Vicky bought 6 and 2/3 yards of one type of ribbon and 4 and 3/4 yards of another type of ribbon to make hair bows. If each bow takes 1 and 1/2 yards, how many hair bows can she make?
To find out how many hair bows Vicky can make, we need to determine the total length of the two types of ribbon she purchased and then divide it by the length required for each bow.
Let's add the lengths of the two types of ribbon together:
6 and 2/3 yards + 4 and 3/4 yards
To make this easier, let's convert 2/3 into a decimal.
2/3 = 0.67
Similarly, let's convert 3/4 into a decimal.
3/4 = 0.75
Now, add the whole numbers and decimals:
6 + 0.67 + 4 + 0.75
We get:
10.67 + 4.75 = 15.42
So, Vicky bought a total of 15.42 yards of ribbon.
Now, let's divide the total length of ribbon by the length required for each bow:
15.42 yards ÷ 1 and 1/2 yards
To make this calculation easier, let's convert 1/2 into a decimal.
1/2 = 0.5
Now divide:
15.42 ÷ 1.5
The answer is approximately 10.28.
Therefore, Vicky can make approximately 10 hair bows with the ribbon she purchased.
To find out how many hair bows Vicky can make, we need to determine how many yards of ribbon are required in total and then divide it by the amount of ribbon needed for each bow.
First, let's add the lengths of the two types of ribbons Vicky bought: 6 and 2/3 yards + 4 and 3/4 yards.
To add fractions, we need to make sure the denominators are the same. In this case, we can convert the mixed numbers to improper fractions:
6 and 2/3 yards = (6 × 3 + 2) / 3 = 20 / 3 yards
4 and 3/4 yards = (4 × 4 + 3) / 4 = 19 / 4 yards
Now we can add: 20/3 + 19/4.
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 4 is 12.
Converting both fractions to have a denominator of 12:
20/3 × 4/4 = 80/12
19/4 × 3/3 = 57/12
Now we can add: 80/12 + 57/12 = 137/12 yards.
Next, we need to divide the total length of ribbon by the amount required for each bow: 137/12 ÷ 1 and 1/2.
To divide by a fraction, we can multiply by its reciprocal:
137/12 ÷ 3/2 = 137/12 × 2/3.
Canceling common factors between the numerators and denominators:
(137 × 2) / (12 × 3) = 274/36.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2 in this case:
274/36 = (2 × 137) / (2 × 18) = 137/18.
So Vicky can make 137 hair bows using the ribbons she bought.
6 2/3 = 20/3
1 1/2 = 3/2
4 3/4 = 19/4
(20/3) / (3/2)
(20/3) * (2/3) = 40/9 = 4 bows
(19/4) / (3/2)
(19/4) * (2/3) = 38/12 = 3 bows