Grade 5Math

- Fractions

Name Number Class Group

Equivalent Fractions and Simplest Form
Equivalent fractions are fractions that represent the same number, even if they
look different. Let us see an example:

𝟏 𝟐 𝟑 𝟒 𝟓
= = = =
𝟐 𝟒 𝟔 𝟖 𝟏𝟎
𝐱𝟐
𝐱𝟐 𝐱𝟑
𝐱𝟒 𝐱𝟓
𝐱𝟑
𝐱𝟒 𝐱𝟓

𝟏
𝟐
In Class:
4
Four-sixths ( ) of the twelve (12) members of the art club decorated the cafeteria
6
for Chuseok.

2
Did two-thirds ( ) of the group members help? How many members helped?
3

_____________________________________________________________________________________________________________________

2
Write two equivalent fractions for .
3

_____________________________________________________________________________________________________________________

Method 1: Number Lines Method 2: Multiplication Method 3: Division

0 1 Find the number to multiply the Find the number to divide the
denominator by. If it is possible denominator by.
0 1 2 3 4 5 6 to multiply them, then they are If it is possible to divide them,
equivalent fractions. then they are equivalent
6 6 6 6 6 6 6
fractions.
0 1 x2 /2 /2

0 2 4 6 8 10 12 4 8 8 4 2
12 12 12 12 12 12 12 6 12 12 6 3

x2 /2 /2
0 1 4 8 2 4 8
and are , , and are
6 12 3 6 12
0 1 2 3
3 3 3 3 equivalent fractions. equivalent fractions. 1
Equivalent Fractions and Simplest Form
In Class:
Fill in the denominator or the numerator.

1 22 6 12 96 24
A. = D. = G. 20
= J.
100
=
2 4 46 23

1 4 20
B.
7
= E.
9
=
H. 3
= K. =
15 30 15 45 25 5

10 1 4 2
4 5 1 I. = L. =
C. = F. 15
= 60 12
14 7

Homework:

32 2 10 6 96
M. = P. = S. = V. =
48 12 3 16 8 100 25

1 25 3 18
N. = Q. = 25 40
5 7 T. = W. =
32 64 120 3

4 8 5 9 1
O. = R. = 11 X. =
19 30 6 U. = 27
33 99

In Class:
A class of 27 students ordered 3 pizzas cut into 36 pieces each.

Y. How many slices can each student have?

_________________________________________________________________________________________________________________ 2
 Equivalent Fractions and Simplest Form
Simplest Form
A fraction is in simplest form when the GCF of its numerator and denominator is 1.

Method 1 Method 2
You can divide the numerator and the Cancel the common factors.
denominator by the GCF of the numbers. Write the prime factorization of the numerator
12 = 2 x 2 x 3 /6 and denominator. Then, cancel the common
18 = 2 x 3 x 3 factors.
12 2
GCF of 12 and 18 18 3 12 𝟐𝒙𝟐𝒙𝟑 2
is 2 x 3 = 6 /6 = =
18 𝟐𝒙𝟑𝒙𝟑 3

In Class:
Reduce the fractions to their simplest forms, and circle the fractions that
cannot be simplified.

36 8 68 24
Z. = DD. = HH. = LL. =
40 110 70 72

95 30 85 25
AA. = EE. = II. = MM. =
100 40 70 20

7 21 36 88
BB. = FF. = JJ. = NN. =
15 14 37 96

50 25 7 24
CC. = GG.
32
= KK.
77
= OO. =
45 25

Homework:
6
PP. Six-sixteenths ( ) of the sixteen (16) lions ate lunch at the Cincinnati Zoo.
16

3
Did of the lions eat their lunch?
8

_____________________________________________________________________________________________________________________
3
Write three (3) equivalent fractions for .
8
__________________________________________________________________________________________________________________ 3
Relate Fractions, Mixed Numbers, and Decimals

Remember: a fraction is a number with a numerator on top of a line over a denominator.

𝟏
Here is an example: 𝟐.

Remember: a mixed number is a number with a whole number and a fraction mixed.
𝟏
Here is an example: 1𝟐.

Remember: a decimal is a number with a period separating one number from another. Here is
the same example written in decimal form: 1.5.

