This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the numbers to be represented. The given numbers are (9)/(7) and -(4)/(7). To represent these on a number line, it's helpful to understand their values relative to integers. For (9)/(7): This is an improper fraction. Convert it to a mixed number: (9)/(7) = 1 (2)/(7). This means it is greater than 1 but less than 2. For -(4)/(7): This is a negative proper fraction. This means it is greater than -1 but less than 0. Step 2: Draw a number line. Draw a straight line and mark integer points like -1, 0, 1, 2. Step 3: Locate (9)/(7) on the number line. Since (9)/(7) = 1 (2)/(7), it lies between 1 and 2. Divide the segment between 1 and 2 into 7 equal parts. Count 2 parts from 1 towards 2. This point represents (9)/(7). Step 4: Locate -(4)/(7) on the number line. Since -(4)/(7) is between 0 and -1, divide the segment between 0 and -1 into 7 equal parts. Count 4 parts from 0 towards -1. This point represents -(4)/(7). Here is the representation on a number line: [<->] (-2.5,0) -- (2.5,0); in -2,-1,0,1,2 (,0.1) -- (,-0.1) node[below] ; % Mark 9/7 [fill=black] (1+2/7,0) circle (1.5pt) node[above] (9)/(7); % Mark -4/7 [fill=black] (-4/7,0) circle (1.5pt) node[above] -(4)/(7); The numbers (9)/(7) and -(4)/(7) are distinct and are represented at different positions on the number line. Last free one today — make it count tomorrow, or type /upgrade for unlimited.