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what are methods used to measure ingredients and their units of measure

volume, weight, count, legth, time, and temperature

Ingredient-recipes are confusing terms.My experience tells me that no matter what name is used ;the background cause of their use came for history so do not try to apply to much logic ! That being said just Google definition for units of the ingredients and some recipes
Scientific recipes are a complete different matter! They are very precise e.g.the MKS (meter kilogram second).
Of fundamental importance is the fact each unit is refrenced to a standard unit and is actually a ratio of the standard unit to the quantity your ar e using
12inches =1foot
1kilogram is 1000 grams
The reference stndard kilogram is kept in laboratory in France and copies are made for use around the world
A simple question but a complex answer

An ingredient is (almost) always an item in a recipe.  Therefore it takes up space, and to measure it, it must be put into something that will hold the amount the recipe calls for.  So an ingredient takes up space and has volume.  Ingredients in recipes are measured either by the volume or weight.  So the units of liquids (cup, pint, quart, gallon) apply; or the units of weight (ounce, pound) apply.  The units of weight correspond (roughly) to the units we use for dry measure:  teaspoon, tablesspoon (1 ounce), cup (8 ounces) of the ingredient. Generally, whatever unit of the ingredient you need, it is leveled at the top of the container that holds it.  Obviously you don't have to do any leveling with a liquid unit, but you do with a dry or semi-solid (butter, shortening) one.   Measuring by weight is ultimately the most accurate, but is not necessary nor practical for most home recipes, though it can be critical when making large amounts.  Different types of flour, for instance, have different weights per cup.

Excellent answer, I would only have added the metric equivilents of the units of measure you mentioned, for those students who view this in other countries where metric units are used.  Good job Christine :)

I'm guessing you are asking about kitchen recipes.  You can look at kitchen utensils or numbers on packages to find some measurements.

Most liquids and powders are measured by volume in the kitchen, because a measuring spoon, cup or bowl is cheap to buy and easy to use.  Most volumes are related.  Common English measures are: 3 teaspoons (abbreviated "t") equals 1 tablespoon (T).  2 tablespoons = 1 fluid ounce (fl. oz. or just oz.).  8 ounces = 1 cup (c).  2 cups = 1 pint (pt).  2 pints = 1 quart (qt).  4 quarts = 1 gallon (gal).

Metric volume is measured in liters (l) or milliliters (ml).  One liter is a little more than a quart.  "Milli" means one-thousandth, so a milliliter is 1/1000 of a liter.  For example, 500 milliliters = 500/1000ths or half of a liter.  5 milliliters make about one teaspoon.

Some foods come already measured in a package. A stick of butter is 4 oz and sometimes has tablespoon markings, so you can cut off the number of tablespoons you want.  Fruits and vegetables are usually just counted.

A few foods are measured by weight.  To measure weight at home, you would need a scale.  Very few people use a scale in the kitchen, so they just buy the size package that already has the right weight.  In English measure, a pound is about the weight of 2 cups of water.  There are 16 ounces in a pound.  Meats are usually measured in pounds at the store.  Metric weights are in grams and kilograms (kilogram means 1000 grams).  A milliliter of water weighs one gram.  A liter of water weighs one kilogram.

I hope that helps.

Excellent answer Spencer.  Your answer was similar to Christine's and you added information about metric units of measure.  This should be very easy to understand for a student using either metric or what we commonly use here in the US.

The customary sizes for kitchen measuring cups and spoons

Dry measuring cups typical sizes typical sizes are 1 cup, ½ cup, 1/3 cup and ¼ cup, sometimes a ¾ cup is included.
Liquid measuring cups typically comes in two cup sizes divided into increment of 1/8 cups. They usually have volume marks for both US/Imperial measurements as well as Metric. Liquid measuring cups can be found in sizes ranging from shot glass size to as large as 1 gallon.
Measuring spoons sets usually include these sizes: 1Tablespoon, 1 teaspoon, ½ teaspoon, and ¼ teaspoon and 1/8 table spoon. In larger sets of spoons there are other increments such as ½ tablespoon, a dash, and a pinch.

