Grade 6 Unit 1 and 2

Addition of Mixed Fractions

Example: what is 3 1 There are 3 simple steps to add mixed fractions.
24 +32 =? Step 1: Convert them to improper fractions.
Step 2: Add (using the addition of fractions)
Step 1: Convert to improper fractions. Step 3: then convert back to mixed fractions.

3 11
24 = 4

17
32 = 2

Common denominator of 4.

11 11
4 stays as 4

7 14
2 becomes 4

(by multiplying top and bottom by 2)

Step 2: Now add.

11 14 25
4 +4=4

Step 3: Convert back to mixed fractions.

25 1
4 =64

Subtraction of Mixed Fractions

There are 3 simple steps to subtract mixed fractions.

Step 1: Convert them to improper fractions.

Step 2: Subtract (using the subtraction of fractions)

Step 3: Then convert back to mixed fractions.

Example:

What is 15 3 5
4 - 86 =?

Step 1: Convert to improper fractions:

3 63 5 53
15 4 = 4 86 = 6

Mathematics 6 41

Common denominator of 12:

63 189
4 becomes 12

53 106
6 becomes 12

Step 2: Now subtract:

189 − 106 83
12 12 = 12

Step 3: Convert back to mixed fractions:

83 11
12 = 6 12

Multiplication of Mixed Fractions

There are 3 simple steps to multiply mixed fractions.

Step 1: Convert to improper fractions.

Step 2: Multiply the fractions.

Step 3: Convert the result back to mixed fractions.

What is 1 1
12 × 25 =?

Step 1: Convert to improper fractions.

13
12 = 2

1 11
25 = 5

Step 2: Multiply the fractions (multiply the top numbers, multiply bottom numbers).

3 11 33
2 × 5 = 10

Step 3: Convert to a mixed number.

33 3
10 = 3 10

43 Mathematics 6

Division of Mixed Fractions

There are 5 simple steps to multiply mixed fractions.

Step 1: Convert to improper fractions.
Step 2: Write a new division problem with the improper fractions.
Step 3: Use the KFC (Keep-Flip-Change) method to rewrite it as a multiplication problem.
Step 4: Solve.
Step 5: Rewrite as a mixed number.

Example:

3 × 1
58 43 =?

Step 1: Convert to improper fractions:

3 43 1 13
58 = 8 43 = 3

Step 2: Write a new division problem with the improper fractions.

43 13
8 ÷3

Step 3: Use the KFC method to rewrite it as a multiplication problem.

43 3
8 × 13

Step 4: Solve!

43 3 129
8 × 13 = 104

Step 5: Rewrite as a mixed number.

129 25
104 = 1 104

Mathematics 6 43

Perform the following operations on the given mixed fractions.

1. 31 2. 14
27 +65 = 20 2 − 4 15 =

3. 11 4. 23
23 ×25 = 24 − 15 =

5. 6 × 5 4 = 6. 3 ÷ 1 =
28 6 35 22

7. 4 3 ÷ 2 1 = 8. 5 − 1 =
4 3 16 8 10 4

9. 7 × 3 = 10. 4 ÷ 9
4 12 24 12 7 2 14 =

44 Mathematics 6

Perform the following operations on the given mixed fractions.

Levi ran 2 1/3 km and Jenny ran 3 1/5. M. S.:

Find the difference between the distance that METHOD:

Levi and Jenny ran.

Matthew and his son went fishing. Matthew M. S.:

caught 3 ¾kg of fish while his son caught METHOD:

2 ½ kg of fish. What is the total weight of the
fish that they caught?

Joan bought 2 ¾ kg of vegetables, 1 ¼ kg of M. S.:
fish and 2 1/3 kg of rice. What is the total mass, METHOD:

in kg of the items that she bought?

Rheina is baking a few cakes for the bake sale M. S.:
for her school. Each cake requires 2 ½ cups of METHOD:

sugar. How many cakes can she bake if she

has 7 1/3 cups of sugar?

