Multiplying Fractions with Whole Numbers

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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

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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

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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

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• 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

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Multiplying Fractions Notes

• Ex 2/3 x 1/4
• 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
• 6

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Multiplication of Fractions with a Picture Draw a
model representing 2/3 of 1/4 .
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Practice Problems

1. 2/3 x 1/4
2. 5/6 of 2/5
3. 1/3 9/10
4. 1/4 x 12

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Reducing Fractions to Simplest Form
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.
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Changing a Mixed Number to an Improper Fraction

• Write 6 ¼ as an improper fraction.
• Multiply the whole number by the denominator.
• 6 x 4 24.
• Add the numerator to this total.
• 24 1 25
• Write as an improper fraction.
• 25/4

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Multiplying Mixed Numbers Notes

• Ex 2 1/7 x 2 2/5
• Change to improper fractions.
• 15/7 x 12/5
• Simplify diagonally (cross simplify)
• /7 x 12/
• Multiply.
• 3/7 x 12/1
• Simplify again.
• 36/7

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Practice

1. 1 2/5 x 4 1/3
2. 2 6/7 1 2/5
3. 1 2/3 x 7 1/2

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Dividing Fractions Notes

• Ex 8 ? 4/5
• Find the reciprocal of the second number.
• The reciprocal of 4/5 is 5/4 .
• Just FLIP the second number.
• Change to multiplication and simplify diagonally
  if you can.
• 8/1 x 5/4
• Multiply.
• 2/1 x 5/1
• Simplify.
• 10/1

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Dividing Mixed Number Notes

• Ex 5 1/3 ? 2 2/5
• Write each mixed number as an improper fraction.
  
• 16/3 ? 12/5
• Find the reciprocal of the second number.
• The reciprocal of 12/5 is 5/12 .
• Change to multiplication and simplify diagonally
  if you can.
• 16/3 x 5/12
• Multiply.
• 4/3 x 5/3
• Simplify.
• 20/9

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• What is the reciprocal of each number?
• 9/7
• 5 2/3
• 8
• 1 6/7
• 1/23

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Practice

1. 3/8 ? 3
2. 7/8 ? 2/7
3. 2 1/2 ? 1 2/5

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Practice

• 4. 1 2/3 ? 1/2
• 5. 1 1/10 ? 1 5/6
• 6. 9/10 ? 3

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• 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