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Transcript of Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture...
![Page 1: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/1.jpg)
Multiplying Fractions with Whole Numbers
• Example: 3/8 of 40
•“of” = multiply • Method #1: Picture • Method #2: Put the whole
number over 1 and then simplify and multiply
![Page 2: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/2.jpg)
Picture Method
• 4/8 of 64
• The picture is worth the whole number
• Divide the picture up into the amount of pieces
• Label each piece
• Shade in the amount of pieces
• Total the amount of pieces
![Page 3: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/3.jpg)
Math Method
• 1) Put the whole number over 1 (make it a fraction)
• 2) Cross simplify/reduce: divide out a common factor from the numbers across
• 3) Re-write the problem• 4) Multiply the numerators• 5) Multiply the denominators • 6) Reduce
![Page 4: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/4.jpg)
• In multiplication, “of” = multiply •So, 2/3 of 4/6 means 2/3 x 4/6
•Simplifying before Multiplying Fractions:–Cross Simplify: Divide out a common factor from the numbers across
![Page 5: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/5.jpg)
Multiplying Fractions Notes
Ex: 2/3 x 1/4 1.Cross reduce/simplify 1/3 x 1/2
2.Multiply the numerators, and then multiply the denominators.• 1 x 1 =
3 x 2 =3.Simplify if possible.• 1 6http://www.xpmath.com/forums/arcade.php?do=play&gameid=29
![Page 6: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/6.jpg)
Multiplication of Fractions with a Picture
Draw a model representing 2/3 of 1/4 .
![Page 7: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/7.jpg)
1.2/3 x 1/4 =
2.5/6 of 2/5 =
3.1/3 · 9/10 =
4.1/4 x 12 =
Practice Problems:
![Page 8: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/8.jpg)
Simplest Form: when the only common factor of the numerator and denominator is 1. Ex: 2/3 is in simplest form since 2 and 3
have only 1 as a common factor.
Write 20/25 in simplest form .
20: 1, 2, 4, 5, 10, 20 25: 1, 5, 25
20/25 = 4/5
List the factors for the numerator and denominator
and find the GCF Divide the numerator and denominator by the GCF
The fraction 20/25 written in simplest form is 4/5.
Reducing Fractions to Simplest Form
![Page 9: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/9.jpg)
Changing a Mixed Number to an Improper Fraction
Write 6 ¼ as an improper fraction.
1.Multiply the whole number by the denominator.• 6 x 4 = 24.
2.Add the numerator to this total.• 24 + 1 = 25
3.Write as an improper fraction.• 25/4
http://www.xpmath.com/forums/arcade.php?do=play&gameid=37
![Page 10: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/10.jpg)
Multiplying Mixed Numbers NotesEx: 2 1/7 x 2 2/5
1.Change to improper fractions.• 15/7 x 12/5
2.Simplify diagonally (cross simplify)• /7 x 12/
3.Multiply.• 3/7 x 12/1 =
4.Simplify again.• 36/7 =
![Page 11: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/11.jpg)
1.1 2/5 x 4 1/3 =
2.2 6/7 · 1 2/5 =
3.1 2/3 x 7 1/2 =
Practice:
![Page 12: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/12.jpg)
Dividing Fractions NotesEx: 8 4/5
1.Find the reciprocal of the second number. • The reciprocal of 4/5 is 5/4 .• Just FLIP the second number.
2.Change to multiplication and simplify diagonally if you can. • 8/1 x 5/4
3.Multiply.• 2/1 x 5/1 =
4.Simplify.• 10/1 =http://www.xpmath.com/forums/arcade.php?do=play&gameid=28
![Page 13: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/13.jpg)
Dividing Mixed Number NotesEx: 5 1/3 2 2/5
1. Write each mixed number as an improper fraction. • 16/3 12/5
2. Find the reciprocal of the second number.• The reciprocal of 12/5 is 5/12 .
3. Change to multiplication and simplify diagonally if you can. • 16/3 x 5/12
4. Multiply.• 4/3 x 5/3 =
5. Simplify.• 20/9 =
![Page 14: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/14.jpg)
What is the reciprocal of each number?
• 9/7
• 5 2/3
• 8
• 1 6/7
• 1/23
![Page 15: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/15.jpg)
1.3/8 3 =
2.7/8 2/7 =
3.2 1/2 1 2/5 =
Practice
![Page 16: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/16.jpg)
4. 1 2/3 1/2 =
5. 1 1/10 1 5/6
6. 9/10 3
Practice
![Page 17: Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify.](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d975503460f94a810bc/html5/thumbnails/17.jpg)
Find each quotient.
• 6 2/5
• 2/5 3/4
• 9/10 3
• 6 1/4 2 1/2
• 1 1/10 1 5/6