whenever you see "of" think multiplication.
half of a dozen is 1/2 * 12 = 6
so, 2/3 of 5 3/4 = 2/3 * 23/4 = 46/12 = 23/6 = 3 5/6
How many pitchers of iced tea did they drink?
Do I subtract to get the answer?
half of a dozen is 1/2 * 12 = 6
so, 2/3 of 5 3/4 = 2/3 * 23/4 = 46/12 = 23/6 = 3 5/6
Mark off 5/8 on the line, mark off another 5/8 and note that 5/8 + 5/8 = 10/8. So, 10/8 ÷ 5/8 = 2.
arithmetically, 10/8 ÷ 5/8 = 10/8 x 8/5 = 80/40 = 2
To solve this problem, first convert the mixed number of pitchers Amber made into an improper fraction.
Amber made 5 3/4 pitchers of iced tea. To convert this mixed number to an improper fraction, multiply the whole number (5) by the denominator (4) and add the numerator (3). This gives us:
5 x 4 + 3 = 20 + 3 = 23
So, 5 3/4 is equivalent to the improper fraction 23/4.
Now, find 2/3 of the iced tea. Multiply the numerator (2) by 23 (the numerator of the fraction that represents the total amount of iced tea). Divide the result by the denominator (3).
(2 x 23) ÷ 3 = 46 ÷ 3 = 15 1/3
Therefore, they drank 15 1/3 pitchers of iced tea.
To find the number of pitchers they drank, subtract the amount they drank from the total amount Amber made:
23/4 - 15 1/3
To subtract mixed numbers, convert them into improper fractions.
15 1/3 is equivalent to the improper fraction (3 x 15 + 1) ÷ 3 = 46/3.
Now subtract:
23/4 - 46/3
To subtract fractions, you need to have a common denominator. In this case, the common denominator is 12 (the least common multiple of 4 and 3).
Multiply the numerator and denominator of the first fraction (23/4) by 3 to get a denominator of 12:
(23 x 3) / (4 x 3) = 69/12
Multiply the numerator and denominator of the second fraction (46/3) by 4 to get a denominator of 12:
(46 x 4) / (3 x 4) = 184/12
Now subtract:
69/12 - 184/12 = -115/12
Therefore, they drank -115/12 pitchers of iced tea.
In this case, the answer is a negative fraction because they drank more tea than was made. To convert this improper fraction to a mixed number, divide the numerator (-115) by the denominator (12).
-115 ÷ 12 = -9 remainder 7
So, they drank -9 7/12 pitchers of iced tea.