4 cross multiplication
TRANSCRIPT
In this section we look at the useful procedure of cross multiplcation.Cross Multiplication
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.
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below.
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below.
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below.
ad bc
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across.
ad bc
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
What we get are two numbers.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across.
ad bc
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
What we get are two numbers.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across.
ad bcMake sure that the denominators cross over and up so the numerators stay put.
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
What we get are two numbers.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across.
ad bcMake sure that the denominators cross over and up so the numerators stay put. Do not cross downward as shown here. a
bcdadbc
Cross Multiplication
In this section we look at the useful procedure of cross multiplcation.
What we get are two numbers.
ab
cd
Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across.
ad bcMake sure that the denominators cross over and up so the numerators stay put. Do not cross downward as shown here. a
bcdadbc
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional Ratios
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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,
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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 as34 S 2
3 F.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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 as34 S 2
3 F.
We have the ratio 34 S : 2
3 F
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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 as34 S 2
3 F.
We have the ratio 34 S : 2
3 F cross multiply we’ve 9S : 8F.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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 as34 S 2
3 F.
We have the ratio 34 S : 2
3 F cross multiply we’ve 9S : 8F.
Hence in integers, the ratio is 9 : 8 for sugar : flour.
Cross Multiplication
Here are some operations where we may cross multiply. Rephrasing Fractional RatiosIf 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 as34 S 2
3 F.
We have the ratio 34 S : 2
3 F cross multiply we’ve 9S : 8F.
Hence in integers, the ratio is 9 : 8 for sugar : flour.
Cross Multiplication
Remark: A ratio such as 8 : 4 should be simplified to 2 : 1.
Cross–Multiplication Test for Comparing Two Fractions Cross Multiplication
When comparing two fractions to see which is larger and which is smaller.
Cross–Multiplication Test for Comparing Two Fractions Cross Multiplication
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.
Cross–Multiplication Test for Comparing Two Fractions Cross Multiplication
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.
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45
we get
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
35
58
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross– multiply 35
58
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross– multiply 35
58
24 25
we get
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross– multiply 35
58
24 25
we get
moreless
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross– multiply 35
58
24 25
Hence 35
58is less than
we get
moreless
.
Cross–Multiplication Test for Comparing Two Fractions
Hence cross– multiply
Cross Multiplication
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.
35
915
=45 45 so35
915=
we get
Cross– multiply 35
58
24 25
Hence 35
58is less than
we get
moreless
.
(Which is more 711
914 or ? Do it by inspection.)
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio:14 B: 2
3 F:
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
14 B: 2
3 F:( )12
We have the three–way ratio: multiply the list by the LCD 12.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Example C. Arrange 3/5, 2/3 and 7/12 from the smallest to the largest.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Example C. Arrange 3/5, 2/3 and 7/12 from the smallest to the largest.
712
35
: 23 :Multiply the list by the LCD = 60.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Example C. Arrange 3/5, 2/3 and 7/12 from the smallest to the largest.
712
35
: 23 :( ) 60Multiply the list by the LCD = 60.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Example C. Arrange 3/5, 2/3 and 7/12 from the smallest to the largest.
712
35
: 23 :( ) 60
36: 40: 35
12 520
Multiply the list by the LCD = 60.
Multiplying by the LCDCross Multiplication
Cross–multiplication is a shortcut for clearing denominators for two fractions. When there are more than two fractions, we use their LCD to clear their denominators when needed.
Example B.A cookie recipe that calls for 1/4 cup of butter, 2/3 cup of flourand 5/6 cup of sugar. Phrase this in terms of whole number.
56 S
We have the three–way ratio: multiply the list by the LCD 12.14 B: 2
3 F:( )123 4 2
3B: 8F: 10S
Hence recipe calls for 3: 8: 10 for butter: flour: sugar.
Example C. Arrange 3/5, 2/3 and 7/12 from the smallest to the largest.
Multiply the list by the LCD = 60. 712
35
: 23 :( ) 60
36: 40: 357
1235
23 Hence <<
12 520
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions
ab
cd±
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions
ab
cd± = ad ±bc
Cross Multiplication
Cross–Multiplication for Addition or Subtraction
ab
cd± = ad ±bc
Cross Multiplication
We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
Cross–Multiplication for Addition or Subtraction
ab
cd± = ad ±bc
bd
Cross Multiplication
We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
± = ad ±bcbd
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – a.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – a.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*5a.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – b.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – b.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – =5*12 – 9*5
9*12b.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – =5*12 – 9*5
9*1215108=b.
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – =5*12 – 9*5
9*1215108=b. 5
36=
Cross Multiplication
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – =5*12 – 9*5
9*1215108=b. 5
36=
Cross Multiplication
In a. the LCD = 30 = 6*5 so the crossing method is the same as the Multiplier Method.
Cross–Multiplication for Addition or SubtractionWe may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator.
ab
cd
Afterwards we reduce if necessary for the simplified answer.
Example D. Calculate
± = ad ±bcbd
35
56 – = 5*5 – 6*3
6*57
30=a.
512
59 – =5*12 – 9*5
9*1215108=b. 5
36=
Cross Multiplication
In b. the crossing method gives an answer that needs to be reduced because the denominator 9*12 =108 is not the LCD.
Ex. Restate the following ratios in integers.
9. In a market, ¾ of an apple may be traded with ½ a pear.Restate this using integers.
12
13 :1. 2. 3. 4.2
312 : 3
413 : 2
334 :
35
12 :5. 6. 7. 8.1
617 : 3
547 : 5
274 :
Determine which fraction is more and which is less.23
34 ,10. 11. 12. 13.4
534 , 4
735 , 5
645 ,
59
47 ,14. 15.
16. 17.7
1023 , 5
1237 , 13
885 ,
12
13 +18. 19. 20. 21.1
213 – 2
332 + 3
425 +
56
47 – 22. 23.
24. 25.7
1025 – 5
1134 + 5
97
15 –
Cross Multiplication
C. Use cross–multiplication to combine the fractions.