Does 2 3 and 1 3 equal a cup?

No, 2 thirds and 1 third do not equal a cup. A cup is a standardized unit of volume measurement used in cooking. 2 thirds plus 1 third equals 3 thirds, which is equal to 1 whole. But a cup is not the same as 3 thirds or 1 whole. A cup is a specific volume measurement defined differently in various parts of the world.

Defining a Cup

A cup is a unit of volume typically used in cooking recipes and defined differently in the US customary system and the metric system.

Cup in the US Customary System

In the US customary system, a cup is defined as exactly 236.5882365 milliliters. It is abbreviated as “c” or “cup”. Some key facts about a US cup:

– 1 US cup = exactly 236.5882365 mL
– 2 US cups = 473.176 US fluid ounces
– 16 US cups = 1 US gallon
– 1 US liquid quart = approx 2 US cups

So a US cup is a standardized volume measurement equivalent to 236.5882365 mL.

Cup in the Metric System

In the metric system, a cup is defined as exactly 250 milliliters. It is abbreviated as “c” or “metric cup”. Some key facts about a metric cup:

– 1 metric cup = exactly 250 mL
– 2 metric cups = 500 mL
– 4 metric cups = 1 liter
– 1,000 metric cups = 1 cubic meter

So a metric cup is a standardized volume measurement equivalent to 250 mL.

3 Thirds Does Not Equal 1 Cup

While 2 thirds plus 1 third equals 3 thirds or 1 whole, 3 thirds does not equal 1 cup. This is because a “third” is not a standardized volume measurement like a cup. A third simply refers to one part when something is divided into three equal parts.

For example, if we take a pie and cut it into 3 equal slices, each slice would be 1 third of the pie. If we took 2 of those slices, we would have 2 thirds of the pie. If we also add the remaining 1 slice, now we have all 3 slices, which represents 3 thirds or the entire pie.

But the volume of those 3 slices does not necessarily equal 1 standardized US or metric cup. The volume depends entirely on the size of the pie. 3 thirds of a very large pie will be much more than 1 cup. And 3 thirds of a tiny pie will be much less than 1 cup.

So while 2 thirds + 1 third = 3 thirds or 1 whole pie, we cannot say that 3 thirds equals 1 cup, since a third is not a fixed volume.

Comparing Thirds and Cups

To demonstrate that 3 thirds does not necessarily equal 1 cup, let’s take a 9 inch pie pan and do some calculations:

Volume of 1 Third of a 9 inch Pie Pan

– Diameter = 9 inches
– Radius = 4.5 inches
– Area of bottom = π x r^2 = π x (4.5 inches)^2 = 63.617 inches^2
– Depth = Typical pie is 1.5 inches deep
– Volume of 1 third = Area of bottom x Depth / 3
= 63.617 in^2 x 1.5 in / 3
= 31.8085 cubic inches

Volume of 1 Cup

– 1 US cup = 236.5882365 mL
– Converting to inches:
– 1 mL = 0.03381402 fluid ounces
– 236.5882365 mL x 0.03381402 oz/mL = 8 fluid ounces
– 1 US fluid ounce = 1.8046875 cubic inches
– 8 fluid ounces x 1.8046875 cubic inches/oz = 14.4375 cubic inches

So 1 US cup equals 14.4375 cubic inches.

Comparing the two volumes:

– 1 third of 9 inch pie pan = 31.8085 cubic inches
– 1 US cup = 14.4375 cubic inches

As we can see, 1 third of this 9 inch pie pan is more than double the volume of 1 US cup. So in this case, 3 thirds certainly does not equal 1 cup. The volume depends on the size of the pie pan, but 3 thirds will be considerably larger than a single cup.

When 3 Thirds Approximates 1 Cup

While 3 thirds does not exactly equal 1 cup, there are some cases where 3 thirds would be approximately or nearly 1 cup, depending on the size of the container.

For example:

3 Thirds of a 6 Ounce Yogurt Cup

– Volume of 6 oz yogurt cup = approx 177 mL
– 1 third = 177 mL / 3 = 59 mL
– 3 thirds = 59 mL x 3 = 177 mL
– 1 US cup = 236.5882365 mL

In this case, 3 thirds (177 mL) is reasonably close to 1 US cup (236.5882365 mL). So with a 6 ounce yogurt cup, 3 thirds would approximate 1 cup.

3 Thirds of a 355 mL Soda Can

– Volume of 355 mL soda can = 355 mL
– 1 third = 355 mL / 3 = 118 mL
– 3 thirds = 118 mL x 3 = 355 mL
– 1 metric cup = 250 mL

Here 3 thirds (355 mL) is reasonably close to 1 metric cup (250 mL). So with a 355 mL soda can, 3 thirds also approximates 1 cup.

So while 3 thirds does not exactly equal 1 cup, in some cases with smaller containers, 3 thirds can approximate or be reasonably close to 1 cup, depending on context. But the volumes are not exactly equivalent.

Converting Between Thirds and Cups

While we cannot definitively equate 3 thirds and 1 cup, we can convert between thirds and cups for a container of known size using simple math:

Converting Thirds to Cups

To convert thirds to cups:

1) Measure the total volume of the container

2) Divide the total volume by 3 to calculate the volume of 1 third

3) Divide the volume of 1 third by the volume of 1 cup (236.5882365 mL for US or 250 mL for metric)

4) Round to the nearest whole number

For example, for a 950 mL mixing bowl:

– Total volume = 950 mL
– Volume of 1 third = 950 mL / 3 = 316 mL
– 316 mL / 250 mL per metric cup = 1.26 cups
– Rounded = 1 cup

So 3 thirds of a 950 mL bowl would be approximately equal to 1 metric cup.

Converting Cups to Thirds

To convert cups to thirds:

1) Determine the number of cups

2) Multiply cups by the volume of 1 cup (236.5882365 mL for US or 250 mL for metric)

3) Divide the total volume by 3 to determine how many thirds

For example, for 2 US cups:

– 2 US cups
– 2 x 236.5882365 mL = 473 mL
– 473 mL / 3 = 158 thirds

So 2 US cups would be approximately equal to 158 thirds.

While the conversion is not exact, this allows us to estimate thirds based on a cup volume and vice versa.

Summary

In summary:

– A cup is a standardized volume measurement, while a third is simply 1 part out of 3 equal parts

– 3 thirds does not exactly equal 1 cup, as a third is not a fixed unit of volume

– The volume of 3 thirds depends entirely on the size of the original container

– For some small containers like a yogurt cup, 3 thirds may approximate 1 cup

– But in most cases, 3 thirds of a larger container will not equal 1 cup

– Simple math can be used to estimate and convert between thirds and cups

So while 2 thirds plus 1 third equals 3 thirds or 1 whole, 3 thirds does not definitively equal 1 cup due to the differences in these units. The volume of thirds depends on the total size, while a cup is a standardized amount.

Conclusion

In conclusion, the answer to the original question “Does 2 thirds and 1 third equal a cup?” is no. While 2 thirds plus 1 third equals 3 thirds or 1 whole, 3 thirds does not equal 1 cup since a third is not a fixed unit of volume like a cup. The volume of 3 thirds depends entirely on the size of the original container being divided. In some cases 3 thirds may approximate 1 cup, but the volumes are not equivalent. To convert between thirds and cups, calculations based on the container size must be used. So simply equating 3 thirds and 1 cup does not work mathematically or in practical cooking terms.

Leave a Comment