Find a rational number (in simplest form) between 6 and 6 1/4?
To find a rational number between 6 and 6 1/4, we can take the average of these two numbers.
First, we need to convert 6 1/4 into a fraction. We can do this by multiplying the whole number, 6, by the denominator of the fraction (4), and then adding the numerator (1). This gives us 6(4) + 1 = 24 + 1 = 25.
So, 6 1/4 can be written as 25/4 as a fraction.
To find the average, we add and divide by 2: (6 + 25/4) / 2 = (24/4 + 25/4) / 2 = 49/4 / 2 = (49/4) * (1/2) = 49/8.
Therefore, a rational number (in simplest form) between 6 and 6 1/4 is 49/8.
Using a number line, what whole number and rational number to the nearest half is √59 between?
To locate √59 on a number line, we need to find the two closest whole numbers and rational numbers to the nearest half.
First, let's find the whole numbers to the left and right of √59.
The square root of 59 is approximately 7.68, so the whole numbers to the left and right of √59 are 7 and 8.
Next, let's find the rational numbers to the left and right of √59 to the nearest half.
To find the rational number to the left of √59, we take 7 and subtract 0.5. This gives us 6.5.
To find the rational number to the right of √59, we take 8 and add 0.5. This gives us 8.5.
Therefore, √59 is between the whole numbers 7 and 8, and between the rational numbers 6.5 and 8.5 to the nearest half.
Using a number line, what whole number and rational number to the nearest half is √59 between?
8.5 and 9?
6 and 6.5?
7 and 7.5?
or
7.5 and 8?
To accurately determine the whole number and rational number to the nearest half that √59 is between, let's calculate an approximate decimal value for √59.
Using a calculator, √59 is approximately 7.68.
On the number line, between which values should we place 7.68?
Looking at the given options, we find that √59 is between 7 and 7.5.
Therefore, when considering whole numbers, √59 is between 7 and 8. From the given options, 7 and 7.5 is the closest pair, so the rational number to the nearest half is 7.5.
To find a rational number between 6 and 6 1/4, we need to consider the fractions that lie between these two numbers.
First, let's convert 6 1/4 into a fraction. To do this, we multiply the whole number (6) by the denominator (4) and add the numerator (1). This gives us 24 + 1 = 25.
So, 6 1/4 can be written as the fraction 25/4.
To find a fraction between 6 and 6 1/4, we need to find a fraction that has a numerator greater than 6 and less than 25, and a denominator larger than 4.
One possible fraction is 7/2. This fraction is greater than 6 (the numerator) and less than 25 (the denominator).
So, a rational number (in simplest form) between 6 and 6 1/4 is 7/2.
To find a rational number (in simplest form) between 6 and 6 1/4, we can first convert the mixed number, 6 1/4, into an improper fraction.
To convert the mixed number into an improper fraction, we multiply the whole number (6) by the denominator (4), and then add the numerator (1). This gives us:
6 × 4 + 1 = 24 + 1 = 25
Now, we divide this result (25) by the denominator (4) to obtain the improper fraction:
25/4
Next, we need to find a rational number between 6 and 6 1/4. Since both numbers have the same whole number part (6), the only difference is the fractional part. To find a rational number between two fractions, we can take their average.
To find the average, add the two fractions together and divide the sum by 2:
(6 + 25/4) / 2 = (24/4 + 25/4) / 2 = 49/4 / 2
Now, divide the numerator by the denominator:
49/4 ÷ 2/1
To divide by a fraction, we multiply the dividend by the reciprocal of the divisor. In this case, we multiply 49/4 by 1/2:
(49/4) × (1/2) = (49 × 1) / (4 × 2) = 49/8
Therefore, the rational number (in simplest form) between 6 and 6 1/4 is 49/8.