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Why must mixed numbers be converted to improper fractions before multiplying or dividing?
Wiki User
∙ 13y ago
You do not need to convert them, but it makes the calculation much simpler.
For example to multiply 31/4 by 71/5:
31/4 = 3 + 1/4
71/5 = 7 + 1/5
31/4 x 71/5 = (3 + 1/4) x (7 + 1/5)
= 3 x 7 + 3 x 1/5 + 1/4 x 7 + 1/4 x 1/5
= 21 + 3/5 + 1 3/4 + 1/20
= 21 + 12/20 + 1 + 15/20 + 1/20
= 22 + 18/20
= 232/5
Or, using improper fractions:
3 1/4 = 13/4
71/5 = 36/5
31/4 x 71/5 = 13/4 x 36/5
= (13 x 36)/(4 x 5)
= (13 x 9)/5
= 117/5
= 232/5
Which with less calculations to be done is simpler and less liable to incur a mistake.
With division the calculations would be horrendous whereas with improper fractions the "invert divisor and multiply" rule can be used very effectively:
31/4 / 71/5
13/4 / 36/5 = 13/4 x 5/36
= 65/144
Wiki User
∙ 13y ago
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Why is it necessary to convert mixed fractions to improper fractions before multiplying or dividing?
Multiplying mixed fractions is very cumbersome and prone to errors. Therefore, it is prudent to convert them to improper fractions. Once that is done, you may simply find the product of all the numerators and divide that by the product of all the denominators. Then you convert back to a mixed number. And there are lots of tricks -- like "canceling out" -- that you can do to simplify the multiplication. Unfortunately, those techniques are very difficult to demonstrate here. It would not be even if it is not an improper fraction and that's why you have to convert
Is there a trick to multiplying mixed numbers?
you have to turn them into improper fractions before you multiply them.
What are the characteristics of improper fractions?
Improper fractions have numerators that are greater than or equal to their denominators.
Are improper fractions integers?
No, they are improper fractions. They can be equivalent to integers if the numerator is a multiple of the denominator.
How are proper and improper fractions different?
proper factions are fractions under a whole number improper fractions are Example: proper: 1/2 improper: 3/2
Why do you change mixed numbers to improper fractions before multiplying and dividing?
Because common denominators allow adding and subtracting of numerators. Improper fractions also have simplified rules over mixed numbers when performing multiplication and division.
How is multiplying mixed numbers different than multiplying fractions?
if you have mixed numbers you make them into improper fractions before you multiply
When dividing fractions does the answer always end with an improper fraction?
Not always. There are times when division of fractions results in a non-improper fraction.
How do add mixed improper fraction?
Mixed numbers can be converted to improper fractions. Improper fractions can be added the same way proper fractions are.
How is dividing mixed numbers the same as dividing fractions?
A mixed number can be converted into an improper fraction. Mixed numbers as improper fractions can be divided just like any other fraction. To convert a mixed number to an improper fraction multiply the whole number by the denominator and add the original numerator to give the new numerator and put this over the original denominator.
Should all improper fractions be converted to mixed fractions?
Yes they should
How is a mixed number and an improper fraction similar?
Mixed fractions can be converted into improper fractions then changed back to a mixed number.
Why is it necessary to convert mixed fractions to improper fractions before multiplying or dividing?
Multiplying mixed fractions is very cumbersome and prone to errors. Therefore, it is prudent to convert them to improper fractions. Once that is done, you may simply find the product of all the numerators and divide that by the product of all the denominators. Then you convert back to a mixed number. And there are lots of tricks -- like "canceling out" -- that you can do to simplify the multiplication. Unfortunately, those techniques are very difficult to demonstrate here. It would not be even if it is not an improper fraction and that's why you have to convert
How to Multiply fractions with integers?
Convert the mixed fractions into improper fractions. Convert the integer into a fraction by simply dividing it by 1
Is there a trick to multiplying mixed numbers?
you have to turn them into improper fractions before you multiply them.
When dividing fractions what is it most helpful to change a mixed number into?
improper fraction
When dividing fractions it is most helpful to change a mixed number into an?
improper fraction
