Martinez bought 8 3/4 yd of fabric. She wants to make a skirt using 1 7/8 yd, pants using 2 3/8, and a vest using 1 2/3 yd.How much fabric will be left over? Please help ASAP!!! :(
Least common multiple of 4 , 8 and 3 is 24
Write:
8 3/4 as 8 3 ∙ 6/ 4 ∙ 6 = 8 18/24
1 7/8 as 1 7 ∙ 3/ 8 ∙ 3 = 1 21/24
2 3/8 as 2 3 ∙ 3/ 8 ∙ 3 = 2 9/24
and
1 2/3 as 1 2 ∙ 8/ 3 ∙ 8 = 1 16/24
Martinez use:
1 7/8 + 2 3/8 + 1 2/3 = 1 21/24 + 2 9/24 + 1 16/24 =
1 + 2 + 1 + 21 / 24 + 9 / 24 + 16 / 24 = 4 + 46 / 24 =
4 + ( 24 + 22 ) / 24 = 4 + 24 / 24 + 22 / 24 =
4 + 1 + 22 / 24 = 5 22/24yd
Leftover = 8 3/4 - 5 22/24 = 8 18/24 - 5 22/24 =
7 + 1 + 18 / 24 - 5 22/ 24 = 7 + 24 / 24 + 18 / 24 - ( 5 + 22 / 24 ) =
7 + 42 / 24 - 5 - 22 / 24 = 7 - 5 + 42 / 24 - 22 / 24 = 2 + 20 / 24 =
2 + 4 ∙ 5 / 4 ∙ 6 = 2 + 5 / 6 = 2 5/6 yd
Well Martinez seems to have quite the fancy wardrobe planned! Let's see how much fabric she'll have left over after making all those garments.
First, let's add up the fabric needed for each item:
Skirt: 1 7/8 yd
Pants: 2 3/8 yd
Vest: 1 2/3 yd
To add these fractions up, we need to have a common denominator. Let's convert everything to eighths:
Skirt: 15/8 yd
Pants: 19/8 yd
Vest: 13/8 yd
Now, let's add them up:
Total fabric needed = 15/8 + 19/8 + 13/8
Adding these fractions, we get:
Total fabric needed = 47/8 yd
Now, to find out how much fabric will be left over, we subtract the total fabric needed from the amount Martinez bought:
Fabric left over = 8 3/4 - 47/8
Subtracting these fractions, we get:
Fabric left over = 70/8 - 47/8
Simplifying further, we find:
Fabric left over = 23/8 yd
So, after making all those garments, Martinez will have 23/8 yards of fabric left over. That's almost enough to make a bow tie for her pet goldfish!
To find the total amount of fabric needed, we need to add up the fabric required for the skirt, pants, and vest.
Skirt: 1 7/8
Pants: 2 3/8
Vest: 1 2/3
To add these fractions together, we need a common denominator. The common denominator for 8, 4, and 3 is 24.
Converting the numbers to have a denominator of 24:
Skirt: (1 * 24/8) + (7/8) = 24/8 + 7/8 = 31/8
Pants: (2 * 24/8) + (3/8) = 48/8 + 3/8 = 51/8
Vest: (1 * 24/8) + (2/3 * 8/8) = 24/8 + 16/24 = 40/24 + 16/24 = 56/24
Now we can add up the fractions to find the total fabric needed:
Total fabric = 31/8 + 51/8 + 56/24
To add fractions, we need a common denominator of 24 again:
31/8 = (31/8) * (3/3) = 93/24
51/8 = (51/8) * (3/3) = 153/24
Total fabric = 93/24 + 153/24 + 56/24 = 302/24
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
302/24 ÷ 2/2 = 151/12
Therefore, Martinez will need a total of 151/12 yards of fabric.
To find the amount of fabric leftover, we need to subtract the total fabric needed from the amount of fabric purchased:
Amount of fabric purchased = 8 3/4
Convert this to an improper fraction:
8 * 4/4 + 3/4 = 32/4 + 3/4 = 35/4
Amount of fabric leftover = Amount of fabric purchased - Total fabric needed
= 35/4 - 151/12
To subtract fractions, we need a common denominator of 12:
35/4 = (35/4) * (3/3) = 105/12
Amount of fabric leftover = 105/12 - 151/12
= (105 - 151)/12
= -46/12
The result is negative, indicating that there isn't enough fabric to complete all of the clothing items. Therefore, there will be no fabric leftover.
To find out how much fabric will be left over, we need to subtract the total fabric used from the total fabric Martinez bought.
1. First, let's convert all the mixed numbers into improper fractions.
8 3/4 = (8 * 4 + 3) / 4 = 35/4
1 7/8 = (1 * 8 + 7) / 8 = 15/8
2 3/8 = (2 * 8 + 3) / 8 = 19/8
1 2/3 = (1 * 3 + 2) / 3 = 5/3
2. Next, let's add up the fractions to find the total fabric used:
Total fabric used = 15/8 + 19/8 + 5/3
To add fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 8 and 3 is 24.
3. Let's convert the fractions to have a common denominator of 24:
Total fabric used = (15/8) * (3/3) + (19/8) * (3/3) + (5/3) * (8/8)
= 45/24 + 57/24 + 40/24
4. Now, let's add the fractions together:
Total fabric used = (45 + 57 + 40) / 24
= 142 / 24
5. Simplify the fraction:
= 71 / 12
6. Finally, subtract the total fabric used from the fabric Martine bought to find the fabric left over:
Fabric left over = 35/4 - 71/12
To subtract fractions, they need to have the same denominator. So, let's again convert the fractions to have a common denominator of 12:
Fabric left over = (35/4) * (3/3) - (71/12) * (1/1)
= 105/12 - 71/12
7. Now, subtract the fractions:
Fabric left over = (105 - 71) / 12
= 34/12
8. Simplify the fraction:
Fabric left over = 17/6
Therefore, after making the skirt, pants, and vest, Martinez will have 17/6 yards of fabric left over.