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neurologyYou need to know

• A fraction has a numerator and a denominator, where the numerator shows how many parts are taken and the denominator shows how many equal parts make one whole.
• The denominator of a fraction cannot be 0.
• A fraction is in its simplest form when the numerator and denominator have no common factor greater than 1.
• Equivalent fractions have the same value even though their numerators and denominators are different.
• Equivalent fractions are made by multiplying or dividing both the numerator and the denominator by the same non-zero integer.
• To write one quantity as a fraction of another, both quantities must be expressed in the same unit before forming the fraction.
• When one quantity is written as a fraction of another, the first quantity becomes the numerator and the second quantity becomes the denominator.
• A fraction can represent part of a whole or part of a set, as long as the parts are equal in size or value.
• Fractions can be simplified before or after a calculation, and simplifying does not change the value of the fraction.
• To add or subtract fractions, the fractions must have a common denominator.
• A common denominator is a common multiple of the denominators, and using the lowest common denominator often makes the calculation simpler.
• When fractions have the same denominator, they are added or subtracted by combining the numerators and keeping the denominator the same.
• To multiply fractions, multiply the numerators together and multiply the denominators together.
• A whole number can be written as a fraction with denominator 1, for example `3 = \frac{3}{1}`.
• To divide by a fraction, multiply by its reciprocal, and division by zero is undefined.
• The reciprocal of a fraction is found by swapping its numerator and denominator, for example the reciprocal of `\frac{2}{3}` is `\frac{3}{2}`.
• Only a non-zero fraction has a reciprocal.
• A final answer to a fraction calculation should usually be given in its simplest form unless a different form is requested.

• Simplify a fraction by identifying the highest common factor of the numerator and denominator and dividing both by it.
• Write one quantity as a fraction of another by converting both quantities into the same unit, placing the first quantity over the second, and simplifying the result.
• Generate equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero integer.
• Find a common denominator for two fractions, rewrite each fraction as an equivalent fraction, and then add or subtract the numerators accurately.
• Add fractions with different denominators and simplify the answer fully.
• Subtract fractions with different denominators and simplify the answer fully.
• Multiply two fractions by multiplying the numerators and denominators, cancelling common factors first where helpful, and simplifying the product.
• Divide one fraction by another by changing the second fraction to its reciprocal, multiplying, and simplifying the answer.
• Check whether a fraction answer is reasonable by comparing it with benchmark values such as 0, `\frac{1}{2}`, and 1 after the calculation.