Express 2½ : 6¼ as a ratio of whole numbers in its lowest terms?
To express 2½: 6¼ as a ratio of whole numbers in its lowest terms, we can convert the mixed numbers to improper fractions.
2½ can be written as 5/2.
6¼ can be written as 25/4.
Now, we can find the lowest terms by simplifying the fractions.
To simplify 5/2, we divide both the numerator and denominator by their greatest common divisor, which is 1 in this case. Therefore, 5/2 is already in its lowest terms.
To simplify 25/4, we divide both the numerator and denominator by their greatest common divisor, which is 1 in this case. Therefore, 25/4 is already in its lowest terms.
So, the ratio of 2½ : 6¼ as whole numbers in its lowest terms is 5/2 : 25/4.
To express the fraction 2½ as a ratio of whole numbers, we can convert it to an improper fraction.
To do that, we multiply the whole number (2) by the denominator (2) and add the numerator (1). This gives us 5 as the new numerator.
Therefore, 2½ can be expressed as the improper fraction 5/2.
Similarly, to express the fraction 6¼ as a ratio of whole numbers, we can convert it to an improper fraction.
To do that, we multiply the whole number (6) by the denominator (4) and add the numerator (1). This gives us 25 as the new numerator.
Therefore, 6¼ can be expressed as the improper fraction 25/4.
Now, we can write the ratio 2½ : 6¼ as the ratio of the two improper fractions:
5/2 : 25/4
To simplify this ratio to its lowest terms, we need to find the greatest common divisor (GCD) of the numerators and denominators.
The GCD of 5 and 25 is 5, and the GCD of 2 and 4 is 2.
Dividing both the numerator and denominator of each fraction by their respective GCDs, we get:
5 ÷ 5 : 25 ÷ 5
2 ÷ 2 : 4 ÷ 2
This simplifies the ratio to:
1 : 5
Therefore, 2½ : 6¼, expressed as a ratio of whole numbers in its lowest terms, is 1 : 5.
To express the fraction 2½ as a whole number ratio, we need to convert the mixed number into an improper fraction.
To convert the mixed number 2½ into an improper fraction, we multiply the whole number part (2) by the denominator (2) and add the numerator (1). This gives us 5 as the numerator. The denominator remains the same (2).
So, 2½ can be written as an improper fraction as 5/2.
Similarly, to convert the mixed number 6¼ into an improper fraction, we multiply the whole number part (6) by the denominator (4) and add the numerator (1). This gives us 25 as the numerator. The denominator remains the same (4).
So, 6¼ can be written as an improper fraction as 25/4.
Now, we can express the ratio of these fractions in its lowest terms by finding the greatest common divisor (GCD) and dividing both the numerator and denominator by the GCD.
The GCD of 5 and 2 is 1.
The GCD of 25 and 4 is 1.
Dividing both the numerator and denominator of the fractions by 1 gives us the lowest terms:
5/2 divided by 1 = 5/2
25/4 divided by 1 = 25/4
Therefore, the ratio of 2½ to 6¼ in its lowest terms is 5/2 to 25/4.