In Class:
A survey found that 0.2 of the visitors to Korea visited Gyeongbokgung Palace. Another survey
2
taken years later found that 5 of the visitors to Korea visited Gyeongbokgung Palace. Did these
two surveys have the same results?

Fraction to Decimal
There are two methods to turn a fraction into a decimal.

Method 1 Method 2
Divide the numerator by the denominator. Find an equivalent fraction that has a number
2/5 divisible by 10 in the denominator.
5 cannot go into 2, so we start by adding a 0. 2
0. To make into , we need to multiply it by 2.
5 10
5 2
We then can add a zero to the 2, making 20. 2𝑥2 4
0. = 10 = 4/10 = 0.4
2𝑥5
5 20
20/5 is 4, so we add a 4 to the top.

0.4
5 20
2 4
The answer is 0.4, , or
5 10

In Class:

2
Are 0.2 and 5 the same number?

_____________________________________________________________________________________________________________________

4
 Relate Fractions, Mixed Numbers, and Decimals
In Class:
Write each decimal as a fraction or mixed number in simplest form.

A. 0.2 = C. 0.68 = E. 0.5 = G. 0.88 = I. 7.77=

B. 9.18 = D. 3.75 = F. 1.23 = H. 4.82 = J. 0.21 =

In Class:
Write each fraction or mixed number as a decimal.

25 82 9
K. 50
=__________ P. 3 100 =________ U. 6 10 =________

95 7 85
L. 1 100 =________ Q. 10
=__________ V.
100
=_________

7 30 24
M. 2 25 =_________ R. 50
=__________ W.
50
=__________

88 19 15
N. =_________ S. 1 100 =________ X. 7 =_________
100 20

10 69 77
O. 25
=__________ T. 100
=_________ Y.
100
=_________

Homework:

1
Z. Susan bought a bag of marbles. The bag contained 32kg of
marbles. She used 1.75kg of marbles for a craft project. How
many kilograms of marbles are left in the bag?

___________________________________________________
5
Compare and Order Fractions and Decimals
Fractions that have the same denominator are said to have a common denominator.
3 5
Here is an example: and . Both fractions have the same denominator. When two
8 8
fractions have a common denominator, comparing them is easy. 5 is bigger than 3,
5 3
thus is bigger than . What if the two fractions have different denominators?
8 8
𝟓 𝟓
Compare and .
𝟔 𝟖

Method 1: Common Method 2: Distance Method 3: Benchmark

Denominator The number with the Which one is closer to 1 or
First find the LCM of the smallest denominator is ½?
denominators. Then, use the usually the number
common denominator and that is the biggest. 5 6
multiply the numerators.
is close to , which is
6 6
Which number is bigger? close to 1.
x4 x3

5 20 15 5 5 4
is close to , which is
6 24 24 8 8 8
x4 x3
close to ½ .
Simplest form
𝟐𝟎 𝟏𝟓 𝟓 𝟓 5 5 5 5
>  > > >
𝟐𝟒 𝟐𝟒 𝟔 𝟖 6 8 6 8

In Class:
Compare the following numbers. Use >, <, or = to compare the numbers.

1 3 1 1
A. 2 4
D. 15 1.5 G. 14 1.25

7 9 3 1
B. 10
0.7 E.
15 5
H. 2.45 2
2

2 7 2 1
C. 0.35 5
F. I. 0.2 5
10 3
6
Compare and Order Fractions and Decimals
Homework:
Write the numbers from highest to lowest.

1 3 7 2 3 9
J. 3
, 0.2 ,
4
K. 1
10
, 1.25 , 1.4 L. 2.5 , 2 , 2
5 10
M. 10
, 0.8 , 0.75

=_______________________ =_______________________ =_______________________ =_______________________

Homework:
5
N. Samuel used kg of clay to make a sculpture.
8
2
Then, Nicholas used kg of clay to make a sculpture.
3
1
Finally, Christian used kg of clay to make a sculpture.
2

Who used the most clay? _____________________________________

Who used the least clay? _____________________________________

Challenge:
3
O. Samuel, Nicholas, and Christian had a pizza party. Samuel ate of the
10
1 2
pizza, Nicholas ate of the pizza, and Christian ate of the pizza.
5 4

