denominators. Write equivalent fractions. Subtract. Estimate 1 1 = 0-1 is a reasonable answer.

12 Example 2: Adding and Subtracting Fractions with Unlike Denominators C. Add. Write the answer in simplest form Multiply the denominators = = = Write equivalent fractions. Add Estimate - + = is a reasonable answer. 21

13 Check It Out D. Add. Write the answer in simplest form = = = = Multiply the denominators. Write equivalent fractions. Divide. Estimate 1/2 + 1 = is a reasonable answer. 30

14 Check It Out E. Subtract. Write the answer in simplest form = = = 1 10 Multiply the denominators. Write equivalent fractions. Subtract. 1 1 Estimate = is a reasonable answer. 10

15 Check It Out F. Add. Write the answer in simplest form = = = Multiply the denominators. Write equivalent fractions. Add 1 1 Estimate - + = Is a reasonable answer. 10

16 End Day #1

17 Day #2

18 Problem of the Day Let A through l represent digits of a number. Replace the letters A through l with the digits 1 through 9, respectively, and verify that the statement is true. ( E CD ) l AB G FH ( ) + ( ) = = = 1

19 1 2 1 = Example 3: Astronomy Application In one Earth year, Jupiter completes about of its orbit around the Sun, while Mars 1 completes about of its orbit. How much 2 more of its orbit does Mars complete than Jupiter? = 6 1 = 5 Mars completes 5 The LCM of the denominators is. Write equivalent fractions using the common denominator. Subtract. 1 more of its orbit than Jupiter does.

20 It takes Michelle takes Luke 1 2 Check It Out 5 hour to drive to work. It hour to drive to work. How much longer does it take Luke to drive to work? = It takes Luke = 6 5 = 1 1 The LCM of the denominators is. Write equivalent fractions using the common denominator. Subtract. hour longer to drive to work.

21 Lesson Quizzes

22 Lesson Quiz Add or subtract. Write each answer in simplest form You need a nail to go through a 7 -inch door and extend an extra 1 8 inch. How long should the nail be? in. 8 1