Fractions » Adding and subtracting fractions

Equal denominators

When you have equal denominators you can immediately add or subract the numerators.

Examples
38 + 28 = 58
57 – 37 = 27
356 + 56 = 446 = 423
Explanation last example using more intermediate steps:
356 + 56 = 3 + 106 = 3 + 66 + 46 = 3 + 1 + 46 = 446 = 423
In the last step, you simplify.

Making the denominators equal

It can happen that you have to add or subtract fractions where the denominators are not equal. In that case you have to make the denominators equal. The ratio in the fraction has to stay the same.

Example
47 + 34 = 1628 + 2128 = 3728 = 1928
The denominators 7 and 4 are not equal, so we have to make them equal ourselves. We will make the denominators 7 × 4 = 28.
The ratio 47 has to have a denominator of 28.
To do that we have to multiply the denominator with 4.
To keep the correct ratio we have to multiply the numerator also with 4.
The ratio 34 also has to have a denominator of 28.
To do that we have to multiply the denominator with 7.
To keep the correct ratio we have to multiply the numerator also with 7. Above and below the division line, you do the same. Only then you can add or subtract and if needed simplify your answer.

More examples

23 + 16 = 46 + 16 = 56
18 + 35 = 540 + 2440 = 2940
23 – 17 = 1421 – 321 = 1121

Greater than 1

Method 1: Take or carry one

If you add mixed numbers (whole number and a fraction) you somethimes have to carry 'one' to the whole number or take 'one' from the whole number.

Examples
347 + 256 = 32442 + 23542 = 55942 = 61742
715 – 334 = 7420 – 31520 = 62420 – 31520 = 3920

In the first example, you cannot leave 5942, so remove 4242 and carry 1.
In the second example 420 – 1520 is not possible, so you have to take 1 and add 2020 to the fraction.

Method 2: Put the whole number entirely into the fraction

When you have to add or subtract mixed numbers, you convert the mixed number into an improper fraction.

Example
715 – 334 = 365 – 154 = 14420 – 7520 = 6920 = 3920

Remember that 7 is the same as 355. So 715 = 355 + 15 = 365.

Of course you can alse make the denominators equal to 20 before you take the whole part of the number into the fraction.