statistic modular 2

What is the LCM of 9 and 6 ?

18

Which of the following is a multiple of 6: 2, 10, 24, or 40

24

5 1/4÷7/10

7 1/2

3/4÷−4/6

-1 1/8

REDUCE -5/20

-1/4

2-8/9÷2-3/5

1 1/9

An inch is 1/12 of a foot. How many inches are in 2/3 of a foot?

2/3=8/12= 8 INCHESIN A FOOT

What fraction with a denominator of 84 is equivalent to 9/14 ?

54/84

MIXED

A mixed number* consists of a whole number and a proper fraction. Note that a negative sign in front applies to both parts of the mixed number. 1-1/3 −8-2/5 14-1/2 We can read these mixed numbers as: One and one-third Negative eight and two-fifths Fourteen and one-half

Dividing Mixed Numbers

Dividing mixed numbers is similar to dividing fractions. However, you must first convert the mixed numbers to fractions. Then, for the final answer you convert the fraction back to a mixed number

Fractions

Fractions* represent parts. In other words, fractions are a means of expressing numbers which are part of a whole. Fractions are something that as a nurse you will work with every day (see highlight box below).

What is a common multiple of 6 and 12 ?

If you just multiplied 6×12 , you would get 72 . Notice, however, that 6 is a factor* of 12 . Another, much smaller, common multiple is 12 itself! In fact, 12 , 24 , 36 , 48 , and 60 are all common multiples as well as 72 .

The mixed number 7-2/5 is equivalent to the improper fraction 37/5 . True or False?

TRUE

Which is of the numbers below is NOT a common multiple of 4 and 6

The answer is c. 16 is divided evenly by 4 so 16 is a multiple of 4 , but 16 is not divided evenly by 6 . Therefore, 16 is not a multiple of 6 and cannot be a common multiple of both numbers.

Are these two fractions equal? 7/3 = 182/78

YES

REDUCING FRACTIONS

When fractions are reduced to lowest terms, it's much easier to multiply, divide, add, and subtract them. To simplify or reduce a fraction to lowest terms, you find an equivalent fraction in which the numerator and denominator have no common factors.

Improper fractions can be converted to mixed numbers by following these steps:

Write division problem with numerator divided by denominator. Divide to determine quotient and remainder. Write mixed number with the quotient as the whole number and the remainder as the numerator over the same denominator.

Divide the following fractions: 1/2÷2/3

educe the fraction to the lowest terms, if necessary 3/4

Multiples and the Least Common Multiple

we learned that factors* are integers that divide a number without a remainder. Factors are necessarily smaller than the integer they divide. Multiples* are, in some sense, the opposite of factors: integers that are created by multiplying the number times another integer. For example, 2 and 3 are factors of 6 , while 6 , 12 , 18 are multiples of 6 . Multiples are needed to add and subtract fractions, and factors are needed to reduce them.

16/-48

1/-3 48DIVIDDED BY 16 IS 3

2 3/8÷4 3/4

1/2

-27/-81

1/3

What fraction with a denominator of 100 is equivalent to 7/50

14/100

Which of the following is a multiple of 3: 1, 5, 15, or 20?

15

fraction contains 2 integers separated by

fraction contains two integers*, separated by a slash, / , or a fraction bar,

What fraction with a denominator of 64 is equivalent to 5/16

20/64

12 and 8. Least common multiple =

24

Fractions can be classified into 1 of 3 categories:

proper, improper, or mixed numbers.

3/8÷11/16

6/11

REDUCE 6/8

List the prime factors of both the numerator and denominator. 6=2X3 8=2X2X2 Cancel, or divide by, all the factors that are common to both the numerator and denominator. In this example, the common factor is 2 . 3 2X2= 3/4

An inch is 1/36 of a yard. How many inches are in 1/2 of a yard?

18

2/3

2 is the numerator and 3 is the denominator. There are 2 equal parts, and 3 equal parts make up one whole unit.

Example Divide the following mixed number and fraction: −2-2/7÷3/7

2-2/7 = -16/7 -16/7x7/3 (reciprocal of 3/7)--112/21= -5-1/3

What multiple of 7 is closest to -40?

-42 To find the multiple of 7 closest to -40, divide -40 by 7, yielding an integer value of -5. 7 x -5 = -35 and 7 x -6 = -42. -40 lies between these values but it is closer to -42. Therefore, the multiple of 7 closest to -40 is -42.