Mathematics 6 45

Mixed Operations Involving Fractions

The same rules of order of operation apply to expressions with fractions. In particular,
the order is

1. Parenthesis
2. Multiplication and Division (from left to right whichever operation comes first)
3. Addition and Subtraction (from left to right whichever operation comes first)

A common technique for remembering the order of operations is the abbreviation
PEMDAS. This phrase stands for “Parentheses, Exponents, Multiplication & Division,
Addition and Subtraction.” For this lesson, we will not discuss exponents.

Let us try using PEMDAS in this example.

2 24
4 3 ÷ (6 5 − 2 7) = ?

Solution

4 2 ÷ (6 2 − 2 4) = Change the mixed
fractions to
3 57
improper fractions.
2 32 18
= 43 ÷( 5 − 7 )

Change the 2 32 7 18 5
fractions into = 4 3 ÷ (( 5 × 7) − ( 7 × 5))
similar fractions.

The LCM of 7 and 2 224 90 Perform the
5 is 35 = 4 3 ÷ ( 35 − 35) operation in the
Parenthesis first.
Perform the next 2 134
operation which is = 4 3 ÷ ( 35 ) Perform the KFC
Method.
Division 14 134
= 3 ÷ ( 35 ) Change the
improper fraction
14 35
= 3 × 134 to a mixed
fraction.
7 35
= 3 × 67

245
= 201

44
= 1 201

46 Mathematics 6

Let us see performing operation without Parenthesis

Example 2: 1+4× 7 =?

3 7 30

= 1 24 71 Multiplication
+172× comes first before
3 3015
1 addition.
= 3 + 15

The LCM of 3 and 15 2
5 is 15 = (3 × 5) + 15

52
= 15 + 15
7
Example 3: = 15

3 58 2
3 4 ÷ 2 12 + 13 × 3 4 =

12

3

First step is to get the quotient of 3 3 ÷2 5. 8 × 3 2.
4
12 Second step is to get the product of 13 4

3 5 15 29 8 2 8 14
3 4 ÷ 2 12 = 4 ÷ 12 13 × 3 4 = 13 × 4

15 12 2 8 14
= 4 × 29 = 13 × 41

15 123 28
= 1 4 × 29 = 13

45 Third step is to get the sum of 45 + 28.
= 29 29
13

45 28 45 × 13 28 × 29
29 + 13 = 29 × 13 + 13 × 29

The LCM of 29 and 585 812
13 is 377. = 377 + 377

1397
= 377

266
= 3 377

This means that 3 3 ÷2 5 + 8 × 32 = 1397 or 3 266 .
4 377 377
12 13 4

Mathematics 6 47

Example 4: 3 58 2
3 4 ÷ (2 12 + 13) × 3 4 =

1

2
3

2 5 + 8. This is how we’re going to solve the
12
First step is to get the sum of 13 mathematical sentence in one go.

3 58 2
3 4 ÷ (2 12 + 13) × 3 4 =.
5 8 29 8
2 12 + 13 = 12 + 13 15 29 8 14
= 4 ÷ (12 + 13) × 4
29 × 13 8 × 12
= 12 × 13 + 13 × 12 15 29 × 13 8 × 12 14
= 4 ÷ (12 × 13 + 13 × 12) × 4
377 96
= 156 + 156 15 377 96 14
= 4 ÷ (156 + 156) × 4
473
= 156 15 47339 147
= 14 ÷ 156 × 4 2
Second step is to get the quotient of 3 3 ÷ 415763.
4 15 156 14
= 4 × 473 × 4
3 473 15 473
3 4 ÷ 156 = 4 ÷ 156 15 × 39 × 7
= 1 × 473 × 2
15 156 39
= 14 × 473 4095
= 946
585
= 473 311
= 4 946
Third step is to get the product of 585 × 3 42.
473

585 2 585 14
473 × 3 4 = 473 × 4

585 14 7
= 473 × 4 2

4095
= 946

311
= 4 946

This means that 3 3 ÷ (2 5 + 8 ) × 32 = 4095 or 4 311 .
4 946 946
12 13 4

48 Mathematics 6

Example 5:

Find the answer to this mathematical sentence (3 × 3 1) ÷ (1 1 − 1) =.
22 5

31 1
(2 × 3 2) ÷ (1 5 − 1) =

12

3

Solution: Answer:

31 1 37 61
(2 × 3 2) ÷ (1 5 − 1) = (2 × 2) ÷ (5 − 1) =

3 7 6 1×5 The LCM of 5 and 1
= (2 × 2) ÷ (5 − 1 × 5) is 5.

