Equivalent Fractions Finder

About Equivalent Fractions Finder

Equivalent fraction refers to a fraction with equal values, which is based on two quantities having a definite proportional relationship. The equivalent fractions have the same value, but they look different because when you multiply or divide the numbers at both the top and bottom of the fraction by the same number, the value of the fraction remains unchanged. Multiplying or dividing both the numbers by the same value both the top and bottom of the fraction can obtain the equivalent fraction. It can be multiplied or divided, but not added or subtracted to obtain the equivalent fraction.

Although this is a simple process, it is not easy to intuitively obtain the equivalent fractions of a certain fraction. Therefore, we have created this Equivalent Fractions Finder, which provides two options: enter a fraction in the first input box, and then enter the number of equivalent fractions to be obtained in the second input box. Click the "Find" button to obtain the list of equivalent fractions, Simple and easy to operate.

Let's continue learning how to use equivalent fractions.

1. Simplify fractions to the fractions in the lowest terms.

1. See if the numerator is greater than the denominator. Such a fraction is called an improper fraction. If an improper fraction is represented as an integer plus a proper fraction (a fraction with a numerator smaller than the denominator), it may be better understood. The combination of an integer and a proper fraction is called a mixed number.
If the numerator is greater than the denominator, then divide the numerator by the denominator. The quotient obtained is the integer part with fractions, and the remainder is the numerator of the new fraction. For example,
148
is an improper fraction. If you divide 14 by 8, the quotient obtained is 1 and the remainder is 6. With a mixed number, it is 1
68
, and its value is the same as
148
.
2. Find the greatest common factor between the numerator and denominator. The greatest common factor is the maximum number that can divide both the numerator and denominator simultaneously. Taking the example of
   68
   with fractions given above, the greatest common factor between numerator 6 and denominator 8 is 2.
3. The quotient obtained by dividing the numerator and denominator by the greatest common factor will become the new numerator and denominator. The quotient of 6 divided by 2 is 3; The quotient of 8 divided by 2 is 4. Therefore, the
   68
   reduction is
   34
   ;
   148
   is simplified to the mixed number, which is 1
   34
   .

2. Adding fractions with different denominators

1. Find the least common denominator. The least common denominator is the least common multiple of all denominators, which is the smallest number that can be divided by all denominators. For example, when calculating
   112
   plus 2
   13
   , the minimum common denominator is 6 (2 X 3 equals 6 and 3 X 2 equals 6); When calculating
   16
   plus
   89
   , the minimum common denominator is 18 (6 X 3 equals 18; 9 X 2 equals 18).
Finding the minimum common denominator is mainly to simplify the calculation. In the second example just now,
112
plus 2
13
, 6 is a common multiple of the denominators 2 and 3. Compared to the common denominator 6, using the minimum common denominator "6" can simplify the calculation as much as possible, making the formula more intuitive and easier to understand.
2. Multiplying the numerator and denominator of each fraction by the same number can convert the denominator of each fraction to the minimum common denominator. That is to say, this can make the denominator values of each fraction equal. For example, when calculating 1
   12
   plus 2
   13
   , we need to change their denominators to 6.
   12
   is converted to
   36
   ;
   13
   is converted to
   26
   . For example,
   16
   plus
   89
   , their minimum common denominator is 18;
   16
   converted to
   318
   ; Convert from
   89
   to
   1618
   .
3. Numerator addition. For example, 1
   12
   plus 2
   13
   can be converted to 1
   36
   plus 2
   26
   , and the sum of the fractional parts is
   (3+2)6
   , which is
   56
   . For example,
   16
   plus
   89
   can be converted to
   318
   plus
   1618
   , and the sum is
   (3+16)18
   , which is
   1918
   .
4. If it is a mixed number, it is necessary to add up the integer parts. For example, 1
   12
   plus 2
   13
   , 1 plus 2 equals 3, so the total sum with fractions is 3
   56
   .
5. If necessary, simplify the result to the fraction in the lowest terms. If the numerator is greater than the denominator, then divide the numerator by the denominator and use the resulting quotient as the integer part with fractions. For example,
   16
   plus
   89
   , its result is represented as an improper fraction of
   1918
   , and ultimately converted to a mixed number of 1
   118
   .

3. Adding fractions with different denominators

1. Find the least common denominator.
2. Multiplying the numerator and denominator of each fraction by the same number can convert the denominator of each fraction to the minimum common denominator.
3. Check if the numerator of the first fraction (subtracted) is smaller than the numerator of the second fraction (subtracted). If so, it is necessary to borrow the values of integer parts with fractions. For example, the minuend is 3
   58
   , and the subtrahend is 1
   34
   ; After converting the subtraction to an equivalent fraction of 1
   68
   , you will find that the numerator of the subtracted number is 5, which is smaller than the numerator of the subtracted number 6, so borrowing the integer part is necessary. Subtract 1 from the integer part of the subtracted number, and add the numerator of the fraction part with the same value as the denominator. After this operation, a new equivalent fraction is generated. 3
   58
   is equivalent to an improper fraction of 2
   138
   .
4. Subtract the subtrahend numerator from the minuend numerator. Using the example just now, the result of the fraction should be
   (13-6)8
   , or
   78
   .
5. If the equation contains a mixed number, then subtract the integer part of the subtrahend from the integer part of the 'minuend'. Due to the necessity of borrowing the integer part in the above example, the result of the integer part should be 2-1 = 1. So, the result of subtracting the subtrahend from the minuend should be 1
   78
6. If necessary, simplify the result to the fraction in the lowest terms.