To divide mixed numbers, follow these steps:

-Change any mixed numbers to improper fractions. -Change the division sign ( ÷ ) to a multiplication sign ( × ). -Write the reciprocal of the second fraction. -Multiply the numerators and denominators as usual. -Change the improper fraction to a mixed number. -Reduce the fraction to the lowest terms, if necessary.

-28/42

-Notice that the numerator and denominator are both divisible by 7. -4/6 Are you finished yet? Notice that fraction begin. numerator: -4 denominator: 6 fraction end. still has a common factor. You are not finished yet and need to reduce further. −4/6=−4÷2/6÷2=−2/3

4=2/5÷3-1/7

1 2/5

Divide the following fractions: 1/2÷1/2 Divide the following fractions:

1/2÷1/2 Note, any number divided by itself is 1 , so we expect the answer to this problem to be 1 , but let's work through it. Change the division sign ( ÷ ) to a multiplication sign ( × ) 1/2× Write the reciprocal of the divisor, or second fraction 1/2×2/1 Please note that we could cancel the 2s in the numerator and denominator, but we will follow this simple problem through with no cancellation.

What is the LCM of 14 and 28 ?

28

What improper fraction is equivalent to the mixed number 7-1/4 ?

29/4Q

What improper fraction is equivalent to the mixed number 3 -5/11 ?

38/11

How many 27 ths are equal to 4/9 ?

4/9 = 12/27

4/9÷1/6=

4/9x6/1=24/9=2-6/9- ==2-2/3

. What improper fraction is equivalent to the mixed number 5 2/9 ?

47/9

24 and 16. Least common multiple =

48

What is 8-3/8−3-2/16 ? Select the answer that is given in the simplest form.

5-1/4 he mixed numbers need to be first changed to improper fractions, then be converted to equivalent fractions with the LCD. The calculation would therefore be: 8-3/8−3-2/16=67/8−50/16=134/16−50/16=84/16=5-4/16 . The fraction can be reduced. Therefore the answer is 5-1/4 .

Least Common Multiples (LCM) of 6 and 8

6 and 8 have a common factor of 2 , so do not multiply them by one another. Begin with the first multiple of 8 , which is 8 . Does 6 divide 8 evenly? No. Next, take the second multiple of 8 , 8×2=16 . Does 6 divide 16 evenly? No. Take the next multiple of 8 : 8×3=24 Does 6 divide 24 evenly? Yes. You have found the LCM. The LCM of 6 and 8 is 24

EQUIVALENT FRACTION OF 2/5 WITH 15 ASA DENOMINATOR

6/15

What mixed number is equivalent to the improper fraction 718

8-7/8

What fraction with a denominator of 82 is equivalent to 40/41

80/82

Which of the following is a multiple of 2: 3, 5, 21, or 86?

86

Least Common Multiples (LCM) of 9 and 27

9 and 27 have a common factor of 9 , so do not multiply them by one another. Begin with the first multiple of 27 , which is 27 . Does 9 divide 27 evenly? Yes. You have found the LCM. The LCM of 9 and 27 is 27

What is the LCM of 9 and 10 ?

90 The two numbers do not share a common factor. Therefore, their LCM is found by multiplying them together and getting 90 .

Multiplying Fractions: The Importance of the Word "Of"

A helpful way to think about the multiplication of fractions is that in solving these types of problems, we are looking for a part OF another. Therefore, it is important to keep in mind that the word "of" can be used to refer to multiplication. For example, what is 12 of 13 . One of the most difficult aspects of working with fractions is remembering how to handle the denominators. In multiplication and division, do not find common denominators. Follow the steps below to multiply: A helpful way to think about the multiplication of fractions is that in solving these types of problems, we are looking for a part OF another. Therefore, it is important to keep in mind that the word "of" can be used to refer to multiplication. For example, what is 12 of 13 . One of the most difficult aspects of working with fractions is remembering how to handle the denominators. In multiplication and division, do not find common denominators. Follow the steps below to multiply: A helpful way to think about the multiplication of fractions is that in solving these types of problems, we are looking for a part OF another. Therefore, it is important to keep in mind that the word "of" can be used to refer to multiplication. For example, what is 12 of 13 . One of the most difficult aspects of working with fractions is remembering how to handle the denominators. In multiplication and division, do not find common denominators. Follow the steps below to multiply: -Multiply the numerators to obtain a new numerator. -Multiply the denominators to obtain a new denominator. -Write the answer in fraction form and reduce it to the lowest terms, if necessary. -Change any improper fractions to mixed numbers.

