Calculate equivalent fractions for any fraction, mixed number, or whole number, check whether two fractions are equal, and solve for a missing numerator or denominator.
Equivalent Fractions Formula
This calculator works in three modes. It can list fractions that equal a fraction you enter, check whether two fractions are equal, and solve for a missing number in a proportion. The mode you choose sets which formula is used.
List mode: a/b = (a*k)/(b*k)
Check mode: a/b = c/d when a*d = b*c
Missing number: a/b = c/d, so the missing value = (the two known cross terms) / (the remaining known term)
- a = numerator (top number) of the first fraction
- b = denominator (bottom number) of the first fraction
- c = numerator of the second fraction
- d = denominator of the second fraction
- k = any whole number you multiply both top and bottom by
In list mode you enter one fraction, mixed number, or whole number and pick how many equivalents you want. The calculator multiplies the numerator and denominator by 2, 3, 4, and so on, so every result is the same value written with larger numbers. In check mode you enter two fractions and the calculator cross multiplies: if the two products match, the fractions are equivalent. In missing number mode you fill three of the four spots in a/b = c/d, and the calculator solves the proportion by cross multiplying and dividing to find the value that completes it.
Equivalent Fractions of Common Fractions
The table below shows the first few equivalent fractions for some common fractions. Each one is found by multiplying the top and bottom by the same number. Use it as a quick check against the calculator.
| Fraction | x2 | x3 | x4 | x5 |
|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 |
Example Problems
Example 1: List equivalent fractions. You enter 3/5 and ask for three equivalents. Multiply the top and bottom by 2 to get 6/10, by 3 to get 9/15, and by 4 to get 12/20. So 3/5 = 6/10 = 9/15 = 12/20.
Example 2: Check two fractions. You want to know if 4/6 and 6/9 are equivalent. Cross multiply: 4 times 9 is 36, and 6 times 6 is 36. The products match, so the two fractions are equivalent.
Frequently Asked Questions
What makes two fractions equivalent? Two fractions are equivalent when they represent the same value. You get an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same nonzero number, which changes how the fraction looks but not its size.
How do I check if two fractions are equal without listing them? Cross multiply. Multiply the numerator of the first by the denominator of the second, then the denominator of the first by the numerator of the second. If the two results are equal, the fractions are equivalent.
How do I solve for a missing number in a/b = c/d? Use cross multiplication. The product of one diagonal equals the product of the other, so you multiply the two known numbers that sit across from each other and divide by the remaining known number to find the missing value.
