John must mount a box which is 10 fraction numerator 3 over denominator 6 end fraction inches wide. He wants to leave 7 fraction numerator 1 over denominator 2 end fraction inches on each side of the box. How many inches across will John need?
To determine how many inches across John will need, we first find the total width of the box by adding the width on each side:
7 1/2 + 10 3/6 = 7 1/2 + 5/2 = 8/2 + 15/2 = 23/2 = <<23/2=11.5>>11.5 inches. Answer: \boxed{11.5}.
To determine how many inches across John will need, we need to calculate the total width of the box, including both sides.
Step 1: Calculate the width of each side:
The box is 10 3/6 inches wide.
Step 2: Convert the mixed fraction to an improper fraction:
10 3/6 is equal to (10 * 6 + 3)/6 = 63/6 inches.
Step 3: Subtract the desired space on each side from the total width:
63/6 - 7 1/2 - 7 1/2
Step 4: Convert the mixed fractions to improper fractions:
63/6 - (7 * 2 + 1)/2 - (7 * 2 + 1)/2
63/6 - (14 + 1)/2 - (14 + 1)/2
63/6 - 15/2 - 15/2
Step 5: Find a common denominator:
63/6 - 15/2 - 15/2
63/6 - (15 * 3)/6 - (15 * 3)/6
63/6 - 45/6 - 45/6
Step 6: Subtract the fractions:
(63 - 45 - 45)/6
(63 - 90)/6
-27/6
Step 7: Simplify the fraction:
-27/6 = -9/2
Therefore, John will need -9/2 inches across.
To find the answer, we need to subtract the width that John wants to leave on each side of the box from the total width of the box.
The total width of the box is given as 10 3/6 inches. To simplify this fraction, we can convert it to a mixed number:
10 3/6 = 10 + 3/6 = 10 + 1/2 = 10 1/2 inches.
The width that John wants to leave on each side of the box is given as 7 1/2 inches. Let's simplify this fraction as well:
7 1/2 = 7 + 1/2 = 7 1/2 inches.
Now, we can subtract the width John wants to leave on each side from the total width of the box:
10 1/2 - 7 1/2.
To perform this subtraction, we need a common denominator for the fractions. In this case, the common denominator is 2:
10 1/2 - 7 1/2 = (10 * 2 + 1)/2 - (7 * 2 + 1)/2
= (20 + 1)/2 - (14 + 1)/2
= (21/2) - (15/2).
Now, subtract the fractions:
(21/2) - (15/2) = (21 - 15)/2
= 6/2
= 3.
So, John will need 3 inches across.