Canceling

At the beginning of the section on fractions, we briefly mentioned simplifying fraction by "canceling," a way of reducing fraction before multiplying them together. In canceling you are essentially dividing the numerator and denominator by the same number. For example, consider the following operation: 7/9×11/4 You might notice that the numerator and denominator have a common factor of 7 . 7 divides 7 and 7 divides 14 . You can "cancel" the 7 s from the numerator and denominator, changing the numerator 7 to " 1 " ( 7÷7=1 ) and changing the denominator 14 to " 2 " ( 14÷7=2 ). The calculation above therefore can be simplified to: Notice that the canceling does not change the result of the operation. You can also perform the multiplication and cancel at the end of the operation. 7/9×11/4=7/126=7÷7/126÷7=1/18 If you do not cancel during the multiplication process, you will need to reduce the fraction to simplest form at the end. You can only cancel across the fraction bar, a numerator with a denominator. You cannot cancel two numerators or two denominators.

What is 6-5/6−2-1/6 ? Select the answer that is given in the simplest form

Because the mixed numbers have the same denominators, it is easiest to do the subtraction without converting them to improper fractions first. Subtracting the integers gives 6−2=4 , and subtracting the fractions gives (5−1)6=4/6=2/3 . Therefore, the answer is 4-2/3 .

Example: Changing a Mixed Number to an Improper Fraction

Change 1-4/5 from a mixed number to an improper fraction. Step 1: Multiply the whole number by the fraction's denominator. 1×5=5 Step 2: Add that product to the numerator of the fraction. 5+4=9 Step 3: The answer from step 2 now becomes the numerator of the improper fraction. Rewrite the answer as an improper fraction. Step 4: Reduce the fraction. No reduction is necessary. 9/5 Here is the same example from above in a more graphical presentation

EXAMPLE OF CONVERTING

Change 95 from a fraction to a mixed number. Step 1: Write the fraction as a division problem: 9 divided by 5 . nine divided by five Step 2: Solve by dividing numerator 9 by denominator 5 . solve by dividing nine by five 5 goes into 9 one time with a remainder of 4 . Step 3: Write the answer using the quotient, 1 , followed by a fraction whose numerator is the remainder, 4 , and whose denominator is the denominator from the original fraction, 5 . one and four-fifths 1=4/5

Multiply the following mixed number and fraction: 6-2/3×1/2

Change any mixed numbers to improper fractions 6-2/3=6×3+2=20 So 6-2/3=20/3 The expresssion is now: 20/3×1/2 Step 2: Multiply the numerators (20×1)=20 We now have: 20(3×2) Step 3: Multiply the denominators 20(3×2)=20/6 Step 4: Convert the improper fraction to a mixed number 20/6=3=2/6 Step 5: Reduce the fraction to lowest terms 3-2/6=3-1/3

To divide fractions, follow these steps:

Change the division sign ( ÷ ) to a multiplication sign ( × ). Write the reciprocal of the second fraction. Multiply the numerators. Multiply the denominators. Write the answer in the form of a fraction. Reduce the fraction to the lowest terms, if necessary.

Let's add the following two mixed numbers: 1-2/5−3/2=?

Change the mixed number to an improper fraction. Here is a reminder of how to change a mixed number to an improper fraction. 1-2/5=7/5 Step 2: Find equivalent fractions with the least common denominator. Convert the fractions to equivalent fractions with the LCD. The lowest common denominator is 5×2=10 , therefore: Multiply the numerator and denominator of 7/5 by 2 Multiply the numerator and denominator of 3/2 by 5 75−32=14/10−15/10 Step 3: Subtract Like Fractions Next, subtract the numerators of the fractions. Remember to keep the same denominator—do not subtract them! 14/10−15/10=−1/10 Step 4: To complete the problem, convert any improper fractions to lowest terms. In this example, the fraction is already reduced to its lowest form.

Let's add the following two mixed numbers: 6-2/3+7-3/4

Change the mixed number to an improper fraction. Here is a reminder of how to change a mixed number to an improper fraction. 6-2/3=20/3 and 7-3/4=31/4 Step 2: Find equivalent fractions with the least common denominator. Convert the fractions to equivalent fractions with the LCD. The lowest common denominator is 3×4=12 , therefore: Multiply the numerator and denominator of 20/3 by 4 Multiply the numerator and denominator of 31/4 by 3 20/3+31/4=80/12+93/12 Step 3: Add like fractions. Next, add the fractions. If this were a subtraction problem, you would simply subtract instead of adding. 80/12+93/12=173/12 Step 4: To complete the problem, convert any improper fractions to lowest terms. 173/12=14-5/12 In this example, the fraction is already reduced to its lowest form.

