Adding Subtracting Fractions Adding Subtracting Fractions Objective 7

Adding & Subtracting Fractions

Adding & Subtracting Fractions Objective: 7. 1. 02 To develop fluency in +, – , x, and ÷ of nonnegative rational numbers. Essential Question: How can I add and subtract fractions with like and unlike denominators?

$Adding & Subtracting Fractions OLD Vocabulary: Simplest Form: the form of a fraction when$

Adding & Subtracting Fractions OLD Vocabulary: Simplest Form: the form of a fraction when the GCF of the numerator and denominator is 1. Like Fractions: two or more fractions with the same denominator. Unlike Fractions: two or more fractions with different denominators. Least Common Denominator: the least common multiple of the denominator of two or more fractions.

Adding & Subtracting Fractions Real World: The total rainfall Monday through Saturday was 3/8 of an inch. If another 4/8 of an inch of rain fell on Sunday, what was the total rainfall for the week? 7/ of an inch 8

Adding & Subtracting Fractions Real World: Mr. Williams ordered pizza for dinner. He ate 3/ of the pizza that night and 2/ of the pizza 8 6 for breakfast the next morning. How much of the pizza did he eat in all? 17 /24 of the pizza

Adding & Subtracting Fractions Rules: +/– Fractions w/ Like Denominators: (1) Find the sum or difference of the numerators; (2) The denominator stays the same (3) Simplify the fraction if possible. Example: 2 + 1 = 3 4 4 4 2 – 1 = 1 4 4 4

Adding & Subtracting Fractions Example #1: 3 8 + 2 8

Adding & Subtracting Fractions Example #1: 3 8 + 2 8 = 3+2 8

Adding & Subtracting Fractions Example #1: 3 8 + 2 8 = 3+2 = 5 8 8

Adding & Subtracting Fractions Example #1: 3 8 + 2 8 = 3+2 = 5 8 8 Example #1: (using models) +

Adding & Subtracting Fractions Example #1: 3 8 + 2 8 = 3+2 = 5 8 8 Example #1: (using models) + =

Adding & Subtracting Fractions Example #1: 3 8 + 2 8 = 3+2 = 5 8 8 Example #1: (using models) + = =

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 =

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 = 2+2 = 6

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 = 2+2 = 4 = 2 6 6 3

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 = 2+2 = 4 = 2 6 6 3 Example #2: (using models) + =

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 = 2+2 = 4 = 2 6 6 3 Example #2: (using models) + = or

Adding & Subtracting Fractions Example #2: 2 6 + 2 6 = 2+2 = 4 = 2 6 6 3 Example #2: (using models) + = or =

Adding & Subtracting Fractions Example #3: 4 5 + 4 = 5

Adding & Subtracting Fractions Example #3: 4 5 + 4 = 4+4 = 8 5 5 5

Adding & Subtracting Fractions Example #3: 4 5 + 4 = 4+4 = 8 = 5 5 5 1 3 5

Adding & Subtracting Fractions Example #3: 4 5 + 4 = 4+4 = 8 = 5 5 5 Example #3: (using models) + = 1 3 5

Adding & Subtracting Fractions Example #3: 4 5 + 4 = 4+4 = 8 = 5 5 5 Example #3: (using models) + = or 1 3 5

Adding & Subtracting Fractions Example #4: 3 8 – 2 8

Adding & Subtracting Fractions Example #4: 3 8 – 2 8 = 3– 2 8

Adding & Subtracting Fractions Example #4: 3 8 – 2 8 = 3– 2 = 1 8 8

Adding & Subtracting Fractions Example #4: 3 8 – 2 8 = 3– 2 = 1 8 8 Example #1: (using models) –

Adding & Subtracting Fractions Example #4: 3 8 – 2 8 = 3– 2 = 1 8 8 Example #1: (using models) – =

