Find three rational numbers between -1 and -2.
Answer (2)
Express -1 and -2 as fractions with a common denominator: -1 = -4/4 and -2 = -8/4.
Find three rational numbers between -4/4 and -8/4, such as -5/4, -6/4, and -7/4.
Simplify the fractions: -6/4 = -3/2.
The three rational numbers between -1 and -2 are − 4 5 , − 2 3 , and − 4 7 .
Explanation
Understanding the Problem We need to find three rational numbers between -1 and -2. Rational numbers can be expressed as a fraction q p , where p and q are integers and q is not zero.
Finding a Common Denominator To find rational numbers between -1 and -2, we can express both numbers as fractions with a common denominator. Let's choose a denominator of 4. Then, -1 = -4/4 and -2 = -8/4.
Identifying Intermediate Fractions Now we need to find three fractions between -4/4 and -8/4. These could be -5/4, -6/4, and -7/4.
Simplifying the Fractions We can simplify the fractions -6/4 to -3/2. So, the three rational numbers between -1 and -2 are -5/4, -3/2, and -7/4.
Final Answer Therefore, three rational numbers between -1 and -2 are − 4 5 , − 2 3 , and − 4 7 .
Examples
Rational numbers are useful in everyday life, especially when dealing with measurements or dividing quantities. For instance, if you have a recipe that calls for a certain amount of an ingredient, but you only want to make a portion of the recipe, you'll need to use rational numbers to calculate the new amounts. Suppose you want to use only a portion of a recipe. If the recipe calls for 1 cup of flour, but you only want to make 4 3 of the recipe, you would need 4 3 of a cup of flour. Similarly, if you want to split a bill of $20 between 3 people, each person would owe 3 20 dollars, which is another rational number.
Three rational numbers between -1 and -2 can be found by expressing them as fractions. These numbers are -\frac{5}{4}, -\frac{3}{2}, and -\frac{7}{4}. Each of these numbers lies in the interval between -1 and -2.
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