3. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
4. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
5. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
a
b
c
d
6. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
a
b
c
d
7. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
a
b
c
d
ad bc
8. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
Take the denominators and multiply them diagonally across.
a
b
c
d
ad bc
9. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
Take the denominators and multiply them diagonally across.
What we get are two numbers.
a
b
c
d
ad bc
10. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
Take the denominators and multiply them diagonally across.
What we get are two numbers.
a
b
c
d
ad bc
Make sure that the denominators cross over and up so the
numerators stay put.
11. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
Take the denominators and multiply them diagonally across.
What we get are two numbers.
a
b
c
d
ad bc
Make sure that the denominators cross over and up so the
numerators stay put. Do not cross downward as shown
here. a
b
cd
bc ad
12. Cross Multiplication
In this section we look at the useful procedure of cross
multiplcation.
Cross Multiplication
Many procedures with two fractions utilize the operation of
cross– multiplication as shown below.
Take the denominators and multiply them diagonally across.
What we get are two numbers.
a
b
c
d
ad bc
Make sure that the denominators cross over and up so the
numerators stay put. Do not cross downward as shown
here. a
b
cd
bc ad
14. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
15. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2,
16. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour.
17. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3.
18. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing.
19. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
20. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
21. Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
Write 3/4 cup of sugar as and 2/3 cup of flour as
3
4
S
2
3
F.
Cross Multiplication
22. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
Write 3/4 cup of sugar as and 2/3 cup of flour as
3
4
S
2
3
F.
We have the ratio
3
4
S :
2
3
F
23. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
Write 3/4 cup of sugar as and 2/3 cup of flour as
3
4
S
2
3
F.
We have the ratio
3
4
S :
2
3
F cross multiply we’ve 9S : 8F.
24. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
Write 3/4 cup of sugar as and 2/3 cup of flour as
3
4
S
2
3
F.
We have the ratio
3
4
S :
2
3
F cross multiply we’ve 9S : 8F.
Hence in integers, the ratio is 9 : 8 for sugar : flour.
25. Cross Multiplication
Here are some operations where we may cross multiply.
Rephrasing Fractional Ratios
If a cookie recipe calls for 3 cups of sugar and 2 cups of flour,
we say the ratio of sugar to flour is 3 to 2, and it’s written as
3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is
2 : 3. For most people a recipe that calls for the fractional ratio
of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to
cross multiply to rewrite this ratio in whole numbers.
Example A.
rewrite a recipe that calls for the fractional ratio of 3/4 cup
sugar to 2/3 cup of flour into ratio of whole numbers.
Write 3/4 cup of sugar as and 2/3 cup of flour as
3
4
S
2
3
F.
We have the ratio
3
4
S :
2
3
F cross multiply we’ve 9S : 8F.
Hence in integers, the ratio is 9 : 8 for sugar : flour.
Remark: A ratio such as 8 : 4 should be simplified to 2 : 1.
28. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
29. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
30. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
31. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45
we get
32. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
33. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
3
5
5
8
34. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
Cross– multiply
3
5
5
8
35. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
Cross– multiply
3
5
5
8
24 25
we get
36. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
Cross– multiply
3
5
5
8
24 25
we get
less more
37. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
Cross– multiply
3
5
5
8
24 25
Hence
3
5
5
8
is less than
we get
less more
.
38. Cross Multiplication
Cross–Multiplication Test for Comparing Two Fractions
When comparing two fractions to see which is larger and
which is smaller. Cross–multiply them, the side with the larger
product corresponds to the larger fraction.
In particular, if the cross multiplication products are the same
then the fraction are the same.
Hence cross– multiply
3
5
9
15
45 = 45 so
3
9
=
5
15
we get
Cross– multiply
3
5
5
8
24 25
Hence
3
5
5
8
is less than
we get
less more
.
(Which is more
7
11
9
14
or ? Do it by inspection.)
43. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
b
c
d
± =
ad ±bc
44. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
b
c
d
± =
ad ±bc
bd
45. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
46. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
a. –
Cross Multiplication
47. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
a. –
Cross Multiplication
48. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
a.
Cross Multiplication
49. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
50. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
5
12
5
9
b. –
Cross Multiplication
51. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
5
12
5
9
b. –
Cross Multiplication
52. Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
5
12
5
9
– =
5*12 – 9*5
9*12
b.
Cross Multiplication
53. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
5
12
5
9
– =
5*12 – 9*5
9*12
15
108
b. =
54. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
b. = 5
5
12
5
9
– =
5*12 – 9*5
9*12
15
108
36
=
55. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
b. = 5
5
12
5
9
– =
5*12 – 9*5
9*12
15
108
36
=
In a. the LCD = 30 = 6*5 so the crossing method is the same as
the Multiplier Method.
56. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
b. = 5
5
12
5
9
– =
5*12 – 9*5
9*12
15
108
36
=
In a. the LCD = 30 = 6*5 so the crossing method is the same as
the Multiplier Method. However in b. the crossing method
yielded an answer that needed to be reduced.
57. Cross Multiplication
Cross–Multiplication for Addition or Subtraction
We may cross multiply to add or subtract two fractions with
the product of the denominators as the common denominator.
a
± c
ad ±bc
=
b
d
bd
Afterwards we reduce if necessary for the simplified answer.
Example B. Calculate
3
5
5
6
– =
5*5 – 6*3
6*5
7
30
a. =
b. = 5
5
12
5
9
– =
5*12 – 9*5
9*12
15
108
36
=
In a. the LCD = 30 = 6*5 so the crossing method is the same as
the Multiplier Method. However in b. the crossing method
yielded an answer that needed to be reduced. we need both
methods.
59. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
60. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways.
61. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct.
62. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
63. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer.
64. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method.
65. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
5
12
5
9
–
66. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
Since the LCD = 36, we multiply and divide by 36.
5
12
5
9
–
67. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
Since the LCD = 36, we multiply and divide by 36.
5
12
5
9
( –
(
*36 / 36
68. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
Since the LCD = 36, we multiply and divide by 36.
5
12
5
9
( –
(
*36 / 36
4 3
69. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
Since the LCD = 36, we multiply and divide by 36.
4 3
5
12
5
9
( –
(
*36 / 36
= (5*4 – 5*3) / 36 = 5/36
70. Cross Multiplication
The Double Check Strategy
One of the most difficult thing to do in mathematics is to know
that a mistake had taken place and to locate the mistake.
The Double Check is to cross check an answer by doing a
problem two different ways. If both methods yielded the same
answer then the answer is likely to be correct. If two answers
are different then we have to clarify the mistake.
When we + or – fractions, we can use the above two methods
to cross check an answer. For example, in part b. above,
we obtain an answer via the crossing method. Let’s cross
check the first answer using the Multiplier Method.
Since the LCD = 36, we multiply and divide by 36.
4 3
5
12
5
9
( –
(
*36 / 36
= (5*4 – 5*3) / 36 = 5/36
This is the same as before hence it’s very likely to be correct.
71. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
72. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
Use this Double Check Strategy for learning!
73. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
Use this Double Check Strategy for learning!
* The Multiplier Method and the Cross Multiplication Method
are two methods to double check addition and subtraction of
small number of fractions.
74. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
Use this Double Check Strategy for learning!
* The Multiplier Method and the Cross Multiplication Method
are two methods to double check addition and subtraction of
small number of fractions. These two methods generalize to
addition and subtraction of fractional (rational) formulas in
later topics.
75. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
Use this Double Check Strategy for learning!
* The Multiplier Method and the Cross Multiplication Method
are two methods to double check addition and subtraction of
small number of fractions. These two methods generalize to
addition and subtraction of fractional (rational) formulas in
later topics. Each method leads to various ways of handling
various fractional algebra problems where each way has its
own advantages and disadvantage.
76. Cross Multiplication
Comments
* The Double Check Strategy is an important tool for learning.
It reassures us if we’re heading in the right direction. It warns
us that a mistake had occurred so we should back track and
locate the mistake.
Use this Double Check Strategy for learning!
* The Multiplier Method and the Cross Multiplication Method
are two methods to double check addition and subtraction of
small number of fractions. These two methods generalize to
addition and subtraction of fractional (rational) formulas in
later topics. Each method leads to various ways of handling
various fractional algebra problems where each way has its
own advantages and disadvantage.
We use both methods through out this database.
77. Ex. Restate the following ratios in integers.
1
2
1
3
2
3
1
2
3
4
1
3
1. : 2. 3. 4.
:
:
2
3
3
4
:
3
5
1
2
1
6
1
7
3
5
4
7
5. : 6. 7. 8.
:
:
5
2
7
4
:
9. In a market, ¾ of an apple may be traded with ½ a pear.
Restate this using integers.
Determine which fraction is more and which is less.
2
3
3
4
4
5
3
4
10. , 11. 12. 13.
,
4
7
3
5
,
5
6
4
5
,
5
9
4
7
7
10
2
3
14. , 15. 16. 17.
,
5
12
3
7
,
13
8
8
5
,
1
2
1
3
1
2
1
3
18. + 19. 20. 21.
–
2
3
3
2
+
3
4
2
5
+
5
6
4
7
7
10
2
5
22. – 23. 24. 25.
–
5
11
3
4
+
5
9
7
15
–
Cross Multiplication
C. Use cross–multiplication to combine the fractions.