Adding & Subtracting Fractions Example #5: 4 7 – 2 7

Adding & Subtracting Fractions Example #5: 4 7 – 2 7 = 4– 2 7

Adding & Subtracting Fractions Example #5: 4 7 – 2 7 = 4– 2 = 2 7 7

Adding & Subtracting Fractions Example #5: 4 7 – 2 7 = 4– 2 = 2 7 7 Example #2: (using models) –

Adding & Subtracting Fractions Example #5: 4 7 – 2 7 = 4– 2 = 2 7 7 Example #2: (using models) – =

Adding & Subtracting Fractions Rules: +/– Fractions w/ Unlike Denominators: (1) Find the LCD of the fractions; (2) Rename each fraction using the LCD; (3) Find the sum or difference of the numerators and keep the denominator; (4) Simplify the answer if possible. Example: 2 + 1 = 5 4 3 6 2 – 1 = 1 4 3 6

Adding & Subtracting Fractions Real World: One week the rainfall from Monday through Saturday was 6/16 of an inch. If the total rainfall for the week was 11/16 of an inch, what was the rainfall for just Sunday? 5/ of an inch 16

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 1 6 +1 3

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 1 = 1 6 6 +1 3 x 2 =+2 6

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 1 = 1 6 6 +1 3 x 2 =+2 6 3 6

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 1 = 1 6 6 +1 3 x 2 =+2 6 3 6 = 1 2

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 +

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 = +

Adding & Subtracting Fractions Example #6: Find 1/6 + 1/3 = + = 3 1 = 6 2

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 8 9 +1 2

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 8 x 2 = 9 x 2 +1 2 x 9 =

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 8 x 2 = 16 9 x 2 18 +1 2 x 9 =+ 9 18

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 8 x 2 = 16 9 x 2 18 +1 2 x 9 =+ 9 18 25 18

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 8 x 2 = 16 9 x 2 18 +1 2 x 9 =+ 9 18 25 18 = 1 7 18

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 + 8/ 9 = 1/ 2

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 + 8/ 9 = 1/ 2 + 16/ 18 9/ 18

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 + 8/ 9 = 1/ 2 + 16/ 18 = 9/ 18

Adding & Subtracting Fractions Example #7: Find 8/9 + 1/2 + 8/ 9 = 1/ 2 + 16/ 18 = 9/ 18 1 7/ 18

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 3 4 – 2 8

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 3 x 2 = 4 x 2 – 2 8 =

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 3 x 2 = 6 4 x 2 8 – 2 8 = – 2 8

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 3 x 2 = 6 4 x 2 8 – 2 8 = – 2 8 4 8

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 3 x 2 = 6 4 x 2 8 – 2 8 = – 2 8 4 8 = 1 2

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 = – =

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 = –

Adding & Subtracting Fractions Example #8: Find 3/4 – 2/8 = – = 4 = 1 8 2

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 8 9 – 1 2

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 8 x 2 = 9 x 2 – 1 2 x 9 =

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 8 x 2 = 16 9 x 2 18 – 1 2 x 9 =– 9 18

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 8 x 2 = 16 9 x 2 18 – 1 2 x 9 =– 9 18 7 18

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 – 8/ 9 – 1/ 2

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 – 8/ 9 – = 1/ 2 = – 16/ 18 – 9/ 18

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 – 8/ 9 – = 1/ 2 = – 16/ 18 – = 9/ 18 =

Adding & Subtracting Fractions Example #9: Find 8/9 – 1/2 – 8/ 9 – = 1/ 2 = – 16/ 18 – = 9/ 18 = 7/ 18

Adding & Subtracting Fractions Rules: +/– Fractions w/ Like Denominators: (1) Find the sum or difference of the numerators and keep the denominator; (2) Simplify the answer if possible. Rules: +/– Fractions w/ Unlike Denominators: (1) Find the LCD of the fractions; (2) Rename each fraction using the LCD; (3) Find the sum or difference of the numerators and keep the denominator; (4) Simplify the answer if possible.

Adding & Subtracting Fractions HOMEWORK