Question

Nancy is completing some homework on number lines. The questions in her homework are about marking the position of fractions and decimal numbers on a number line. She needs to mark these points correctly and accurately.

Part A
Nancy has to mark and on this number line. How many spaces does she need between the integers 1 and 2, and between -1 and -2, to show and on the number line?

Answer 1

Nancy needs to divide the number line into equal parts that correspond to the fractions' denominators in order to accurately place fractions and decimals. She also needs to understand the placement of digits in whole numbers, using intuition to help with operations on fractions.

Step-by-step explanation:

The student, Nancy, is asked to place fractions and decimal numbers on a number line between the integers 1 and 2, and -1 and -2. In order to correctly represent fractions and decimals, the number line must be divided into equal segments that correspond to the denominators of the fractions. For example, if Nancy needs to represent 1/4 or 0.25, she would divide the segment between the integers into four equal parts. This division would then allow her to place the fraction 1/4 exactly one part to the right of the integer 1. Similarly, if she has to place 3/4 or 0.75, she would count three parts to the right of integer 1.

When working with whole numbers, we pay attention to the placement of digits in a number and understand that the absence of a decimal point implies it being at the right end of the number.

Our intuition can guide us in the addition and subtraction of fractions by helping us visualize the process on the number line. By creating common denominators through multiplication, we can combine fractions more easily without losing sight of their relative sizes on the number line.