Recognize Fractions
1. Write two fractions for each picture: the colored part and the white part.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
How to draw pie models
Thirds: draw lines
at 12 o'clock, 4
o'clock, and 8
o'clock.
Sixths: First draw
thirds, then split
those
Fifths: First draw a line at 12
o'clock. Then draw as a man
doing jumping jacks.
Eighths: First
draw fourths,
then split those.
2. Divide the circle into fractions and color the right amount the illustrate the fraction.
a.
1
2
b.
2
5
c.
1
6
d.
3
5
e.
2
3
f.
1
8
g.
1
4
h.
6
8
i.
4
5
j.
3
8
k.
1
3
l.
4
4
6
Fractions
1. Color parts. Write the colored part and the white part as fractions.
a. Color 1 part.
1
b. Color 5 parts.
c. Color 8 parts.
d. Color 3 parts.
and
and
and
and
12
2. Write one whole as a fraction.
|—|—|—|—|—|
b. 1 =
a. 1 =
c. 1 =
e. 1 =
d. 1 =
3.
a. The Jackson's ate
3
of the pie.
4
b. Jerry ate
How much is left?
1
of the cake.
6
How much is left?
c. Five boys shared a chocolate bar equally. So, each one got
of the bar.
4. Color. Write an addition sentence, adding the colored and white parts. What is the sum?
a. Color 1 part.
1
6
+
b. Color 10 parts.
c. Color 3 parts.
d. Color 15 parts.
=
5. What is missing from 1 whole?
a.
3
4
+
=1
b.
1
8
+
=1
c.
7
40
100
+
=1
d.
+
56
100
=1
Fractions
1. Mark on this number line the following fractions:
1 1 1 1 3 5 2 5
, , , , , , ,
4 2 6 3 4 12 3 6
2. Draw pictures to illustrate these fractions, and write them as mixed numbers.
a.
10
6
12
7
b.
c.
18
5
3. Draw pictures to illustrate these addition problems.
a.
6
7
+ =
8
8
b. 1
1
5
+
6
6
c. 1
8
5
+1
9
9
4. Draw pictures to illustrate these equivalent fractions.
=
a.
1
2
=
b.
3
4
=
c.
12
2
3
=
6
2
5
d.
=
10
5. Compare mentally, without changing to equivalent fractions. Notice the similarities!
a.
1
5
1
10
e.
1
15
7
15
i.
1
2
16
20
b.
1
120
1
75
f.
72
80
71
80
j.
6
15
1
2
c.
4
7
4
9
g.
20
2000
2
2000
k.
1
2
4
9
d.
15
65
15
34
h.
540
300
450
300
l.
7
13
1
2
8
Mixed Numbers
1. Write what mixed numbers the pictures illustrate.
a.
b.
c.
d.
e.
f.
g.
h.
2. Find matching pairs.
1
3
4
9
4
1
1
8
7
4
2
1
4
11
8
1
3
8
9
8
3. Draw pictures to illustrate these mixed numbers.
a. 1
1
2
b. 2
2
3
c. 2
9
3
4
Mixed Numbers
1. Draw the mixed numbers.
a. 1
3
b. 1
4
d. 4
1
c. 2
8
2
e. 3
3
1
6
3
8
2. Color. Add the colored parts and white parts. Write one addition sentence using fractions,
another using mixed numbers. What is the sum?
a. Color 5 parts.
5
4
1
1
4
+
+
3
4
3
4
=
b. Color 4 parts.
c. Color 8 parts.
d. Color 5 parts.
8
4
= 2
3. Write whole numbers as fractions.
a. 2 =
c.
b.
4. Answer.
a. Jack had 2 granola bars. He and his
friends ate 1
1
2
b. A 5-inch pencil is cut into 2 equal
pieces. How long are the pieces?
of them. How much is left?
c. A measuring cup can hold 2 cups when full. Jill poured
1 1/4 cups of water into it. How much will still fit?
