Fractions can be added or subtracted if, and only if, they have the same denominator. If the denominator is not the same, we can expand the fractions. Expanding means that we multiply both the numerator and the denominator with the same number. Expanding is marked to the left of the fraction.
When multiplying fractions we multiply the numerators and the denominators.
During division, the first fraction is multiplied by the inverse of the latter fraction. If we have 2/5 and divide it by 2, then only 1/5 remains. If we multiply the same number (2/5) by half, i.e. 1/2, in other words, take half of it, then 1/5 is left. Dividing by two is the same as multiplying by half. The inverse of 2 is 1/2. Dividing by half is the same as multiplying by two.
When we multiply a fraction by an integer, only the numerator is multiplied. If we have 2/5 and multiply it by 2, we get 4/5. Initially, we have two fifths and "multiply" them twice, the result is four fifths.
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