List 5 rational numbers between:
(1) 6/2 and 5+89
(2) 1 and 2
(3) 6/9 and 7/3
(4) 2/3 and 2/5
Answer (2)
We listed rational numbers between four pairs: 4, 10, 50, 80, 90 between 3 and 94; 1.1, 1.5, 1.7, 1.9, 1.99 between 1 and 2; 1, 1.5, 2, 2.1, 2.2 between 0.67 and 2.33; and 15 7 , 15 8 , 15 9 , 30 13 , 30 14 between 3 2 and 5 2 .
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Scenario 1: Evaluate 6/2 * (5+89) = 282 and find five rational numbers close to it: 281.1, 281.2, 281.3, 281.4, 281.5.
Scenario 2: List five rational numbers between 1 and 2: 1.1, 1.2, 1.3, 1.4, 1.5.
Scenario 3: Evaluate 6/ ( 9 6 ∗ 3 7 ) = 7 27 ≈ 3.857 and find five rational numbers close to it: 3.81, 3.82, 3.83, 3.84, 3.85.
Scenario 4: Convert 3 2 and 5 2 to fractions with a common denominator of 30, which gives 30 20 and 30 12 respectively, and find five rational numbers between them: 30 13 , 15 7 , 2 1 , 15 8 , 30 17 .
Explanation
Problem Overview We are asked to find five rational numbers that satisfy certain conditions in four different scenarios. Let's analyze each scenario separately.
Scenario 1: Simplifying the Expression Scenario 1: Find 5 rational numbers close to the number resulting from the expression 6/2w 5 + 89 . Assuming 'w' means 'with', the expression is interpreted as 6/2 * (5+89). First, we simplify the expression: 6/2 ∗ ( 5 + 89 ) = 3 ∗ 94 = 282 Now, we need to find 5 rational numbers close to 282.
Scenario 1: Finding Rational Numbers Five rational numbers close to 282 can be 281.1, 281.2, 281.3, 281.4, and 281.5.
Scenario 2: Finding Rational Numbers Between 1 and 2 Scenario 2: Find 5 rational numbers between 1 and 2.
Scenario 2: Listing Rational Numbers Five rational numbers between 1 and 2 can be 1.1, 1.2, 1.3, 1.4, and 1.5.
Scenario 3: Simplifying the Expression Scenario 3: Simplify the expression 6/ w 9 6 ⋅ 3 7 and find 5 rational numbers close to it. Assuming 'w' means 'with', the expression is interpreted as 6/ ( 9 6 ∗ 3 7 ) . First, we simplify the expression: 6/ ( 9 6 ∗ 3 7 ) = 6/ ( 3 2 ∗ 3 7 ) = 6/ 9 14 = 6 ∗ 14 9 = 14 54 = 7 27 ≈ 3.857 Now, we need to find 5 rational numbers close to 7 27 .
Scenario 3: Listing Rational Numbers Five rational numbers close to 7 27 can be 3.81, 3.82, 3.83, 3.84, and 3.85.
Scenario 4: Finding Common Denominator Scenario 4: Find 5 rational numbers between 3 2 and 5 2 . To find rational numbers between these two fractions, we first find a common denominator. The least common denominator for 3 and 5 is 15. So, we convert the fractions: 3 2 = 15 10 5 2 = 15 6 Now, we need to find 5 rational numbers between 15 6 and 15 10 .
Scenario 4: Listing Rational Numbers To find 5 rational numbers between 15 6 and 15 10 , we can rewrite the fractions with a larger denominator, such as 30: 15 6 = 30 12 15 10 = 30 20 Now we can easily find 5 rational numbers between 30 12 and 30 20 . These can be 30 13 , 30 14 , 30 15 , 30 16 , 30 17 which simplify to 30 13 , 15 7 , 2 1 , 15 8 , 30 17 .
Final Answer In summary: (1) Five rational numbers close to 282 are 281.1, 281.2, 281.3, 281.4, and 281.5. (2) Five rational numbers between 1 and 2 are 1.1, 1.2, 1.3, 1.4, and 1.5. (3) Five rational numbers close to 7 27 are 3.81, 3.82, 3.83, 3.84, and 3.85. (4) Five rational numbers between 3 2 and 5 2 are 30 13 , 15 7 , 2 1 , 15 8 , 30 17 .
Examples
Rational numbers are useful in everyday life. For example, when you're cooking, you often need to measure ingredients using fractions or decimals, which are rational numbers. If a recipe calls for 3 2 cup of flour, and you want to make half the recipe, you need to calculate half of 3 2 , which is 3 1 . Similarly, when you're splitting a bill with friends, you use rational numbers to divide the total cost equally. Understanding rational numbers helps in accurate calculations and fair distribution.
