MEASUREMENT
Numbers had no meaning in the old days without some unit of measurement such as an arm or foot. The unit of measurement is the measurement label. Without a unit or label, measurement has no meaning. 2 what? 2 arms or 2 feet? Examples—arm, foot, inch, cent, mile. Single and plural labels such as foot or feet are regarded as the same units.
QUANTITY
A quantity tells us how much or how many and always has two parts—a number and label. For example, do we want 2 feet or 3 feet or 3 miles? Every number must have a unit of measurement or label in order to be a quantity. Example—6 students, 30 cents, 8 inches, $5
RATE
A rate is a comparison of two different quantities. A rate tells us the quantity of one thing per quantity of a second thing. For example, 55 miles per hour, 25 students per teacher, $5 for 3 gallons of gas, 96 cents for 3 candy bars are all rates. These rates can each be written as fractions:.
55 miles 25 students $5 96 cents
1 hour 1 teacher 3 gallons 3 candy bars
RECIPROCAL RATE
The reciprocal rate is a rate that is reversed or turned around. For example, the reciprocal rate of
96 cents is 3 candy bars
3 candy bars 96 cents
CONVERSION RATE
A conversion rate is a special rate where the quantities are equal, but the units of measurement are different. In other words, the two quantities are equal and each quantity can be changed into the other quantity in the rate. Examples are
12 inches 1 yard 5 fingers
1 foot 3 feet I hand