21 6 5
= ( 4 ) ÷ (5 − 5)

21 1
= 4 ÷5

21 5
= 4 ×1

105
=4

1
= 26 4

Example 6

Find the answer to this mathematical sentence 11 + 3 × 20 + 1 7 =.
14 4 21 8

11 + 3 × 20 + 1 7 =
14 4 21 8

1

2
3

11 3 20 7 11 3 20 15
14 + 4 × 21 + 1 8 = 14 + 4 × 21 + 8

11 1 5 15
= 14 + 1 × 7 + 8

11 5 15
= 14 + 7 + 8

Mathematics 6 49

11 × 8 5 × 16 15 × 14 The LCM of 14, 7
= 14 × 8 + 7 × 16 + 8 × 14 and 8 is 112.

88 80 210 Answer
= 112 + 112 + 112

378 14 =
= 112 × 14

27
=8

3
= 38

Work out the following equations.

1. (3 1 + 2 59) × 1 2 2. (8 2 × 3 1) − 4 1
6 3 5 4
2

3. 6 1 + 1 4 ÷ 9 4. 5 − 7 ÷ 3
2 5 10 12 13 26

5. (1 4 + 6 32) − 3 1 6.4 1 + 5 5 × 2 1
9 3 2 6 3

50 Mathematics 6

Word Problems Involving Fractions
Example 1:

A container had 6 2 liter of orange juice. Honey drank 1 1 liter of the orange juice.
3 6

The remaining orange juice was the poured equally into bottles that has a

capacity of 1 liter each. How many bottles of orange juice are left?
2

What is asked? The number of bottles of orange juice left.

What are given?

6 2 = amount of orange juice
3
11
= Honey drank this amount of orange juice
6
1 = capacity of water bottles
2

Mathematical Sentence

2 11
(6 3 − 1 6) ÷ 2 =

Solution
2 1 1 20 7 1

(6 3 − 1 6) ÷ 2 = ( 3 − 6) ÷ 2
20 × 2 7 1

= ( 3 × 2 − 6) ÷ 2
40 7 1

= ( 6 − 6) ÷ 2
33 1

= 6 ÷2
33 2

= 6 ×1
33 1

= 3 ×1
33 1

= 3 ×1

= 11

Answer

There are 11 bottles of orange juice left.

Mathematics 6 51

Example 2:

John is 8 1/2 years old. Lee is 2 2/3 times as old as John.
James is 6 ¾ years older than Lee. How old is James?

Mathematical Sentence

(8 1 × 2 2 + 6 3 = ′
2 3) 4

Solution

1 2 3 17 8 27
(8 2 × 2 3) + 6 4 = ( 2 × 3) + 4

17 4 27 Perform the
= ( 1 × 3) + 4 operation in the
parenthesis first.
68 27
= 3+4 Add the fractions
next.

68 × 4 27 × 3
= 3×4 + 4×3

272 81 The LCM of 4 and
= 12 + 12 3 is 12.

353
= 12

5 James is 29 5 years old or 29 years and 5 months old.
= 29 12
12

Example 3

Rope A is 6 7/8 m long. Rope B is 3/5 times as long as Rope A. Rope B is cut into 5
equal pieces. What is the length of each piece of Rope?

Mathematical Sentence

Solution 73
(6 8 × 5) ÷ 5 =
73 55 3
(6 8 × 5) ÷ 5 = ( 8 × 5) ÷ 5 Perform the
operation in the
parenthesis first.

