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What number can be added to both the numerator and denominator of sixty one over seventy eight to make four over five?
Sisters1
(61+n)/(78+n)=4/5
Solving for n gives n=7
Wiki User
∙ 13y ago
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What algorithms will produce the correct result for the sum a b where a and b each represent rational numbers?
You are basically asking how to add two fractions together: Assuming your rational numbers are in the form of a fraction with a numerator over a denominator (could be stored as an ordered pair, or an ordered triple [for mixed numbers]). If the numbers are mixed numbers the first step is to convert them to improper fractions. To add rational numbers the denominators must be the same. If they are not the same then the fractions need to be converted into equivalent fractions with the same denominator. Then the fractions are added by adding together the numerators Finally the result is simplified by dividing the numerator and denominator by their Highest Common Factor (HCF). If the numerator is greater than or equal to the denominator, then the fraction is converted to a mixed number. To convert a mixed number to an improper fraction, the new numerator is the whole number multiplied by the denominator plus the original numerator; the new denominator is the original denominator. To find the new denominator for equivalent fractions it is best done by finding the lowest common multiple (LCM) of the denominators. To find the LCM, there are various methods, but I would suggest* using the fact that the product of the HCF and LCM of two number is the product of those two numbers; then the LCM is the product of the numbers divided by their HCF. The HCF of two numbers is easily found by using Euclid's method: to find the HCF of two numbers a and b: 1) find the remainder (r) of the first number (a) divided by the second (b) 2) If the remainder is 0, the HCF is the second number; otherwise 3) replace the first number (a) by the second number (b) 4) replace the second number (b) bu the remainder (r) 5) repeat from step 1. (If a < b the first time through the algorithm will swap a and b so that a > b.) There is no need to check for denominators being the same as the LCM will work out to be the current denominator. To convert a fraction with one denominator to an equivalent fraction with a new denominator, the new numerator is found by multiplying the old numerator by the new denominator and divide by the current denominator (which is the same as finding out how many times the current denominator divides into the new denominator and multiplying the numerator by this). I To do the addition, the numerators are added together and the denominator is kept. To simplify the fraction find the HCF of the numerator and denominator and divide each by this HCF. (No real need to check for HCF = 1 → fraction already as simple as possible but dividing by 1 will leave the numerator and denominator as they are!) To convert an improper fraction to a mixed number, divide the numerator by the denominator to get a whole number quotient and a remainder. The remainder is the numerator over the denominator for the fraction of the mixed number with the quotient as the whole number. If the whole number is zero, then the fraction is a proper fraction; if the remainder is zero, then the fraction is a whole number. ----------------------- * This suggestion means the LCM function becomes: LCM(a, b) = a * b / HCF(a, b) And only the HCF function need be worked out in a full algorithm. For two numbers Euclid's method provides an easy function. For more than 2 numbers I would use the prime factorization method.
Does a ratio remain unchanged if 1 is added to both the numerator and denominator?
You should not do that...1/4 and 2/5 are not the same thing(1 divided by 4 = 0.25) (2 divided by 5 = 0.4)
Adding and subtracting unlike denominators?
Fractions can only be added or subtracted if the denominators are the same. If the denominators are different, then the fractions need to be made into equivalent fractions with the same denominator. The new denominator can be found simply by multiplying the denominators together, but this can lead to some large fractions with which to work. A better new denominator is the lowest common multiple of (all the) denominators. (Once the new denominator is found, the fractions' new numerators are found by multiplying their current numerator by the new denominator divided by their current denominator to make their equivalent fractions with the new denominator.) Once all the fractions are converted into equivalent fractions with the new denominator then the fractions can be added or subtracted, with the result being simplified (if possible).
What is 2 and 8 12 as in improper fractions?
To convert from mixed number to improper fractions, you first need to multiply the whole part by the given denominator. In this case, the denominator is 12 and the whole part is 2. Multiplying gives: 2x12 = 24. This is then added on to the existing numerator: 24+8 = 32 And so as an improper fraction the answer is 32/12 Note that this can still be simplified down to 8/3
One ninth plus five sixths?
5/9 + 1/6 First find the common denominator You can multiply both the 9 and the 6 to make 18. (9x2) (6x3) Because you multiply the denominator, you also have to multiple the numerator. 5x2=10 and 1x3=3 You now have 10/18 + 3/18 Now add the numerator 10+3=13 Your answer to the added numerator goes over the common denominator. 13/18.
What number must be added to the denominator of 9 over 16 so that when the numerator is doubled the result is 1?
Doubling the numerator gives 2 × 9 = 18 To have a result of 1, the numerator and denominator must be the same. Thus the denominator needs to be 18. 18 - 16 = 2 → 2 must be added to the denominator.
How can you make a reciprocal out of a mixed number?
First you need to make the mixed number into a improper fraction. To do this, take the denominator times the number in front. Then add the result to the numerator. Then the improper fraction is that result over the denominator. _______________________________________________________________ If X is the leading number, D is the denominator, N is the numerator: X and N/D=(X*D+N)/D _______________________________________________________________ Then take this new fraction and flip the numerator and the denominator: D/(X*D+N) _______________________________________________________________ So to get the reciprocal of a mixed number in one step, the reciprocal's: numerator is equal to the denominator of the mixed number; denominator is equal to the leading number multiplied by the denominator added to the numerator.
What happens if you have a mixed number how do you make it a reciprocal?
