Evaluate the absolute value of negative one and two-thirds multiplied by the absolute value of two-sevenths.
The absolute value or magnitude of any number is its distance from zero. This means that the absolute value of any constant will always be positive. The absolute value of negative 𝑎 is 𝑎, and the absolute value of 𝑎 is also 𝑎, where 𝑎 is a positive constant.
In this question, we will begin by working out the absolute value of negative one and two-thirds and the absolute value of two-sevenths. These are equal to one and two-thirds and two-sevenths, respectively, as these are the distances from zero.
Before we can multiply these two fractions, we need to convert one and two-thirds into an improper or top-heavy fraction. One whole is equal to three-thirds. This means that one and two-thirds is equivalent to five-thirds. One way of calculating this is to multiply the whole number by the denominator and then add the numerator. One multiplied by three is three, and adding two gives us five. One and two-thirds is equal to five-thirds.
Our final step is to multiply this by two-sevenths. Multiplying the numerators gives us 10, and multiplying the denominators gives us 21. As this fraction cannot be simplified, five over three or five-thirds multiplied by two over seven is equal to 10 over 21. The absolute value of negative one and two-thirds multiplied by the absolute value of two-sevenths is 10 over 21.