you have 10 inches of ribbon and want to create some headbands for some toys. the headbands require 2 and 1/3 inches of ribbon, how many complete headbands can you make and explain your thinking
To determine the number of complete headbands that can be made, we need to divide the total length of the ribbon by the length required for each headband.
Given that we have 10 inches of ribbon and each headband requires 2 and 1/3 inches, we first need to convert the mixed number into a fraction.
2 and 1/3 inches can be written as a fraction: 2/1 + 1/3 = 6/3 + 1/3 = 7/3 inches.
Now, let's divide 10 inches by 7/3 inches.
10 inches ÷ (7/3 inches) = 10 inches × (3/7 inches) = (30/7) inches.
To find the number of complete headbands, we divide the total length by the required length for one headband.
(30/7) inches ÷ (7/3) inches = (30/7) inches × (3/7 inches) = 90/49 ≈ 1.84 headbands.
Since we cannot have a fraction of a headband, we can only make the complete number of headbands, which is 1.
To calculate the number of complete headbands you can make, divide the total length of ribbon (10 inches) by the length required for each headband (2 and 1/3 inches).
Step 1: Convert 2 and 1/3 inches to a decimal.
To convert a mixed fraction to decimal, we multiply the whole number (2) by the denominator (3) and add the numerator (1). Then, we divide the result by the denominator.
2 * 3 = 6
6 + 1 = 7
7 ÷ 3 = 2.3333 (rounded to four decimal places)
Now we have the decimal equivalent of 2 and 1/3 inches, which is approximately 2.3333 inches.
Step 2: Divide the total length of ribbon by the length required for each headband.
10 inches ÷ 2.3333 inches ≈ 4.29
We get approximately 4.29, meaning you can make 4 complete headbands.
Explanation: Since you have a total of 10 inches of ribbon and each headband requires 2 and 1/3 inches, you can make 4 complete headbands with the available ribbon. There will be a little bit of leftover ribbon, approximately 0.29 inches, which is not enough to create another complete headband.
To determine the number of complete headbands you can make with 10 inches of ribbon, you need to divide the total length of ribbon by the length required for each headband.
First, convert the length of one headband from a mixed number (2 1/3 inches) to a proper fraction. To do this, multiply the whole number (2) by the denominator (3) and add the numerator (1). Then put the result over the denominator:
2 * 3 + 1 = 7
7/3
Now divide the total length of ribbon (10 inches) by the length required for each headband (7/3 inches):
10 / (7/3)
To divide by a fraction, multiply by its reciprocal. The reciprocal is obtained by flipping the numerator and denominator. Therefore, the reciprocal of 7/3 is 3/7:
10 * (3/7)
Multiply across:
(10 * 3) / 7 = 30/7
The result is a proper fraction, which we can further simplify by dividing the numerator by the denominator:
30 ÷ 7 = 4 remainder 2
So you can make 4 complete headbands with 2 inches of ribbon left over.
In conclusion, you can create 4 complete headbands and have 2 inches of ribbon remaining.