25 and 40. Least common multipLE

Correct. 25 and 40 share factors, so find the multiple of 40 that 25 divides. The first multiple of 40 is 40, which 25 does not divide The second multiple of 40 is 80, which 25 does not divide The third multiple of 40 is 120, which 25 does not divide The fourth multiple of 40 is 160, which 25 does not divide The fifth multiple of 40 is 200, which 25 does divide. The least common multiple of 25 and 40 is 200.

6 and 14. Least common multiple =

Correct. 6 and 14 share factors, so find the multiple of 14 that 6 divides. The first multiple of 14 is 14, which 6 does not divide; 28, which 6 does not divide; 42, which 6 does divide. The least common multiple of 6 and 14 is 42.

What multiple of 11 is closest to -124?

Correct. To find the multiple of 11 closest to -124, divide -124 by 11, yielding an integer value of -11. -11 x 11 = -121 and -11 x 12 = -132. -124 lies between these values but it is closer to -121. Therefore, the multiple of 11 closest to -124 is -121.

What multiple of 6 is closest to 62?

Correct. To find the multiple of 6 closest to 62, divide 62 by 6, yielding an integer value of 10. 10 x 6 = 60 and 11 x 6 = 66. 62 lies between these values but it is closer to 60. Therefore, the multiple of 6 closest to 62 is 60.

If you divide by the Greatest Common Factor*, you will reduce the fraction to its lowest terms. The steps for the common factors method are as follows:

Divide numerator and denominator by a common factor. Continue to divide by common factors. Write the reduced factor.

Let's now transform 1/3 and −2/7 each into their equivalent fractions that share a common denominator of 21 , which we found in the example above. First, convert 1/3 to an equivalent fraction with a denominator of 21 .

Divide the LCD (the new denominator) by the current denominator. 21÷3=7 Multiply the numerator and denominators by 7 . (1×7)(3×7)=7/21 Now, let's transform −2/7 into an equivalent fraction with the common denominator Divide the LCD (the new denominator) by the current denominator. 21÷7=3 Multiply the numerator and denominators by 3 . (−2×3)(7×3)=−6/21 ur two new fractions with a common denominator are: 7/21 and −6/21

EQUIVALENT FRACTIIONS

Equivalent fractions* are fractions that have the same value, such as one-half and two-fourths. In numerical terms, 12=24 . It is often necessary to transform one fraction into another fraction that is equivalent to the first fraction.

IMPROPER FRACTIONS

In an improper fraction*, the numerator is greater than the denominator, and therefore, the value is greater than 1 (except if the fraction is negative, which we will discuss later). We can read these fractions as seven over four, six over one, and five over two. 7/4 6/1 5/2

Subtract the following fractions: 2/3−5/9=?

Find the least common multiple (LCM) of both 3 and 9 . The LCM of 3 and 9 is 9 . Step 2: Convert fractions to have like denominators. 2/3−5/9=(2⋅3)(3⋅3)−59=6/9−5/9 Step 3: Subtract the like fractions. 6/9−5/9=1/9 Therefore: 2/3−5/9=1/9

Add the following fractions: 1/4+1/3

Find the least common multiple (LCM) of both 4 and 3 The LCM of 4 and 3 is 12 . Step 2: Convert fractions to have like denominators: Multiplying both the numerator and denominator by 3 is equivalent to dividing each of the old parts into 3 parts. Multiplying the numerator and denominator by 4 is equivalent to dividing each of the old parts into 4 parts. The amount of each fraction (shaded region of the pies) remains the same, but we have the thinner slices in each pie. The point is we have the same thinner slices for each of the pies. 1/4+1/3=(1⋅3)(4⋅3)+(1⋅4)(3⋅4)=3/12+4/12 Now, we can add the like fractions: 3/12+4/12=7/12

Let's determine the least common denominator of 3/4 and 1/6 .

Find the least common multiple of the denominators. Do 4 and 6 have a common factor? Yes. This is situation 2. Take the larger number, 6 , and divide 4 into multiples of it. 4 does not divide 6 , but it divides 6×2=12 , so 12 is the least common multiple. 12 is the LCD for 3/4 and 1/6 Transforming Fractions

Generally, when finding common multiples, you will be asked to find the least common multiple (LCM)*,

Generally, when finding common multiples, you will be asked to find the least common multiple (LCM)*, the common multiple whose positive value is smallest. 12 is the least common multiple of 6 and 12 .