5. What is missing from the next whole number?
a. 1
1
+
4
=2
b. 1
2
+
10
=2
c. 3
10
4
+
10
=
d. 5
1
+
5
=
Fractions to Mixed Numbers
1. Write as mixed numbers.
6
=
5
a.
8
=
5
9
=
5
b.
8
=
6
11
=
6
9
=
6
c.
12
=
10
1
2
1
d. 5
14
=
10
16
=
10
19
=
10
2. Write as fractions or mixed numbers.
5
4
fraction
7
5
4
3
8
7
11
7
14
10
14
12
10
6
mixed
number
1
2
10
1
3
5
2
6
1
e. 4
11
=
6
e.
14
1
2
3
3. Rename the fractional part. Write as mixed numbers.
a. 1
5
1
=2
4
4
b. 3
3
=
2
13
=
12
c. 2
4. Add. Rename the result if needed.
a.
+
3
4
2
1
4
1
2
b.
+
6
8
7
2
8
3
c.
+
3
5
4
2
5
7
d.
+
6
10
8
5
10
2
+
6
9
5
3
9
5
1
=3
4
4
5. Solve the word problems.
a. Two sides of a rectangle are 2 1/4 inches
and 3 1/4 inches.
What is its perimeter?
b. Each side of a triangle is 2 3/8 inches.
What is its perimeter?
c. A movie lasted 1 3/4 hours and a meal
afterwards took 1 1/4 hours. How much
time did these take in total?
d. Baby blocks are 1 1/8 in. tall.
How tall is a stack of ten of them?
11
1
7
12
Fractions and Mixed Numbers
1. Write the fractions as mixed numbers. Draw a picture in c.
a.
11
6
b.
16
7
c.
17
10
2. Draw a picture of these mixed numbers. Write them as fractions, too.
3
4
a. 1
b. 1
3
12
c. 2
4
9
3. Shade parts, and add to make the next whole number.
a. 1
2
+
5
=2
b. 2
1
+
5
=
c. 1
6
+
10
=
d. 2
2
+
7
=
4. Add to make the next whole number.
a.
7
+
9
e. 2
i. 6
=
2
+
12
3
+
11
=
c.
f. 1
3
+
10
=
g. 5
j. 7
3
1
+ +
9
9
b.
=
6
4
+ +
12 12
=
=
8
+
12
=
d.
5
+
6
=
h. 3
k. 10
2
1
+ +
6
6
=
6
+
7
=
2
+
5
=
l. 4
3
5
+ +
11 11
7
11
5
=
5. Change the fractions to mixed numbers and vice versa.
Fraction
5
4
13
4
7
5
21
5
13
8
9
6
34
10
43
11
Mixed
Number
1
12
1
3
4
1
3
2
2
9
4
5
12
2
5
8
8
5
10
Equivalent Fractions
1. Write the fractions under the pictures. Remember the = sign too.
=
a.
1
3
=
=
2
6
=
b.
c.
=
d.
2. Look at the pictures, and connect those fractions that show the same amount with a line.
Write the name of each fraction beside it.
1
2
3. Split all the pieces (both the colored and uncolored ones). Write the equivalent fractions.
a. Split all pieces
two ways.
b. Split all pieces
three ways.
=
2
5
=
d. Split all pieces
two ways.
c. Split all pieces
two ways.
=
=
1
2
=
e. Split all pieces
three ways.
2
3
=
f. Split all pieces
two ways.
=
=
=
=
=
=
13
Equivalent Fractions
1. Halves and fourths. Write the numbers that have halves with fourths instead, and vice versa.
2
=
4
1
1
=
2
2
2
=
4
5
1
=
2
3
=
2
6
=
4
2. Thirds and sixths. Write the numbers that have thirds with sixths instead, and vice versa.
1
=
3
2
=
3
2
1
=
3
5
4
=
6
4
2
=
6
4
=
3
3. Fifths and tenths. Write the numbers that have fifths with tenths instead, and vice versa.
2
=
10
2
=
5
4
=
5
1
6
=
10
3
3
=
5
8
=
10
4. Halves, fourths, and eights. Convert. Shade the pictures.
=
1
4
a.
