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Add and subtract fractions with unlike denominators (medium)

3/4+1/2=?

Adding and subtracting fractions

If the denominators (the bottom numbers) are the same, we just need to add or subtract the numerators (the top numbers).

$$5/7+1/7=6/7$$
$$4/9−3/9=1/9$$

If the denominators (the bottom numbers) are different, we need to find the least common denominator. We can do this by following these steps:

$$1/4+1/2$$

Step 1: Convert fractions to have the same denominator (by multiplying):

$$1/4+1/2×2/2=1/4+2/4$$
Step 2: Add or subtract the numerators (the top numbers), and write the result over the same denominator (the bottom number).
$$1/4+2/4=3/4$$

Sometimes is better to divide one of the fractions:

$$4/6+2/3={4÷2}/{6÷2}+2/3=2/3+2/3=4/3$$

And in some cases you have to multiply or divide both fractions:

$$4/7−1/3=4/7×3/3−1/3×7/7=$$
$$=12/21−7/21=5/21 $$

If you are adding/subtracting fractions and whole numbers, you can turn the whole number into a fraction with the same denominator.

$$1/5+1=?$$
$$1=1/1=2/2=3/3=4/4=5/5$$
$$\;→\;1/5+5/5=6/5$$
$$13/3−4=?$$
$$4=4/1=8/2=12/3\;→\;13/3−12/3=1/3$$

   
   

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