Download Multiplication of Fractions

Multiplication of Fractions
Fractions can be interpreted as:
 Part of a whole. 3 slices out of a 4 slice pizza=3/4 of the pizza
 Part of a set. 3 students play a sport out of 4 students in the
class = ¾ of the class
 A particular point between two whole numbers on a number
line.
0
3/4
1
2
 A division expression (numerator divided by denominator).
3 boxes of cookies shared evenly among 4 people. 3 boxes
divided by 4 people results in each person getting ¾ of a box.
To find a fraction of a number: (EX: Find
2
of 36)
3
 Divide the whole number by the denominator (36 ÷ 3 = 12)
Multiply the quotient by the numerator (12 • 2 = 24)
2
of 36 is 24
3
OR
 Multiply the numerator by the whole number (2 • 36 = 72)
Divide the product by the denominator (72 ÷ 3 = 24)
2
of 36 is 24
3
 Finding a fraction of a number is the SAME as multiplying a
fraction by a number:
2
2
of 36 = • 36
3
3
To estimate products:
 Multiplying a given number by a number less than 1 results in a
product less than the original number. Multiplying by a number less than
1 means you are finding a part of the given number, so the product will be less than the
given number.
 Multiplying a given number by a number greater than 1 results
in a product greater than the original number. Multiplying by a
number greater than 1 means you are finding more than one group of the given number,
so the product will be more than the given number.
 Any number multiplied by 1 is equal to the original number.
Area model for multiplication:
 Use a grid to model a rectangle with the side lengths equal to
the 2 numbers you are multiplying.
 EX: 3
2
•8
3
Divide the 4th row into thirds and shade in 3 and 2/3 rows.
Count the total unit squares. 3 rows of 8 is 24 unit squares, and 8
columns of 2/3 is
16
1
1
1
or 5 . 24 + 5 = 29
3
3
3
3
Multiplying Fractions:
 Multiply straight across: Numerator • Numerator and
Denominator • Denominator
 Simplify before you multiply to make it easier to get…
the product in lowest terms, so try not to forget!
Multiplying by Mixed Numbers:
 Method 1: Convert mixed numbers to improper fractions,
simplify then multiply.
 Method 2: Use the distributive property. Multiply by the
whole number, then multiply by the fraction, then add the
products together.
1
3
 EX: 4 • 5 = 4 • 5 + 4 •
1
4
1
1
= 20 + = 20 + 1 = 21
3
3
3
3
DIVISION OF FRACTIONS
Change all mixed numbers to improper fractions first!
 Keep the first fraction
 Change divide to multiply
 Flip the second fraction (if it’s a whole number remember to
write it with a denominator of 1).
 Follow rules for multiplication!
To divide fractions,
You keep the first fraction.
Change divide to multiply and flip the second one.
Simplify then Multiply.
Then shout, “Hooray, this is fun!”
Remember to check your work and now you are done!