Compute: 6/7÷3/5 . Simplify the answer if possible.
the answer to the original question is 1 3/7
George has a wooden board that is 3 1/4 feet long. He needs to cut it into sections that are 3/4 foot long. How many sections can he cut from this board?
To find out how many sections George can cut from the wooden board, we need to divide the length of the board by the length of each section.
The length of the board is 3 1/4 feet, which can also be written as 3 + 1/4 feet.
Now, let's convert both the length of the board and the length of each section to the same denominator, which is 4:
3 + 1/4 feet = 12/4 + 1/4 = 13/4 feet
Each section is 3/4 feet.
Now, we can divide the length of the board by the length of each section:
(13/4) ÷ (3/4) = (13/4) * (4/3) = (13 * 4) / (4 * 3) = 52/12 = 4 4/12 = 4 1/3
Therefore, George can cut 4 and 1/3 sections from the wooden board.
Bryan has 5 2/3 feet of leather cord to use to make friendship bracelets. He needs 1/2 foot of cord for each one. How many whole bracelets can Bryan make?
To find out how many whole bracelets Bryan can make, we need to divide the length of the leather cord by the length needed for each bracelet.
The length of the leather cord is 5 2/3 feet, which can also be written as 5 + 2/3 feet.
Now, let's convert both the length of the leather cord and the length needed for each bracelet to the same denominator, which is 3:
5 + 2/3 feet = 15/3 + 2/3 feet = 17/3 feet
Each bracelet needs 1/2 foot of cord.
Now, we can divide the length of the leather cord by the length needed for each bracelet:
(17/3) ÷ (1/2) = (17/3) * (2/1) = (17 * 2) / (3 * 1) = 34/3 = 11 1/3
Therefore, Bryan can make 11 whole bracelets with some leftover cord.
A bakery orders 6 1/2 pounds of gluten-free flour. Each gluten-free cake uses 3/4 pound of the special flour. How many full cakes can the bakery make from this order? Your answer should be a whole number.
To find out how many full cakes the bakery can make, we need to divide the weight of the gluten-free flour by the amount of flour needed for each cake.
The weight of the gluten-free flour is 6 1/2 pounds, which can also be written as 6 + 1/2 pounds.
Now, let's convert both the weight of the gluten-free flour and the amount of flour needed for each cake to the same denominator, which is 2:
6 + 1/2 pounds = 12/2 + 1/2 pounds = 13/2 pounds
Each cake requires 3/4 pound of the special flour.
Now, we can divide the weight of the gluten-free flour by the amount of flour needed for each cake:
(13/2) ÷ (3/4) = (13/2) * (4/3) = (13 * 4) / (2 * 3) = 52/6 = 8 2/6 = 8 1/3
Therefore, the bakery can make 8 full cakes from this order.
To compute the division of fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
Step 1: Find the reciprocal of the second fraction.
Reciprocal of 3/5 = 5/3
Step 2: Multiply the first fraction by the reciprocal of the second fraction.
6/7 * 5/3 = (6 * 5) / (7 * 3) = 30/21
Step 3: Simplify the fraction.
To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and the denominator, which is 3.
Dividing both the numerator and the denominator by 3 results in:
30 ÷ 3 / 21 ÷ 3 = 10/7
Therefore, the simplified answer is 10/7.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, we have:
6/7 ÷ 3/5 = 6/7 × 5/3
Now, let's multiply the numerators and denominators separately:
6 × 5 = 30
7 × 3 = 21
So, the simplified answer is 30/21.
To compute the given expression 6/7 ÷ 3/5, we can follow these steps:
Step 1: Invert the second fraction, which means finding its reciprocal. The reciprocal of 3/5 is 5/3.
Step 2: Now multiply the first fraction by the reciprocal of the second fraction.
6/7 * 5/3 = (6 * 5) / (7 * 3) = 30/21
Step 3: Simplify the resulting fraction if possible. In this example, we can simplify by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3.
30 ÷ 3 / 21 ÷ 3 = 10/7
Therefore, the simplified answer is 10/7.