1. During a baseball game, Matthew hit 6 out of 8 homeruns attempted. Julian hit 8 out of 12 homeruns attempted. Write the fraction that represents each and compare. Who was the most successful?
2. Write 4.40 as a mixed number or fraction in simplest form
1.
Matthew hit 6 out of 8 = 6 / 8 = 2 ∙ 3 / 2 ∙ 4 = 3 / 4 = 0.75
Julian hit 8 out of 12 = 8 / 12 = 4 ∙ 2 / 4 ∙ 3 = 2 / 3 = 0.666
Matthew was the most successful.
2.
4.40 = 4.40 ∙ 10 / 10 = 44 / 10 = 2 ∙ 22 / 2 ∙ 5 = 22 / 5
OR
4.4 = 4 + 0.4 = 4 + 4 / 10 = 4 + 2 ∙ 2 / 2 ∙ 5 = 4 + 2 / 5 = 4 2/5
To answer the first question, we need to find the fraction representing the successful attempts for each player.
1. To find Matthew's fraction of successful homeruns, we divide the number of successful homeruns by the total number of attempts: 6 successful homeruns ÷ 8 attempts.
This can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 2 in this case: (6 ÷ 2) ÷ (8 ÷ 2) = 3 ÷ 4.
So, Matthew hit a fraction of 3/4 successful homeruns.
2. Similarly, we find Julian's fraction of successful homeruns: 8 successful homeruns ÷ 12 attempts.
Simplifying this by dividing both numbers by their GCD, which is 4: (8 ÷ 4) ÷ (12 ÷ 4) = 2 ÷ 3.
So, Julian hit a fraction of 2/3 successful homeruns.
To compare the two fractions, we need to convert them to a common denominator, which in this case is 12.
Matthew's fraction can be rewritten as: (3/4) × (3/3) = 9/12.
Since Julian's fraction already has a denominator of 3, we can rewrite it as: (2/3) × (4/4) = 8/12.
Now we can see that Matthew hit 9 out of 12 homeruns, while Julian hit 8 out of 12. Thus, Matthew was the most successful.
Moving on to the second question, we need to write 4.40 as a mixed number or fraction in simplest form.
To convert a decimal to a fraction, we count the number of decimal places and use that as the denominator with the digit(s) after the decimal point as the numerator.
In this case, we have two decimal places, so the denominator will be 100. The numerator will be the number without the decimal point, which is 440.
So, 4.40 can be expressed as the fraction 440/100.
To simplify this fraction, we divide both the numerator and denominator by their GCD, which is 20: (440 ÷ 20) ÷ (100 ÷ 20) = 22 ÷ 5.
Thus, 4.40 can be written as the simplest fraction 22/5.