=
=
1
2
b.
=
=
6
8
c.
=
=
1
2
d.
=
5. Thirds, sixths, and twelfths. Convert. Shade the pictures.
=
2
3
a.
=
=
10
12
b.
=
=
1
3
c.
=
=
8
12
d.
=
6. So where do you need to know equivalent fractions? When you add fractions that have
different sized parts. Try these problems - use your work in exercises 1-5 as help.
a.
1
2
+
1
4
=
1
3
+
1
6
=
1
2
+
2
4
=
1
3
+
2
6
1
2
+
3
4
=
1
3
+
3
6
b.
1
4
+
1
8
=
=
1
4
+
3
8
=
1
4
+
5
8
c.
14
1
5
+
1
10
=
=
1
5
+
3
10
=
=
1
5
+
7
10
=
d.
Equivalent Fractions 1
1. Shade parts to show the fractions. Split the pieces further in the second picture.
=
1
4
a.
=
=
b.
8
1
2
=
3
5
e.
=
=
e.
8
2
3
=
=
=
f.
1
2
1
2
d.
6
=
=
g.
Split each piece into
five new pieces.
Split each piece into
two new pieces.
=
1
3
=
12
=
3
4
h.
=
Split each piece into
three new pieces.
=
Split each piece into
three new pieces.
2. Write the equivalent fraction. Split each piece...
a. ...into three
new pieces.
b. ...into two
new pieces.
c. ...into six
new pieces.
d. ...into four
new pieces.
e. ...into five
new pieces.
3
=
4
5
=
6
1
=
2
2
=
3
1
=
2
f. ... into six
new pieces.
g. ... into five
new pieces.
h. ... into ten
new pieces.
i. ... into three
new pieces.
j. ... into three
new pieces.
2
=
3
1
=
3
1
=
2
3
=
3
1
=
6
3. Think: How many new pieces is each piece split into?
a.
1
=
2
6
b.
2
=
3
6
c.
2
4
=
5
d.
3
=
4
8
e.
3
=
4
16
f.
1
5
=
3
g.
2
6
=
6
h.
4
=
5
20
i.
1
5
=
4
j.
1
8
=
2
4. Write chains of equivalent fractions.
1
=
2
4
1
=
1
2
=
=
6
3
=
=
=
=
=
=
=
=
=
=
15
Equivalent Fractions 2
1. Write equivalent fractions in each box.
c.
d.
e.
f.
3
10
7
20
9
6
3
4
40
40
12
24
18
50
60
24
48
40
21
80
80
36
96
70
30
100
100
54
100
a.
b.
3
5
4
3
15
9
25
2
2
2. Write the letters in the boxes that correspond to the equivalent fractions.
What message will you receive?
10
45
36
81
4
8
75
100
70
100
20
40
50
60
14
80
20
75
5
10
30
100
21
49
4
18
8
30
40
72
14
20
15
18
7
14
28
63
10
20
12
27
10
25
21
30
8
20
!
Key:
A
C
E
F
I
L
N
O
R
S
T
Y
1
2
3
4
7
10
2
9
3
10
2
5
5
9
3
7
4
9
5
6
4
15
7
40
16
Equivalent Fractions / LCM
1. Draw two other number lines under this one, one with thirds, the other with 24th parts.
Illustrate with your number lines that:
a.
2
=
3
12
b.
5
=
12
24
2. Write the equivalent fractions.
1
=
8
48
a.
b.
2
=
7
42
c.
9
=
11
110
d.
5
=
14
56
8
=
13
39
e.
f.
5
=
12
60
3. Jerry and Mark worked it so the fractions have the same denominator. Fill in.
3
10
a. Jerry just multiplied
10 and 14 to find a
common
denominator _____.
42
and
and
5
14
3
10
b. Mark used the
LCM of 10 and 14
(which is _____)
as a common
denominator.