Who ate the most pizza? __________________________________________

Who ate the least pizza? ___________________________________________

7
Add Fractions With Different Denominators
Adding fractions with different denominators is difficult, but if we follow the same
rules for comparing fractions, we see that it is not as difficult as it seems. Let us see
an example.
1 3
Tim has cup of kimchi, while Aidan has cup of kimchi. They want to add their cups
4 8
of kimchi together to make some. How much kimchi do they have now?
To add fractions with different denominators, you need to make the denominators
the same by finding the least common denominator (LCD). Remember, multiply
both the numerator and the denominator.
1 3
In our example, when we compare with , we need to find the least common
4 8
denominator between 4 and 8, which would be 8. What do we have to do now?
1 2 2 3
First, we take and multiply it by . This gives us . Then, we take and multiply it by
4 2 8 8
1 3 2 3
. This gives us . Finally, we add and . Remember, the denominator STAYS THE
1 8 8 8
5
SAME when we add fractions. This gives us a total of .
8
5
Tim and Aidan now have cup of kimchi.
8

Method 1 for Equivalent Denominators

Step 1: Find the least Step 2: Use the LCD to find Step 3: Add the fractions, and
common multiple (LCM) of the equivalent fractions. then simplify.
the denominators. This is the x3 x2
least common denominator 21 10 31
7 21 10 5 + =
(LCD). 24 24 24
8: 8, 16, 24, 32 8 24 24 12
31 24 7 7
12: 12, 24, 36 x3 x2 = + =1
24 24 24 24
The LCD of the fractions is 24.

Method 2 for Equivalent Denominators

Step 1: Write the fractions. Step 2: Multiply one Step 3: Add together and
denominator by the other. simplify.
7 5 x12 x8
+ 84
+
40
=
124
=1+
28
8 12 7 84 40 5 96 96 96 96
8 96 96 12
Simplify
x12 x8
28 4 7
1( / ) =1
96 4 24 8
Add Fractions With Different Denominators
In Class:
Solve the problems and simplify them.

1 1 5 2 1 3
A. 2
+ = ___________ D.
4
+ = ___________ G. 2
+ = ____________
4
6 3

1 4 7 3 1 6
B. 10
+ = ___________ E.
5
+ = __________ H. 10
+ = ___________
7
15 5

1 2 3 2 6 3
C. 5
+ = ___________ F.
5
+ = ___________ I. 13
+ = ________
5
10 3

Homework:
Solve the problems and simplify them.

1 1 2 4
J. 3
+ = __________
4
O. 5
+ = __________
7

2 3 3 5
K. 5
+ = __________
8
P. 8
+
12
= _________
5 1 2 1
L. 6
+ = __________
2
Q. 9
+ = __________
5

3 2 5 3
M. 7
+ = __________
9
R. 6
+
10
= _________
4 1 4 2
N. 11
+ = _________
3
S. 11
+ = _________
7

Homework:
3 3
T. Jean mixed cup of peanuts with cup of almonds. How many cups of nuts did she
8 4
have?

_______________________________________________________
7 1
U. Mizuki added cup of water to cup of orange juice concentrate. How many cups of
8 2
orange juice did she have?

_______________________________________________________
9
Add Mixed Numbers With Different Denominators
If you remember from last week’s lesson, we learned about adding
fractions with different denominators. This week, we will review that and
add something new. We will not only add fractions with different
denominators, but also fractions with whole numbers.
4
A fraction with a whole number looks like this: 1 . This is called a mixed
12
number.

In Class:
Three (3) students bought seven(7) pizzas. The students cut the pizzas into
twelve (12) pieces each.

How much pizza does each student get? Write the answer with a mixed
number if necessary.

______________________________________________________________________________________________

Method for Equivalent Denominators

Step 1: Find the least Step 2: Use the LCD to find Step 3: Add the fractions, and
common multiple (LCM) of the equivalent fractions. then simplify.
the denominators. This is the x3 x2
least common denominator 21 10 31
(LCD). 7 21 10 5 + =
24 24 24
8: 8, 16, 24, 32 8 24 24 12
12: 12, 24, 36 x3 x2 31 24 7 7
The LCD of the fractions is 24. = + = 1
24 24 24 24

Homework:
Solve the problems below.

