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Being able to measure things is critical in today’s world. Measuring tells us how big things are, how long, deep, tall, wide, heavy or even how much something is worth (it’s cost). In this unit, we will be learning how to measure an item’s distance. In other words, how long, tall or wide an object is. The metric system of measurement is an archaic, inferior system that is used by almost every civilized nation on earth… except the United States. -Murphy’s Laws on Drafting The metric system is based upon units of ten (10). Each unit of measurement is divided by ten to make a smaller unit, or multiplied by ten to make a larger unit. The metric system uses the term meters for it’s base unit. Each unit smaller or larger than a meter has a prefix attached to it to give it value. Example: meter = one deci = one tenth centi = one hundredth milli = one thousandth Therefore, there are ten (10) decimeters in one meter, one hundred (100) centimeters in one meter, and one thousand (1,000) millimeters in one meter. A metric ruler looks like this: 0 1 2 3 4 5 6 7 8 9 10 Each number on this ruler equals one centimeter. Notice that there are ten spaces between each number. Each of those spaces equals one millimeter. When reading a metric ruler, you either note your measurements in terms of millimeters or centimeters. For example… 0 1 2 3 4 5 6 7 8 9 10 If you were to measure the bar shown above the ruler, the length would either be listed as: 44 millimeters Or 4.4 centimeters Get worksheet #1: Metric Questions from your packet and complete this sheet. After completing the sheet, go on to the next screen. Unlike the metric system, which is based upon the number ten, the English system of measurement is based upon halves. Fractions are used for the measurements, as each unit is divided in half, thus making it smaller. You will need to get the English Questions worksheet out and complete it as you go through this next section. Think of the English system as a pizza. When you cut the pizza, you normally cut it in half, then half again and again. This system of measurement works the same way. The pizza is whole, so you only have one piece. The number therefore = 1 If you cut the pizza in half, you now have two equal pieces. The fraction that represents this = ½. If you cut the pizza in half again, you will now have four equal pieces. Each piece is therefore one fourth of the pizza. The fraction that represents this = ¼. Because there are four parts, each part has a different value. These values are listed as: 4/4 1/4 1/4 2/4 (reduce to ½) 3/4 2/4 3/4 4/4 (simplify to 1) If you cut the pizza in half again, you now have eight equal pieces. Each piece is worth one eighth of the pizza. The fraction that represents this = 1/8. Because there are eight parts, each part has a different value. These values are listed as: 8/8 1/8 1/8 2/8 (reduce to ¼) 7/8 2/8 3/8 4/8 (reduce to ½) 6/8 3/8 5/8 6/8 (reduce to 3/4) 7/8 5/8 4/8 8/8 (simplify to 1) If you cut the pizza in half again, you now have sixteen equal pieces. Each piece is worth one sixteenth of the pizza. The fraction that represents this = 1/16. Because there are sixteen parts, each part has a different value. These values are listed as: 16/16 1/16 1/16 9/16 15/16 2/16 2/16 (reduce to 1/8) 10/16 (reduce to 5/8) 3/16 11/16 14/16 3/16 4/16 (reduce to 1/4) 12/16 (reduce to 3/4) 13/16 4/16 5/16 13/16 12/16 5/16 6/16 (reduce to 3/8) 14/16 (reduce to 7/8) 7/16 15/16 11/16 6/16 8/16 (reduce to ½) 16/16 (simplify to 1) 10/16 7/16 9/16 8/16 This is a good time to talk about proper fractions and reducing. You will notice that there are several fractions that have notes after them stating that they are reduced to other numbers. The numbers that need to be reduced include: 16/16 1/16 15/16 2/16 2/16 (reduce to 1/8) 10/16 (reduce to 5/8) 14/16 3/16 4/16 (reduce to 1/4) 12/16 (reduce to 3/4) 13/16 4/16 12/16 5/16 6/16 (reduce to 3/8) 14/16 (reduce to 7/8) 11/16 6/16 8/16 (reduce to ½) 16/16 (simplify to 1) 10/16 7/16 9/16 8/16 Fractions have two parts to them: the numerator, which is the number on the top, and the denominator, which is the number on the bottom. 1 Numerator 2 Denominator When dealing with ruler based fractions, as long as the numerator is odd, and the denominator is even, then you have a proper fraction. Proper fractions do not need to be reduced or simplified. 1 ½ is a proper fraction. 2 When dealing with fractions, if the numerator is even, and the denominator is even, then you have an improper fraction. Improper fractions need to be reduced or simplified. 