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For example, to multiply \frac{1}{4} \times \frac{2}{3} , you would calculate 1 \times 2 = 2 and 4 \times 3 = 12 , resulting in \frac{2}{12} , which simplifies to \frac{1}{6} .
Dividing by a fraction is the same as multiplying by the reciprocal of that fraction. The reciprocal is just the top and bottom flipped.
For example, to divide \frac{1}{4} by \frac{2}{3} , you multiply \frac{1}{4} by \frac{3}{2} to get \frac{1 \times 3}{4 \times 2} = \frac{3}{8} .
For example, to add \frac{1}{4} + \frac{1}{3}, convert them to \frac{3}{12} + \frac{4}{12}, then add the numerators to get \frac{7}{12}.
For instance, \frac{3}{4} - \frac{1}{2} becomes \frac{3}{4} - \frac{2}{4} = \frac{1}{4} .
Simplified Fraction - a fraction written in simplest form, where the numerator and denominator do not have any other factors except 1:
For example, to simplify \frac{18}{24} , find the GCD of 18 and 24, which is 6, and divide both by 6 to get \frac{3}{4} .
Fractions are everywhere!
Fractions are used considerably in real life. Examples are cooking, to measure ingredients; construction, to divide land or materials; finance, for calculating interest and investment; and many more situations where ratios are important, for example, mixing substances or making solutions.Here are some examples:
Cutting a pizza into slices (1/8 of the pie, anyone?)
Following a recipe (2 1/2 cups of flour)
Measuring distances on a map (the scale might be 1 inch = 1/4 mile)
Sharing things fairly (dividing candy between friends)
Representing probabilities (the chance of it raining is 3/5)
Did you know？
The word 'fraction' comes from the Latin word 'fractio', which directly means 'to break'. Fractions of the measurement of land and ingredients were loved by the ancient Egyptians. There are also special symbols for fractions that rise above the horizontal line, such as diagonal fractions that are used in engineering.
Fractions are a jumping-off point for more sophisticated mathematical concepts: ratios, percentages, and decimals.
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