Fractions: With Grid Model

~
U
NUlne.at••
Den.ln.nalo
v
Total number of objects (or pieces to be
shaded) we actually have
~ Number of equal pieces which a whole
or unit was originally divided into
,
~4
., I +~
4
., I ~
4
~ Number of pieces in one unit (pie cuts into 4 slices, 1 pie=1 unit)
4 /4 (1 unit or pie)
II
I
I
3/4
II
I
Want to
add 1/4 + 1/q.:
,-·r 1 1
I
You can see that 1/4 + 1/4 =2/4 or 1/2
F.action ••ithllletici When the denom inators are the same, add the numerators.
Adding the numerators gives the total number of
pieces. This number must be referenced to a
standard number of pieces needed to form a whole
.+.=
2
1+2
4
III _
.+.
1+2
I
=
4
2
; 1; +
; 1­
II
.. IN +
111 1. UI
II
..•
..
UI
II
!.
,.
..
w iN
E <1111..
+
II
,...g
••
,.
Adding A Salll.acling Unlille F.actions How can we aelel l /II anell/l?
• Relate to something that lI.eall easilp into thi.d o •
..ua.te. such a. foot, a clap, monep.
• Consicle, a foot (12 inches). 'I. of. f.ot is I inches
ana 1/1 of a foot is 4 inches
• 'ogethe., thep ..aile 7 inches, which i. 7/12 of a f •••
1 2
3
=1
1
2
1
- + 1
­
4
3
3
~/
Whole
4
!.m
4 \V
4
+ - =
12
12 Notice. 10 a .... the.e, Ihep ha" 10 be w.itlen with t he .anle whole! Addition of ',acllons with G,ld Model
1
2
1
3
+! 4
r- 31 -I
3
~
~~
T
1 ~ 1/4 ~1~
I
2I
I
.I -
I
•
3
I
4
L
I~
1 + 1
3
4
... ( ~
+~)
12 = (4+3) = ­7
12
I
·1
12 Note. The hatcheel .qua.e. (ove.lap) are common to each fraction anel
woulel therefo.e lie aeleleel twice.
Sarah and Cindy won the Math Project. Sarah worbed 3/8 hour on their project, and Cindy worbed 4/7 hour on the project. How much time did they wort? all together? 1
1
2_
2
345678
3
4
-+­
8
7
=
21
56
+
24
56
=
49
56
3
4
5
6
7
~ + ~ _21+24
56
-
56
--
49
56
Mibe libes to mat:?e healthy snact:?s. His recipe mixes 1/3
cups of mini-pretzels with 2/5 cups of yogurt-covered
cranberries. How much snacb does this recipe mabe?
1
2
\~
3
I
,
1
1
-
3
2
YT-~- - 1 -- - - 1
3
I
T
4
2
I"··~.
~
-~ ~
5
r- 3! -.\ Whole (..nil g.leI) =•• 5
~ + ~ .. ( ~ + ~ )
1~
= (5 + 6) = 11 1~
15 I. C.eate a J Itp 5 g.id and we define •• oa. Unil Grid.
2. Notice that the.e ••e II .m.11 .......e. in the Unil
Grill. The denomin.to•••how ... how to c.eate the
Unll Gri", while the n..me••tor••how ... how mach
of the Unit G.icl to .h.de.
J. One-third.
of the U"il Grid(5 'lIa••e.) h.ve been
.hacled with line. going f.om the bottom lef. to the
top right. ~
4. 'wo-fifth. of the Unil Grill( ........ e.) have Iteen
.h.ded with line. going f.om the top left to the
bottom .ight. ~
5. The total number of 'Claa,e. i. 5 + 6
=II, out
0' a unit
numDer of 15. In other words 10/15, is tile an.wer.
Thu•• 5/15 + 6/15=11/15, whichi. III + 2,1
jogged ~ of a mile on Saturday and ~ of a
P,actlce Hugo
mile on Sunday. Find the total distance he jogged on
those two days 1
2 3 4 5 6 7 123
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
5 + 6
8
7
-
4
567 o
..
I:
Which Is blgge. 2/10' 1/4! Relate the fractions to something that brea~s
easily into thirds or quarters such as a foot, a
day, or money.
• Consider a foot. ~ of a foot is 8 inches and
of a foot is 9 inches. (one foot =12 inches) • So, 9 inches exceeds 8 inches by 1 inch.
• Now, we can subtract the fractions
3 -2 -_ -9 .. -8
-4 3
12 12
-
1
­
12
l
Define a Unit Grid (whole) that is 4 by 3, so there are 12 equal squares. Find how many squares are represented by the two fractions and then subtract. Ignore the hatched squares completely, loobing only at the remaining squares.
3
2
1
2
3
4
3
-.
1
2
I
3
4
3 • 2
4
3
.. .
--12
-9
L
I"'"
8
12 I
~I
=(~ - ~ ) = (9 - 8) = 1
12
12 12
SlIbt.aet F.aetlen with Unlille Denealinato
Lily practices for a swim meet by warming up for ~ of an hour,
and swimming slow laps for
! of an hour. For how much longer
does Lily swim slow laps than swim her warm up?
2
1
3
4
5
1
6
1 ~~
2
W"~
...,
W~
3
IW"~
-.-
W"'~
4
IIU
i /fITi
3 _1
4 6
-
-18 _ -4
24 24
2
3
4
5
6
~
1
11
16
2
3
11
~
4
18 - 4
14
24
24
OR
7
12
Igno.e the hatched.qaa.e. completelp, looiling onlp at the .emainlng .qua.e••
15 - 1
24
14
24
OR
7
12 Mani runs the same route each day. It's ~ miles on River
Road, ; miles on BacR Street. How much farther does Mani
run on River Road than BacR Street? 1
1
2
3
4
5
1
1
2
2
3
3
4
4
5
5
6
6
5 Z
_
-
6 5
-.­
2
3
4
5
.....
•
II
•
II
•
.....
•
+
III
.....
.. n
..... ..•
II
.....
+
.....
..
..
.......• ....
... UI
.....
=
...... ~
-.J
a>
,I;a
~
N
-*
~
N
......
III
III
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o a
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