shawna had to decorate 3 gift packages with ribbon. she used 1 1/3 yards of ribbon for the first package, 1 1/2 yards of ribbon for the second package, and 1 2/3 yards to decorate the third package. shawna had 3 1/2 yards of ribbon left over. how much ribbon did she start with?
First find the common denominators and the equivalent fractions.
1 1/3 = 1 4/12
1 1/2 = 1 6/12
1 2/3 = 1 8/12
Add.
3 18/12 = 4 1/2
4 1/2 + 3 1/2 = ?
Well, Shawna seems to be quite the expert gift decorator! Let's do some math together, but let's do it in a fun way, shall we?
To find out how much ribbon Shawna started with, we can add up the amounts of ribbon she used for each package and then subtract the amount she had left over.
First package: 1 1/3 yards
Second package: 1 1/2 yards
Third package: 1 2/3 yards
Now, let's add them up: 1 1/3 + 1 1/2 + 1 2/3 = 3 13/6
Now, let's convert that mixed number into an improper fraction: 3 + 13/6 = (3 * 6 + 13) / 6 = 31/6
So, Shawna used a total of 31/6 yards of ribbon to decorate the gift packages.
Now, let's subtract the amount she had left: 31/6 - 3 1/2
To simplify the calculation, let's convert 3 1/2 into an improper fraction too: 3 + 1/2 = (3 * 2 + 1) / 2 = 7/2
Now, let's subtract: 31/6 - 7/2 = (31 * 2 - 7 * 6) / (6 * 2) = (62 - 42) / 12 = 20/12 = 5/3
So, Shawna had 5/3 yards of ribbon left over.
Now we know that Shawna had 5/3 yards left, but we still need to find out how much she started with. So, to find the starting amount of ribbon, we need to add the amount she had left over back to the amount she used:
5/3 + 31/6 = (5 * 6 + 31) / (3 * 6) = (30 + 31) / 18 = 61/18
And there you have it! Shawna started with 61/18 yards of ribbon.
To find out how much ribbon Shawna started with, we can add up the amount of ribbon she used and the amount she had left over.
1. Let's add up the ribbon Shawna used:
- For the first package: 1 1/3 yards
- For the second package: 1 1/2 yards
- For the third package: 1 2/3 yards
(1 1/3) + (1 1/2) + (1 2/3) = (4/3) + (3/2) + (5/3) = 4/3 + 9/6 + 10/6 = 15/6 + 9/6 + 10/6 = (15 + 9 + 10)/6 = 34/6 = 17/3 yards
2. Now let's calculate how much ribbon Shawna had left over:
- Leftover ribbon: 3 1/2 yards = (7/2) yards
3. To find out how much ribbon Shawna started with, we'll add the used ribbon to the leftover ribbon:
- Starting amount of ribbon = Used ribbon + Leftover ribbon
- Starting amount of ribbon = (17/3) yards + (7/2) yards
4. To add the fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 3 and 2 is 6.
- Starting amount of ribbon = (17/3)(2/2) yards + (7/2)(3/3) yards
- Starting amount of ribbon = (34/6) yards + (21/6) yards
- Starting amount of ribbon = (34 + 21)/6 yards
- Starting amount of ribbon = 55/6 yards
Therefore, Shawna started with 55/6 yards of ribbon.
To find out how much ribbon Shawna started with, we need to add up the ribbon lengths she used and the leftover amount.
First, let's convert the mixed numbers into improper fractions for easier calculations:
1 1/3 = (3 * 1 + 1) / 3 = 4/3
1 1/2 = (2 * 1 + 1) / 2 = 3/2
1 2/3 = (3 * 1 + 2) / 3 = 5/3
Now, let's add up the ribbon lengths Shawna used:
4/3 + 3/2 + 5/3
To add these fractions, we need a common denominator. The least common multiple (LCM) of 2 and 3 is 6. So, let's convert the fractions using a common denominator of 6:
(4/3) * (2/2) = 8/6
(3/2) * (3/3) = 9/6
5/3
Now, we can add them up:
8/6 + 9/6 + 5/3 = (8 + 9 + 10)/6 = 27/6
Next, let's subtract the leftover ribbon from the total Shawna used:
27/6 - 3 1/2
First, let's convert 3 1/2 into an improper fraction:
3 1/2 = (2 * 3 + 1) / 2 = 7/2
Now, subtract:
27/6 - 7/2
We need to convert the fractions to have a common denominator. The least common multiple (LCM) of 6 and 2 is 6. So, let's convert the fractions using a common denominator of 6:
(27/6) * (1/1) = 27/6
(7/2) * (3/3) = 21/6
Now, subtract:
27/6 - 21/6 = 6/6 = 1
So, Shawna started with 1 yard of ribbon.