A mixed number is simply a whole number and a fraction. The value of a mixed number would be the whole number added to the fraction. To find its reciprocal: _______________________________________________________________ 1. You need to make the mixed number into a improper fraction. To do this, take the denominator times the number in front. Then add the result to the numerator. Then the improper fraction is that result over the denominator. A mixed number is formatted as a leading number and a fraction. If X is the leading number, D is the denominator, N is the numerator: X and N/D=(X*D+N)/D _______________________________________________________________ 2. Then take this new fraction and flip the numerator and the denominator: D/(X*D+N) _______________________________________________________________ So to get the reciprocal of a mixed number in one step, the reciprocal's: numerator is equal to the denominator of the mixed number; denominator is equal to the leading number multiplied by the denominator added to the numerator: D/(X*D+N)
How do you change improper fractions into a mixed fraction?
1. See how many times the denominator or numerator goes into the numerator or denominator.2. Write the answer as a whole number.3. Draw a fraction bar next to it and write the original denominator.4. On top, write the number of how much is left.5. There is your answer!Example: 8/3 How much times does the denominator go into the numerator? 2 times. So, 2 is the whole number.The original denominator given is 3, so you put it in like this: 2 /3 (2 is there because it is the whole number, and you must keep it next to it.)After, see how much is left. If you add 2 to the denominator, you will get the numerator's number. Put the added number as the numerator So, the answer will be: 2 and 2/3.
What fraction equivalent to 34 that and numerator and denominator when added together equal 84?
3/4 = 36/48.
If a fraction becomes 2 when 9 is added to its numerator and 1 when 2 is substracts from its denominator then the fraction is?
It is 5/7.
What algorithms will produce the correct result for the sum a b where a and b each represent rational numbers?
You are basically asking how to add two fractions together: Assuming your rational numbers are in the form of a fraction with a numerator over a denominator (could be stored as an ordered pair, or an ordered triple [for mixed numbers]). If the numbers are mixed numbers the first step is to convert them to improper fractions. To add rational numbers the denominators must be the same. If they are not the same then the fractions need to be converted into equivalent fractions with the same denominator. Then the fractions are added by adding together the numerators Finally the result is simplified by dividing the numerator and denominator by their Highest Common Factor (HCF). If the numerator is greater than or equal to the denominator, then the fraction is converted to a mixed number. To convert a mixed number to an improper fraction, the new numerator is the whole number multiplied by the denominator plus the original numerator; the new denominator is the original denominator. To find the new denominator for equivalent fractions it is best done by finding the lowest common multiple (LCM) of the denominators. To find the LCM, there are various methods, but I would suggest* using the fact that the product of the HCF and LCM of two number is the product of those two numbers; then the LCM is the product of the numbers divided by their HCF. The HCF of two numbers is easily found by using Euclid's method: to find the HCF of two numbers a and b: 1) find the remainder (r) of the first number (a) divided by the second (b) 2) If the remainder is 0, the HCF is the second number; otherwise 3) replace the first number (a) by the second number (b) 4) replace the second number (b) bu the remainder (r) 5) repeat from step 1. (If a < b the first time through the algorithm will swap a and b so that a > b.) There is no need to check for denominators being the same as the LCM will work out to be the current denominator. To convert a fraction with one denominator to an equivalent fraction with a new denominator, the new numerator is found by multiplying the old numerator by the new denominator and divide by the current denominator (which is the same as finding out how many times the current denominator divides into the new denominator and multiplying the numerator by this). I To do the addition, the numerators are added together and the denominator is kept. To simplify the fraction find the HCF of the numerator and denominator and divide each by this HCF. (No real need to check for HCF = 1 → fraction already as simple as possible but dividing by 1 will leave the numerator and denominator as they are!) To convert an improper fraction to a mixed number, divide the numerator by the denominator to get a whole number quotient and a remainder. The remainder is the numerator over the denominator for the fraction of the mixed number with the quotient as the whole number. If the whole number is zero, then the fraction is a proper fraction; if the remainder is zero, then the fraction is a whole number. ----------------------- * This suggestion means the LCM function becomes: LCM(a, b) = a * b / HCF(a, b) And only the HCF function need be worked out in a full algorithm. For two numbers Euclid's method provides an easy function. For more than 2 numbers I would use the prime factorization method.
How do you borrow from a whole number for the numerator?
In any mixed number, one whole will equal whatever the denominator is over itself. 3 and 1/4 = 2 and 5/4 because we took 4/4 out of 3 and added it to 1/4
Why do you multiply the whole number by the denominator to get a mixed fraction?
You don't. But you do. When converting a mixed number into an improper fraction. A mixed fraction contains a whole number and a proper fraction, for example 23⁄4. To convert this to an 'improper' fraction, the whole number is multiplied by the denominator and added to the numerator to obtain the new numerator. See. but WHY? The denominator remains unchanged (unless, of course, you wish to simplify the fraction). This is unrelated! At no point did you actually provide an answer to this question.Continuing with the original example, for 23⁄4, (2 · 4 + 3) = 11, so the new fraction is 11⁄4.Ps. Anything in italics has been improved by another person.
What number must be added to three hundred seventy five to get the number one thousand?
625
What is the sum of two thirds and four ninths?
Only fractions with the same denominator can be added directly. Addition of such fractions can be achieved by adding their numerators to form the numerator of the sum, with the common denominator of the added fractions constituting the denominator of the sum. In this instance, 2/3 = 6/9, and 4/9 + 6/9 = 10/9.
How do you use rectangular models for multiplying fractions?
Draw as many rectangles as the whole number you are multiplying by. Then, draw the fraction you are multiplying by in all of the rectangles. Shade in the top number in the fraction [numerator] in your rectangles. Count all the shaded in parts of all your rectangles. Leave the bottom number of your fraction [denominator] the same and put the number you got when you added the shaded parts of the rectangles on top as your denominator of the fraction. That is your answer!
