Locating , rac{1}{3}, rac{6}{5}, - rac{7}{4}, rac{9}{2}, , and - rac{8}{3} on a Number Line
To locate these diverse values on a number line, handle integers, proper fractions, and improper fractions systematically. Plot the integers and directly on their respective tick marks. The proper fraction rac{1}{3} lies between and ; by dividing that numerical interval into thirds, it is plotted precisely at the first mark. Finally, convert all improper fractions into mixed numbers to easily pinpoint their valid target intervals: rac{6}{5} = 1 rac{1}{5} (situated just past ), - rac{7}{4} = -1 rac{3}{4} (positioned three-quarters of the way moving from toward ), rac{9}{2} = 4 rac{1}{2} (landing perfectly halfway between and ), and - rac{8}{3} = -2 rac{2}{3} (planted two-thirds of the distance from toward ).
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
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Ordering Negative Fractions and Mixed Numbers Using Inequality Symbols
A quality control technician is training a new hire on how to read a custom scale marked in fractions. The technician explains that to locate a measurement like 3/5 on a number line, one must first divide the unit interval into equal segments. Which part of the fraction 3/5 tells the new hire the total number of segments to create?
A quality control inspector is using a manual gauge marked in fractional increments. To correctly plot measurements on this scale, match each mathematical term with its descriptive role on the number line.
Locating Improper Fractions on a Measurement Scale
A quality control inspector needs to mark a measurement of -2/5 on a scale. Arrange the following steps in the correct order to accurately plot this negative proper fraction on a number line based on the strategy described in your course.
A construction technician is marking a measurement of -5/2 inches on a specialized layout tool. True or False: According to the strategy for plotting fractions, converting -5/2 to the mixed number -2 1/2 indicates that the measurement should be plotted between the integers -1 and -2.
A quality control technician is marking a custom measurement rail that functions as a number line. According to the standard strategy for locating values, the technician should first plot the ________ numbers because they fall directly on the labeled tick marks, providing a reference for the fractions that follow.
Strategy for Marking Fractional Intervals on a Scale
Precision Tool Scale Calibration
A logistics supervisor is calibrating a digital scale that tracks weight deviations in fractional units. When marking the location for a negative proper fraction (a fraction where the numerator is smaller than the denominator, such as -2/5), between which two integers on the scale will this value always be located?
A machinist is marking a measurement of 9/4 inches on a precision gauge. According to the strategy for locating improper fractions on a number line, arrange the following steps in the correct order to accurately plot this measurement.
Locating , rac{1}{3}, rac{6}{5}, - rac{7}{4}, rac{9}{2}, , and - rac{8}{3} on a Number Line
Locating , rac{2}{3}, rac{7}{5}, - rac{7}{4}, rac{7}{2}, , and - rac{7}{3} on a Number Line
Locating Decimals on a Number Line
Example of Locating , rac{3}{4}, - rac{1}{4}, , rac{6}{5}, - rac{5}{2}, and rac{7}{3} on a Number Line
Example of Locating rac{1}{5}, - rac{4}{5}, , rac{7}{4}, - rac{9}{2}, , and rac{8}{3} on a Number Line
Learn After
A quality control technician is marking measurement deviations on a precision scale where 0 represents the standard. Match each recorded value with its correct location description on the scale's number line.
A quality control technician is monitoring the deviation in the length of precision bolts compared to a target standard of millimeters. If a bolt has a recorded deviation of rac{9}{2} millimeters, where should this value be located on the technician's measurement number line?
A technician is monitoring the pressure deviation in a vacuum chamber relative to a baseline of psi. The deviation is recorded as psi. True or False: To plot this value accurately on the gauge's number line, the technician should place the mark two-thirds of the distance moving from the integer toward the integer .
A technician is marking measurement deviations on a precision number line where represents the standard. Arrange the following steps in the correct order to accurately locate the recorded value of on the number line.
A quality assurance technician is tracking calibration offsets on a measurement number line. One instrument has an offset recorded as units. To accurately plot this improper fraction, the technician converts it to the mixed number , which indicates the mark should be placed two-thirds of the distance moving from the integer toward the integer ____.