1 1 1 2 7 3
A. 1 + 2 = ________C. 6 + 1 = ________E. 2 + 2 =_______
2 4 5 5 15 5

1 4 5 2 3 2
B. 310 + 55 = _______ D. 3 + 4 = ________F. 8 + 4 =_____
6 3 10 3
10
 Add Mixed Numbers With Different Denominators
Homework:
Solve the problems below.

1 4 1 1 1 2
G. 3 10 + 5 5 = ______ L. 4 4 + 3 2 = _______ Q. 3 + 2 3 = _______
2

1 2 3 1 1 3
H. 6 5 + 1 5 = _______ M. 5 4 + 2 3 = _______ R. 4 + 5 4 = _______
8

3 1 5 1 5 1
I. 2 8 + 4 4 = _______ N. 3 + 1 = _______ S. 7 + 2 5 = _______
6 8 6

2 5 2 3 3 2
J. 7 3 + 2 6 = _______ O. 2 5 + 4 10 = ______ T. 1 + 3 3 = _______
4

2 4 3 2 1 4
K. 1 3 + 3 5 = _______ P. 6 4
+ 1 3 = _______U. 5
3
+ 2 5 = _______

Homework:

V. How many total hours did

Jerome and Jeff exercise on
Monday?

________________________
W. Who exercised the most?

_______________________

11
 Subtract Fractions With Different Denominators
Subtracting fractions with different denominators is difficult, but if we follow the
same rules for adding fractions, we see that it is not as difficult as it seems.
Start by choosing either method 1 or method 2.
Simplify the fractions and subtract them.

Method 1 for Equivalent Denominators

Step 1: Find the least Step 2: Use the LCD to find Step 3: Subtract the fractions.
common multiple (LCM) of the equivalent fractions. Write the sum in simplest
the denominators. This is the x3 x2 form.
least common denominator
7 21 10 5
(LCD). 21 10 11
8: 8, 16, 24, 32 8 24 24 12
- =
12: 12, 24, 36 x3 x2 24 24 24
The LCD of the fractions is 24.

Method 2 for Equivalent Denominators

Step 1: Write down the Step 2: Multiply one

fractions. denominator by the other. Step 3: Subtract and simplify.
x12 x8
84 40 44
7 5 7 84 40 5 - =
- 8 96 96 12
96 96 96

8 12 x12 x8
Simplify
44 4 11
( / ) =
96 4 24

In Class:
Solve the problems and simplify them.

1 1 5 2 7 3
A. 2
- = ________
4
D. - 3 = ________ G. 8
- = ________
4
6
9 4 11 3 3 1
B. 10
- 5 = ________ E. - 5 = ________ H. 10
- 10 = ________
15
4 2 7 2 6 1
C. - 5 = ________ F. - 3 = ________ I. - 5 = ________
5 10 13
12
 Subtract Fractions With Different Denominators
In Class:
Solve the problems and simplify them.

3 3 2 1 1 2
J. 7
- = ____________ M.
8 5
-
10
= ___________ P.
3
- = ____________
9

4 2 7 1 5 3
K. 6
- = ____________ N.
8 12
- = ___________ Q.
4 8
- = ____________
8
4 1 7 1 2 1
L. - = ____________ O. 12
- = ___________ R.
4
- = ____________
9 3 7 5

Homework:
Solve the problems and simplify them.

5 4 5 2 2 1
Q. - 9 =__________ T. - 5 =__________ W. 3
- 6 =__________
9 6

3 1 1 1 4 2
R. 4
- 2 =__________ U. - 8 =__________ X. 5
- 5 =__________
4

7 3 3 1 7 1
S. 10
- 5 =__________V. - 8 =__________ Y. 8
- 10 =__________
7

Homework:

7
Z. A bucket with some water in it weighs kg. After pouring some water out, it now
8
1
weighs kg. How heavy was the water that was poured out?
4

__________________________________________________________________
AA. Look at the following pattern. What four fractions do you think come next? Why?
1 2 3 4
, , , , ?, ?, ?, ?
2 3 4 5

_______________________________________________________________
13
 Subtract Mixed Numbers With Different Denominators

If you remember from last week’s lesson, we learned about subtracting

fractions with different denominators together. This week, we will review
that and add something different. We will not only subtract fractions with
different denominators, but also mixed numbers.

