What is the absolute value of subtracting these rational numbers on a vertical number line diagram? −22 − 1 1/2
To find the absolute value of subtracting these rational numbers, we first need to evaluate the subtraction and then take the absolute value.
So, -22 - 1 1/2 can be written as -22 - 3/2.
To subtract these numbers, we need a common denominator. The common denominator of 2 and 2 is 2.
-22 can be written as -22/1.
Now, -22/1 - 3/2 can be rewritten as -44/2 - 3/2.
Subtracting the numerators, we get -47/2.
To find the absolute value, we ignore the negative sign and keep the value positive.
Therefore, the absolute value of -22 - 1 1/2 is 47/2.
To find the absolute value of subtracting the rational numbers −22 and 1 1/2, you can follow these steps:
Step 1: Convert the mixed number 1 1/2 to an improper fraction. To do this, multiply the whole number (1) by the denominator (2), and then add the numerator (1). This gives us (1 * 2 + 1 = 3) over the denominator (2), resulting in 3/2.
Step 2: Subtract the two rational numbers: −22 - 3/2. To subtract a whole number and a fraction, first convert the whole number to a fraction by giving it the same denominator (2). So the equation now becomes -22/1 - 3/2.
Step 3: To find a common denominator, we multiply the denominators (1 and 2), which gives us 2.
Step 4: Adjust the fractions. Multiply the numerator and denominator of the first fraction (-22/1) by 2, resulting in -44/2. The second fraction (3/2) remains the same.
Step 5: Subtract the fractions: -44/2 - 3/2. Since the denominators are now the same, we can directly subtract the numerators, which gives us -47/2.
Step 6: Simplify the fraction, if necessary. The fraction -47/2 cannot be simplified any further.
Step 7: Determine the absolute value. The absolute value disregards the negative sign and gives us the positive value of the expression. Hence, the absolute value of -47/2 is 47/2.
Therefore, the absolute value of subtracting −22 and 1 1/2 is 47/2.