Adding two 1/3 cups gives you 2/3 cups. In decimals, 1/3 of a cup is .33 cups, therefore .33 cups pluns .33 cups equates to .66 cups. The United States customary cup holds 8 fluid ounces. Since 1/3 or .33 of 8 ounces is 2.64 ounces, 2/3 U.S. fluid cups or 1/3 U.S. cups plus 1/3 U.S. cups is equivalent to 5.28 U.S. fluid ounces. The British imperial cup holds 10 imperial ounces. This means that 1/3 or .33 of 10 ounces is 3.3 ounces. Thus, 1/3 imperial cups plus 1/3 imperial cups is 6.6 ounces.

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Fractions are defined as a part of a whole, written with a top number called a numerator, and a bottom number is called the denominator. A division line called a vinculum separates the numerator and denominator in fractions.

Fractions are often presented with a numerator of a lower number than the denominator. However, there are fractions with numerators that are greater than their denominators. Such fractions are called "improper fractions." Improper fractions may be converted into mixed fractions, which is a whole number accompanied by a fraction, such as in 1 1/2.

Adding Fractions

Adding fractions is easy. With fractions that have an identical denominators such as in 1/3 + 1/3, add the numerators and retain the denominator. Thus 1/3 + 1/3 = 2/3. In fractions that don"t have an identical denominator, such as in 1/2 + 1/3, multiply the numerators with the denominators of the other fraction, and then add the results which will be your new numerator.

Since multiplying 1x2 gives you 2 and 1x3 gives you 3, adding 2+3 will give you 5, which becomes your new numerator. Next, multiply the denominators of the two fractions, and the result will be your new denominator. Thus, 1/2 + 1/3 equals 5/6.

Converting Fractions to Decimals

Fractions resemble division formulas because they represent division. In other words, 1/3 means 1÷3, which gives you 0.33. 1/3 cups, therefore, is equivalent come .33 cups and 0.33 cups plus .33 cups amounts to .66 cups.

Cups in U.S. Customary and British Imperial Systems

Both the U.S. customary and British imperial system units of measurements are based on the old English system. While the units measurements for length, weight, distance, and area are identical in both the U.S. customary and imperial systems, their units for volume such as fluid ounces, cups, pints, quarts, and gallons differ.

Using the metric system for volume as, a U.S. fluid ounce is equivalent to 29.573 milliliters (mL). Since a U.S. fluid cup holds 8 fluid ounces, one U.S. cup holds 236.48 mL ― 1/3 or .33 of which is 78.04 mL. This makes 2/3 of a cup equivalent to 156.07.

The imperial fluid ounce holds 28.413 ml. Since 1 imperial cup holds 10 imperial fluid ounce, 1 imperial cup is equivalent to 284.13 mL. Using the same calculations as above, 1/3 of an imperial cup is 93.76 mL, and 2/3 of an imperial cup is equivalent to 187.52 mL.

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The Metric System Cup

Although seldom used, the metric system also has its own version of the cup. One metric system cup measures 250 mL. One-third of a metric system cup is 82.5 mL. Therefore, 1/3 metric system cup plus 1/3 metric system cup equals 2/3 metric system cups, which is 165 mL.