Method for Equivalent Denominators

Step 1: Find the least Step 2: Use the LCD to find Step 3: Subtract the fractions.
common multiple (LCM) of the equivalent fractions. Then simplify.
the denominators. This is the x3 x2
least common denominator
7 21 10 5 21 10 11
(LCD).
8: 8, 16, 24, 32 8 24 24 12 - =
12: 12, 24, 36 x3 x2
24 24 24
The LCD of the fractions is 24.

In Class:
Solve the problems below.

1 1 5 2 7 3
A. 2 2 - 14 =________ D. 6 - 3 = ________ G. 28 - 14 = ________
6 3
9 4 11 3 3 1
B. 3 10 - 15 =_______ E. 8 - 7 =________H. 7 - 5 =______
15 5 10 10

4 2 7 2 6 1
C. 4 5 - 15 =________ F. 9 - 5 = _______ I. 313 - 15 = _______
10 3

14
 Subtract Mixed Numbers With Different Denominators

Homework:
Solve the problems below.

3 3 1 1 5 6
A. 10 7 - 48 = _______ L. 6 8 - = _______ W. 19 6 - = ______
5 7
3 3 3 3 3 6
B. 5 10 - 44 = _______ M. 14 9 - 2 9 = _______ X. 12 - = ______
4 7
1 7 3 9 2 5
C. 15 3 - 8 = ________ N. 20 4 - = ______ Y. 24 - = ______
10 4 6
2 2 5 1 1 3
D. 8 5 - 3 = _________ O. 7 - 2 = ______ Z. 9 5 - = ______
6 3 5
2 2 1 4 3 4
E. 8 5 - 3 = _________ P. 16 - = ______ AA. 21 4 - = ______
2 5 9
1 2 1 1 1 3
F. 15 3 - 25 = _______ Q. 11 - = ______ BB. 13 - = ______
3 6 2 4
2 1 4 2 2 3
G. 8 5 - 1 6 = _______ R. 9 - 1 = ______ CC. 10 7 - = ______
7 3 4
7 3 1 4 4 8
H. 5 12 - = ________ S. 22 - = ______ DD. 27 5 - = ______
4 5 5 9
1 2 3 3 1 2
I. 12 4 - 3 3 = _______ T. 13 - = ______ EE. 14 3 - 49 = ______
8 4
3 1 1 2 5 3
J. 9 5 - = _______ U. 17 - = ______ FF. 23 6 - 76 = ______
10 9 9

1 5 2 5 2 4
K. 18 3 - = _______ V. 8 - = ______ GG. 16 9 - 5 9 = _____
9 3 6

15
 Fractions - Test
Signature __________________ ____/22

Find TWO (2) equivalent fractions for each fraction.

1 2 3 4 5
1. 2
= 2. 3
= 3. 4
= 4. 5
= 5. 6
=

___________ ___________ ___________ ___________ ___________

___________ ___________ ___________ ___________ ___________

Write each number as a decimal.

83
6. 100
=_____________________________________________

7
7. 10
=______________________________________________

43
8. 100
=_____________________________________________

2
9. 5
=_______________________________________________

13
10. =______________________________________________
20

16
 Fractions - Test
Add the mixed numbers and fractions. Give the answer in simplest form.

1 1 2 3 3 1 2 1 7 1
11. 3 + 3 = 12. 17 + 37 = 13. 4
+2= 14. 45 + 4 = 15. 58 + 110 =

___________ ___________ ___________ ___________ ___________

Subtract the mixed numbers and fractions. Give the answer in simplest form.

5 1 4 1 7 3 2 1 1 1
16. 6 - 6 = 17. 47 - 27 = 18. - = 19. 85 - 6 = 20. 72 - 45 =
10 5

___________ ___________ ___________ ___________ ___________

Solve the word problem below.

2
Michael bought 1.75kg of bananas. Then, Lisa bought 1 kg of bananas.
3
7
Finally, Margaret bought 1 kg of bananas.
8

21. Who bought the largest amount of bananas?

___________________________________________________________

22. Who bought the least amount of bananas?

___________________________________________________________ 17