Which cup to use
When working with ingredients needed for a recipe, as in cooking, or a formula as in baking, it is important to use the right utensils for measuring. (In professional baking, bakers use the term formula instead of recipe.)

When a recipe calls for 1 cup of dry ingredients and 1 cup of wet ingredients. You cannot use the same utensil.

Why?

Because there are dry measuring cups for mass and liquid measuring cups for volume.

Though 1 cup of liquid is 8 fluid ounces in volume it does not necessarily weigh or have a mass of 8 ounces when scaled (weighed on a scale). The mass or weight varies based on the density of the liquid. For example, a cup of water does not weigh the same amount as a cup of corn syrup. In summary: liquids of equal volume does not necessarily have equal mass or weight.

As with liquid, the same can be said for dry ingredients. For example, the mass of a cup of flour varies from about 4 ½ ounces about 6 ounces, depending on the type and density of the flour as well as if the recipe calls for a sifted cup or a packed cup. In a similar way a cup of oat meal does not have the same mass or weight as a cup of sugar.

Something to try: measure a cup of flour in two ways –
(1) Sift some flour and use a spoon to lightly fill a dry measuring cup. Leave the top with a knife and weigh the flour on a food scale
(2) Scoop some unsifted flour into the same measuring cup, pack it lightly (tap gently on the counter); level it with a knife and weigh the flour.

Notice that both cups of flour, though they have the same volume, they do not have the same weight or mass.

You can however, use the same measuring spoons for both dry and wet ingredients because those amounts are so small.

Here are some equivalencies
Liquid Measures: Volume
1 gallon (gal) = 4 quarts (qt.) = 8 pints (pt.) = 16 cups (C.)= 128 (fl. oz.) fluid ounces
Dry Measures: Mass
1 C = 16 tablespoons (Tbsp) = 48 teaspoons (tsp)
1 Tbsp = 1 tsp
Quick Equivalency:
3 tsp = 1 Tbsp (dry)
2 Tbsp = 1/8 cup = 1 fl. Oz
5 Tbsp + 1 tsp = 1/3 cup (liquid)
8 Tbsp = ½ cup (liquid)
4 cups = 2 pints = 1 qt (liquid)
16 oz =1 pound (dry)
A dash or pinch is less than 1/8 tsp

To convert from US Customary units or Imperial measurements to Metric requires some simple mathematical calculations.
Volume:
Fluid ounces X by 29.57 = milliliters (mL)
Gallons X 3.785 = liters (L)
Mass:
Ounces X 28.35 = grams (g)
Pounds X .454 = kilograms (kg)

Summary: To measure ingredients for a recipe you use dry measuring cups for dry ingredients and liquid measuring cups for liquid ingredients. Measuring spoons are use for both dry and liquid ingredients.

weight (American): oz (ounces), lbs (pounds), tons

weight (metric): grams

volume (American): tablespoon, teaspoon, oz (fluid ounces), cup, pint, quart, gallon

volume (metric): litres or cubic centimeters (cc's)

count.....?

legth (American): inches, feet, yards, miles

length (metric): meters

time: seconds, minutes, hours, days, weeks, months, years, decades, centuries, millenii

temperature: degrees fahrenheit, degrees celsius, degrees kelvin

Metric follows rules of 10. Kilo, hecta, deca, base, deci, centi, mili. (King Henry Died By Drinking Chocolate Milk.) Kilometers = 1000 m. Hectameters= 100 m. Decameters= 10 m. Base= meters. Decimeters= .1 meter. Centimeters= .01 m. Milimeters= .001 m.

Are we talking about cooking with ingredients?  In which case you could use a kitchen balance which should measure either grams (metric) or pounds and ounces (imperial).  Alternatively the cup measurements are very popular in the USA. (1 cup, 0.5 cups etc) combined with teaspoons (tsp) and tablespoons (tbsp) for smaller measurements).  We could also measure liquids by volume ie pint or litres/milimetres.

In a lab we would use a balance and usually measure in metric, miligrams, grams, kilograms.  We could also measure by volume using syrynges, measuring cylinders, pipettes etc.  In this case we would use mL (mililitres) or centremetres cubed.;