Question

Allan is ordering a set of rational numbers that includes positive values, negative values, fractions, and decimal numbers. How can he order them?

Answer 1

Answer:

Sample Response: First, Allan should write the fractions as decimals by dividing the numerator by the denominator. Then he can plot the points on the number line. Reading the plotted points from left to right gives the points in order, from least to greatest.

Step-by-step explanation: Sample Response

Answer 2

Allan can order the set of rational numbers including positive values, negative values, fractions and decimal numbers in the following way-

• It is known that all positive numbers are on the right side of the number line; ie they are greater than zero, whereas all negative numbers are on the left side of the number line.
• This done, Allan should first shift his attention to the subset of positive numbers. Each number greater than the other in magnitude is to be placed to the right of the number of lesser magnitude. For instance, 16 is to the right of 2.
• For negative numbers, Allan should keep in mind that the larger the magnitude of the number, the smaller the number actually is, and should be kept to the left of the number with a smaller magnitude. For example, -110 should be kept to the left of -17.
• Now comes the turn of decimals. for this, Allan should note the number to the left of the decimal point. This done, he should then place the decimal number in between the number noted and the number greater than that number. For instance, he should place 2.45 between 2 and 3.
• For fractions, it is advisable that Allan divide the numerator by the denominator of the fraction to arrive at a decimal value which can be dealt with in the same way as mentioned in the last point.

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