Pregunta
Find the reciprocals (i.e., the multiplicative inverses) of the given rational numbers. Show each number and its reciprocal on the number line. (a) The reciprocal of \( \frac{4}{3} \) is \( \square \). (Simplify your answer.)
Ask by Stanley Mills. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The reciprocal of \( \frac{4}{3} \) is \( \frac{3}{4} \).
Solución
To find the reciprocal (multiplicative inverse) of a number, we simply flip its numerator and denominator. For the number 4/3, the reciprocal is computed as follows:
Reciprocal = 1 ÷ (4/3) = 3/4
Thus, the reciprocal of 4/3 is 3/4.
To illustrate on a number line:
1. Mark 4/3, which is approximately 1.33.
2. Mark 3/4, which is approximately 0.75.
For example, you might draw a number line with evenly spaced points, labeling 0, 0.75 (for 3/4), 1, and 1.33 (for 4/3) so that both the original number and its reciprocal are clearly shown.
Therefore, the answer is: The reciprocal of 4/3 is 3/4.
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Simplifique esta solución The Deep Dive
The reciprocal of \( \frac{4}{3} \) is \( \frac{3}{4} \). This means if you multiply \( \frac{4}{3} \) by \( \frac{3}{4} \), you get \( 1 \), since \( \frac{4}{3} \times \frac{3}{4} = \frac{12}{12} = 1 \). On the number line, \( \frac{4}{3} \) is located a little more than 1 (specifically, \( 1.33 \)), while \( \frac{3}{4} \) is located a little less than 1 (around \( 0.75 \)). This visual representation will help you see how these two numbers relate to each other and to 1!
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