PROPER FRACTIONS

In a proper fraction*, the numerator is less than the denominator, and therefore, the value is less than 1 . We can read these fractions as four-fifths, one-half, and seven-eighths. 4/5 1/2 7/8

Reducing Fractions Using Common Factors

Many people prefer not to find every prime factor. If you can identify a common factor in both the numerator and denominator, you can simply divide the numerator and denominator by that common factor until no more common factors remain. This method seems easier to many people, but be careful when using it to make sure that there are no more common factors before writing down the answer. The danger in this method is you might miss a common factor.

Adding & Subtracting Mixed Numbers

Mixed Numbers Change the mixed numbers* to improper fractions*. Find the least common denominator (LCD) if the fractions have different denominators and convert to equivalent fractions with the LCD. Add or subtract the numerators of all the fractions in the expression. Keep the denominator the same. Change improper fractions to a mixed number (if needed). If necessary, reduce the fraction to lowest form.

Changing Mixed Numbers Into Improper Fractions Mixed numbers can also be converted to improper fractions by following these steps:

Multiply the whole number by the denominator of the fraction. To the product given by step 1, add the number of the numerator. Write the result of step 2 as the numerator of the improper fraction. The denominator of the improper fraction should be the denominator of the original fraction. Simplify the improper fraction by diving the numerator and denominator by all common factors.

Multiplying Mixed Numbers

Multiplying mixed numbers is similar to multiplying fractions. However, you will change the mixed number to an improper fraction to multiply, then change it back to a mixed number before reducing. To multiply mixed numbers, follow these steps: -Change any mixed numbers to improper fractions. -Multiply the numerators to obtain a new numerator. -Multiply the denominators to obtain a new denominator and write the answer in fraction form. -Change the improper fraction back to a mixed number. -Reduce the mixed number to the lowest terms, if necessary.

Are the fractions 5/50 and 10/500 equivalent? (Enter Yes or No)

NO

In this example, let's take a look at an example where the final answer needs to be reduced. 5/6−1/6=?

Remember the denominator stays the same. (5−1)6=4/6 Step 2: Reduce the fraction (if necessary). 4/6 Notice that the both the numerator, 4 , and the denominator, 6 , are both divisible by 2 . Therefore we can reduce this fraction to: (4÷2)(6÷2)=2/3

Adding & Subtracting Fractions with the Same Denominator

Same Denominators Add or subtract the numerators of all the fractions in the expression Keep the same denominator! (The temptation to add the two denominators is very strong—resist.) If necessary, reduce the answer. 2/7+3/7=5/7 Reduce the fraction (if necessary). 5/7 can not be reduced

For the numbers 7 and 9 , is the common multiple 63 also the least common multiple?

Since the two numbers do not share a common factor, their LCM is their product 7×9=63 . Therefore, the common multiple 63 is also the least common multiple.

How do you find the least common multiple?

Situation 1: If the two numbers do NOT share a common factor, multiply them together to find the least common multiple. For example, 2 and 3 have no common factors, so the LCM is 6 Situation 2: If the two numbers do have a common factor, you can list out the multiples of the greater number and divide the smaller number into each multiple. The first multiple of the greater number that the smaller number evenly divides is the LCM. Situation 3: Sometimes the smaller of the two numbers will divide the larger. The larger number then is the LCM for both numbers. For example, 12 is a multiple of 6 because 6×2=12 . Therefore, 12 is the LCM of 12 and 6 .

Least Common Multiple

Sometimes we want to find common multiples of two or more numbers. The easiest way to find a common multiple is to multiply the numbers by one another What is a common multiple of 2 and 3 ? To find a common multiple, multiply 2×3=6 . Clearly, both 2 and 3 evenly divide 6 , so 6 is a multiple of both. (Note that any multiple of 6 will be a common multiple of 2 and 3 . 2 and 3 both divide 6 evenly. If 6 divides another number evenly (all of its multiples) then both 2 and 3 will divide that number.)