50
21
and
and
5
14
25
Who is right, or both? _____________________________________.
The main advantage of using the LCM is that it makes further calculations easier.
4. Convert the fractions so they have a same denominator. Then write < or > between them.
a.
2
8
and
3
14
b.
2
9
and
4
15
2
10
c.
and
3
15
d.
5
12
and
7
16
5. Jenny used the LCM as the common denominator, and Nancy did not. Explain if the answers
are the same, or not, and why.
5
7
+
12
10
Nancy:
=
120
+
120
5
7
+
12
10
Jenny:
=
=
120
17
60
+
60
=
60
Compare Fractions
1. Draw the fraction and compare. Write > or < or = .
a.
b.
2
3
1
3
d.
c.
1
5
4
5
e.
6
8
7
8
g.
3
8
5
9
1
6
4
4
2
4
6
10
7
10
f.
1
8
h.
1
9
3
6
i.
5
12
3
12
What do you notice about comparing two fractions when the denominators are the same?
_______________________________________________________________________
2. Draw the fractions and compare them. Write > or < or = .
a.
b.
1
2
1
3
d.
c.
1
5
1
8
e.
3
6
3
8
1
6
1
2
4
8
4
5
f.
2
4
2
3
What can you notice about comparing two fractions when the numerators are the same?
_______________________________________________________________________
18
Comparing Fractions
1. Same kind of parts. Draw the fractions and compare.
3
4
a.
1
4
b.
3
8
7
8
2
6
c.
5
6
d.
7
12
6
12
2. Same amount of parts. Draw the fractions and compare.
1
2
a.
1
3
b.
2
6
2
8
c.
3
5
3
3
d.
5
10
5
12
3. Compare to one half. Write <, >, or = .
a.
1
2
2
3
b.
1
2
3
7
c.
3
6
1
2
d.
3
4
1
2
e.
1
2
7
12
f.
1
2
2
5
g.
5
10
1
2
h.
4
10
1
2
4. Same kinds of parts - or same amount of parts - or comparing to 1/2? Write < , > , or = .
a.
1
7
3
7
b.
1
2
5
6
c.
4
5
1
2
d.
3
6
3
4
e.
2
8
2
4
f.
5
12
3
12
g.
5
12
5
6
h.
4
5
1
5
i.
1
2
3
4
j.
1
2
2
7
b.
4
4
6
9
c.
6
5
2
2
d.
5
3
10
10
e.
7
8
3
3
5. Compare to one.
a.
5
7
3
3
19
Comparing Fractions
1. Write <, >, or = between the fractions. Note if they have the same denominator,
or same numerator, or if it is comparing to 1/2.
a.
1
7
1
2
b.
2
2
5
6
c.
4
5
4
9
d.
3
5
3
12
e.
1
8
1
4
f.
1
2
4
12
g.
3
8
1
2
h.
3
5
3
4
i.
1
2
3
4
j.
2
9
2
7
2. Draw and compare when fractions have a different denominator.
a.
b.
3
4
c.
1
2
1
4
d.
3
8
5
6
2
3
8
12
2
3
3. Convert to equivalent fractions so the fractions have a common denominator. Then compare.
a.
5
8
3
4
?
5
8
7
12
f.
b.
9
12
?
3
4
c.
5
6
?
3
4
d.
5
9
?
2
3
e.
2
3
?
5
6
g.
2
3
?
8
12
h.
1
5
?
3
10
i.
1
3
?
2
9
j.
1
3
?
3
12
e.
1
10
6
8
?
3
4
4. Find the equivalent fraction when denominator is 100.
a.
1
=
2
100
b.
3
=
10
100
c.
6
=
10
100
d.
1
=
4
100
e.
1
=
5
100
f.
2
=
10
100
g.
3
=
4
100
h.
2
=
5
100
7
10
75
100
5. Compare with hundredth parts.
a.
1
2
40
100
b.
6
10
42
100
c.
20
d.
1
4
23
100
9
100