11 3 5 Divide the fractions
= ( 8 × 1) ÷ 1 next.

33 1
= 8 ×5

33 The length of each piece of rope is 33 m.
= 40
40

52 Mathematics 6

Drop your Word Problems
answer here!
Answer the word problems.
Drop your Honey had 2 7/8 of milk powder. She used 1/5 of the milk
answer here! powder to bake cakes. She then used ¾ kg of the remaining
milk powder to bake cookies. How much flour was left?
Drop your
answer here! Ciara is making a new wedding dress. She needs 2 ½ yards
of fabric for the shawl. She need 1 ¾ yards of fabric for the
Drop your dress. If she 3 yards of fabric, how much more does she
answer here! need? If each yard of fabric costs 280 baht, how much
money does she need?

Kento spent ¼ of his incentive pay, saved 5/12 of it and gave
the rest equally among his siblings. Each sibling received 1/6of
his salary. How many siblings does he have?

Joy read a book in 2 1/2 hours. Mark spent 5/6 hours more
than Joy in reading the same book. Jones spent 2/6 the
amount of time as Mark to read the book. How many hours
did Jones take to read the book?

Mathematics 6 53

SUMMARY

✓ Mixed numbers - A whole number and a fraction combined into one
"mixed" number. Example: 1½ (one and a half) is a mixed fraction.

To convert an improper fraction to a mixed fraction, follow these steps:
Divide the numerator by the denominator.
Write down the whole number answer.
Then write down any remainder above the denominator.

To convert a mixed fraction to an improper fraction, follow these steps:
Multiply the whole number part by the fraction's denominator.
Add that to the numerator.
Then write the result on top of the denominator.

The same rules of order of operation apply to expressions with fractions. In
particular, the order is:

Parenthesis
Exponents 106
Multiplication and Division × ÷
Addition and Subtraction + –

A common technique for remembering the order of operations is the abbreviation
PEMDAS. This phrase stands for “Parentheses, exponents, multiplication, division,
addition and subtraction”

54 Mathematics 6

M A ST E R Y P RA C TI C E

Circle the letter of the correct answer.

1.

321 . 7 . 3 . 2
24+25−12 =
15 15 5

2. . 51 . 5 1 . 3 1

14 7 10 10 10
3 + 7 × 30 =

3. Add the quotient of 6 5 and 3 to 2 2.

84 3

1 29 3
. 11 2 . 6 32 . 11 6

4. This phrase stands for 5. A whole number anda
fraction combined into one
“Parentheses, exponents, number.

multiplication, division, addition and a. Fraction
b. Ordering
subtraction” c. Mixed numbers
d. Order of Operation
a. MDAS
b. PEMDAS
c. HDAS
d. PMDAS

Mathematics 6 55

Solve the following equations

1. 3 4 − 4 2 ÷ 2 1 + 4 = 2. 3 4 − 4 2 ÷ (2 1 + 4) =
5 3 2 7 5 3 2
7

3. (3 2 ÷ 4) + (6 4 − 2 4) = 4. 3 1 ÷ 6 + 2 3 × 2 − 2 =
3 8 27 573
3 7

John found 3 of a pie in the refrigerator. He ate one-half of it and divided the
4

rest to his 3 siblings. What part of the cake did each of John’s sibling receive?

Mathematical Sentence:

Answer the problem.

Answer:

56 Mathematics 6

At the end of the activity the students will be able to:

1. Create fraction noodles.

2. Compare fractions using concrete objects

3. Add fractions using concrete objects.

Materials

pool noodle marker

scissors ruler

Directions:
1. Measure 12 inches on a noodle.
2. Cut at the 12-inch mark.
3. Write number one on the piece.
4. Cut the other color of pool noodle into two 6-inch pieces and write ½ on each.
5. Cut the first color of noodle into three 4-inch piece for 1/3, then alternate
colours for four 3-inch pieces for 1/4, six 2-inch pieces for 1/6 and eight 1.5-
inch pieces for 1/8.

Scan this for a video
guide:

Mathematics 6 57