The Butterfly Method: Identifying Equivalent Fractions

Suppose we have two fractions and want to know whether they are equal. Let's use 3/8 and 15/40 as an example. 3/8 ≟ 15/40 A simple way to determine whether these fractions are equal is to cross-multiply. In this example, cross-multiplying means multiplying 3×40 and 8×15 . If the two products are equal, the fractions are equivalent, or equal. Since 3×40=120 and 8×15=120 , we know that 3/8=15/40 The Butterfly Method* is a way to cross-multiply two fractions to determine whether they are equal. To use the Butterfly Method:

Situation 1: Least Common Multiples (LCM) of 7 and 8

The multiples of 7 are: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 ... The multiples of 8 are: 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 ... Notice that since 7 and 8 have no common factors, the LCM of 7 and 8 is 7×8=56

Transforming Fractions

The next step in preparing to add or subtract fractions is to transform each fraction into an equivalent fraction with the common denominator. To do this, we multiply the numerator and denominator by the same number. For example, if we want to transform 2/4 to a fraction with a denominator of 8 , we must multiply both the numerator and denominator by 2 . When we do that we get a numerator of 4 ( 2⋅2=4 ) and a denominator of 8 ( 2⋅4=8 ), or 4/8 . See below:

numerator and denominator

The number that is written before the slash, or above the fraction bar, is known as the numerator*. The second number, written after the slash, or below the fraction bar, is known as the denominator*. The numerator represents the number of equal parts. The denominator indicates how many of these equal parts make up one whole unit.

Reducing Fractions Using Prime Factorization

The steps to reduce a fraction through prime factorization are as follows: List the prime factors of both the numerator and denominator. Cancel the factors that are common to both the numerator and denominator. Multiply across the numerator and denominator.

Multiplying Fractions: Example #1 What is 3/5 of 1/5 ?

To answer the question we would multiply the fractions: 3/5×1/5 Step 1: Multiply the numerators to obtain a new numerator (3×1)=3 Step 2: Multiply the denominators to obtain a new denominator (3)(5×5)=3/25 Step 3: Write the answer in fraction form and reduce, if necessary 3/25 This fraction is already in its reduced form.

5/12 and 13/30 LCD

To find the least common denominator, we must find the least common multiple of the two denominators. The multiples of 30 that 12 divides is 60. The least common denominator (LCD) of 512 and 1330 is 60.

4/33 and 5/22 LCD

To find the least common denominator, we must find the least common multiple of the two denominators. The multiples of 33 are: 33, 66, which 22 divides. The least common denominator (LCD) of 4/33 and 5/22 is 66.

What multiple of 11 is closest to 112 ?

To find the multiple of 11 closest to 112 , divide 112 by 11 , yielding an integer value of 10 . 10×11=110 and 11×11=121 Since 112 lies between these values but it is closer to 110 , the multiple of 11 closest to 112 is 110 .

Finding least common multiples is key to adding and subtracting fractions because adding and subtracting fractions requires the fractions to have a common denominator.

To make the denominators of two fractions with different denominators the same, we need to first find the least common multiple* of those different denominators. In the context of working with fractions, we call this number the least common denominator*. For example, if we want to find the least common denominator for the fractions 27 and 114 , we would find the least common multiple of the two denominators: 7 and 14 . Since 7 divides 14 , the LCM is 14 . 14 is also the least common denominator.

in order to subtract fraction or mixed number what needs to be the same

Use the Tools In order to add or subtract fractions or mixed numbers, the denominators must be the same. When you encounter fractions or mixed numbers with different denominators, you must first transform them into fractions with a common denominator.

The Butterfly Method* is a way to cross-multiply two fractions to determine whether they are equal. To use the Butterfly Method:

Write the fractions as if they are equal with a question mark over the equal sign. Now draw "butterfly wings" around the opposite numerators and denominators. Multiply the numbers in each of the "butterfly wings." If the products are equal, then the fractions are equivalent.

Let's determine whether: 6/17 ≟ 36/101

Write the fractions as if they are equal, but put a question mark over the equal sign: 6/17 ≟ 36/101 Now draw "butterfly wings" around the 6 and the 101 , and around the 17 and the 36 , like this: Multiply the numbers in each of the butterfly wings: 6×101=606 17×36=612 Since the products are not equal ( 606≠612 ), the fractions are not equal.

Are these two fractions equal? 13/25 = 91/175

YES

Dividing fractions

much like multiplying fractions, except you use the reciprocal* of the divisor, that is the number which if you multiply it by the divisor, gives you 1. Consider the following operation: 4/5 and 5/4 are reciprocals because their product equals 1 . dividing by a fraction requires multiplying by the reciprocal.

You are given the fractions x/ 10 and 5/ y . What will the product x · y have to be for the fractions to be equal? Enter the letter than corresponds with your answer.

multiply the numbers in each of the butterfly wings. One product is 10 · 5 = 50, and the other one is x · y. For the fractions to be equal, the products must be the same. Therefore, x · y has to be 50 for the fractions to be equal. X*Y=50