2 2/4 is an improper fraction. 4 To reduce or simplify a ruler based fraction, divide both the numerator and the denominator by two. If the resulting number has an odd numerator and an even denominator, then it has been reduced successfully. If both the numerator and denominator are still even, repeat the process. 2 2 1 4 2 2 Dividing 2/4 by 2/2 gives you the fraction ½. This is a proper fraction. Complete the English Measuring – Fractions worksheet before going on. Get the English Ruler worksheet out to complete the next section. Now we will convert the “pizza” into an actual ruler. The same idea applies to this system. We start with a whole number (one) and continue to divide it in half. This time, however, we are working along a straight line instead of a circle. Once again, we start off with whole numbers. These are usually listed on most rulers, and are obvious. 0 1 2 3 4 Each of the whole numbers are then split in half. The fraction (1/2) will remain the same from number to number, you simply add the whole number in front of the fraction. 0 1 2 3 4 Example: ½ inch 1-½ inch 2-½ inch 3-½ inch Each of the half numbers are then split in half. The fractions (1/4 or 3/4) will remain the same from number to number, you simply add the whole number in front of the fraction. 1 /4 1/2 3 /4 1 /4 1/2 3 /4 1 /4 1/2 3 /4 1 /4 1/2 3 /4 0 1 2 3 4 Example: 1/4 inch 1-1/4 inch 2-1/4 inch 3-1/4 inch 3/4 inch 1-3/4 inch 2-3/4 inch 3-3/4 inch Each of the numbers are then split in half again. The fractions (1/8, 3/8, 5/8 or 7/8) will remain the same from number to number, you simply add the whole number in front of the fraction. 1 /8 3 /8 5 /8 7 /8 1 /8 3 /8 5 /8 7 /8 0 1 2 Example: 1/8 inch 5/8 inch 1-1/8 inch 1-5/8 inch 3/8 inch 7/8 inch 1-3/8 inch 1-7/8 inch Each of the numbers are then split in half again. The fractions (1/16, 3/16, 5/16, 7/16, 9/16, 11/16, 13/16 and 15/16 ) will remain the same from number to number, you simply add the whole number in front of the fraction. Example: 1 /1 6 3 /1 6 5 /1 6 7 /1 6 9 / 1 6 1 1 /1 6 1 3 /1 6 1 5 /1 6 1 / 1 6 3 /1 6 5 /1 6 7 /1 6 9 / 1 6 1 1 /1 6 1 3 /1 6 1 5 /1 6 0 1 2 1/16 inch 9/16 inch 1-1/16 inch 1-9/16 inch 3/16 inch 11/16 inch 1-3/16 inch 1-11/16 inch 5/16 inch 13/16 inch 1-5/16 inch 1-13/16 inch 7/16 inch 15/16 inch 1-7/16 inch 1-15/16 inch The system could continue, making smaller and smaller spaces. If you divide 1/16 in half, you would get 1/32, and therefore have 32 sections to mark. Likewise, if you divide 1/32 in half, you would get 1/64, and therefore have 64 sections to mark. The standard English ruler only extends to 1/16th of an inch. This is true for classroom rulers, tape measures and yardsticks. The smaller measurements are used primarily for engineering design, such as automobiles, airplanes and electronics, where smaller, more accurate measurements are needed. The English system of measurement is based upon halves. Fractions are used for the measurements, as each unit is divided in half, thus making it smaller. The standard English ruler only extends to 1/16th of an inch. This is true for classroom rulers, tape measures and yardsticks. The smaller measurements are used primarily for engineering design, such as automobiles, airplanes and electronics, where smaller, more accurate measurements are needed. This is a representation of a standard English ruler, from one to two inches. Notice that the whole numbers do not have fractions at them, and the counting starts at the first line past the whole number. 1 - 11/16 1 - 13/16 1 - 15/16 1 - 1/16 1 - 3/16 1 - 5/16 1 - 7/16 1 - 9/16 11/16 13/16 15/16 1/16 3/16 5/16 7/16 9/16 1 - 1/8 1 - 1/4 1 - 3/8 1 - 1/2 1 - 5/8 1 - 3/4 1 - 7/8 1/8 1/4 3/8 1/2 5/8 3/4 7/8 0 1 2 When dealing with fractions, if the numerator is even, and the denominator is even, then you have an improper fraction. Improper fractions need to be reduced or simplified. 2 2/4 is an improper fraction. 4 To reduce or simplify a ruler based fraction, divide both the numerator and the denominator by two. If the resulting number has an odd numerator and an even denominator, then it has been reduced successfully. If both the numerator and denominator are still even, repeat the process. 2 2 1 4 2 2 Dividing 2/4 by 2/2 gives you the fraction ½. This is a proper fraction. Once you have completed this presentation, and the worksheets that go with it, you may proceed to the next unit. See your teacher for instructions .