Transcript Mixed Numbers and Improper Fractions

MIXED NUMBERS AND
IMPROPER FRACTIONS
• NS 2.1 Solve problems involving addition, subtraction,
multiplication, and division of positive fractions and
explain why a particular operation was used for a given
situation.
• Today’s objective: learn how to convert between mixed
numbers and improper fractions
• Learning target: Convert at least 3 of the 4 mixed
numbers and improper fractions correctly on the exit
ticket.
• What is a
mixed
number?
• A number with an
integer and a proper
fraction.
• Examples:
• Non-examples:
• What is an
improper
fraction?
• A fraction whose
numerator is greater
than the denominator.
• Examples:
• Non-examples:
• When is it
useful to use
mixed
numbers?
• When is it
useful to use
improper
fractions?
• When you need to see
how many whole parts
there are.
• When we are
multiplying or dividing
two amounts.
• How do we
convert
mixed
numbers
into
improper
fractions?
• Let’s slice up all 4 wholes into 8 pieces each to match the
fraction at the end.
• How many pieces do we have now?
• The 4 wholes each became 8 pieces, so there are
4×8 = 32 pieces from those. Then add the 7 pieces we
started with: 32 + 7 = 39 pieces. It still takes 8 pieces to
form a whole circle, so the denominator remains 8.
• How do we
convert
mixed
numbers
into
improper
fractions?
• Multiply the
denominator by the
whole number and
add the numerator to
get the new
numerator. The
denominator remains
the same.
• Convert into
improper
fractions:
• How do we
convert
improper
fractions into
mixed
numbers?
• How many wholes can we make out of these
pieces?
• Since the denominator is 4, we need 4 pieces to
form one whole. To find how many groups of 4 there
are in 13, do the long division:
• We can form 3 whole circles and will have 1 out of
the 4 pieces required to make another circle.
• How do we
convert
improper
fractions into
mixed
numbers?
• Divide the numerator
by the denominator.
The quotient is the
whole number, the
remainder is the new
numerator, and the
denominator remains
the same.
• Convert into
mixed
numbers:
Direct Station
• We will do word problems that involve real-life situations
that require converting between mixed numbers and
improper fractions.
Collaborative Station
• We will play the card game “War” in which each player
flips over a card and whoever’s number is greater adds
both cards to the bottom of their deck.
• Write down the work showing how you figured out whose
number was greater.
• The goal is to get all of the cards in your deck.
Collaborative Station Example
• The cards are evenly divided between Partners A and B.
•
•
•
•
They each hold their decks face down.
Both partners flip over the top card of their deck. Partner
A’s card is 7/2 and Partner B’s card is 4 1/2.
The partners calculate that 7/2 = 3 ½ OR The partners
calculate that 4 ½ = 9/2.
Partner B’s card is worth more so he puts both cards on
the bottom of the deck.
If for one round you compared by turning the mixed
number into an improper fraction, for the next round turn
the improper fraction into a mixed number instead.
Independent Station
• We are continuing ST Math’s unit on fraction addition and
subtraction.
• Make sure you are writing down your calculations.