John must mount a box which is 10 3/6 inches wide. He wants to leave 7 1/2 inches on each side of the box. How many inches across will John need?
To find how many inches John will need across, first add the inches on each side to find how much space those inches take up: 7 1/2 inches + 7 1/2 inches = 15 inches
Then subtract that number from the total width of the box to find the remaining space: 10 3/6 inches - 15 inches = 4 inches. Answer: \boxed{4}.
To find out how many inches across John will need, we can subtract the inches he wants to leave on each side from the width of the box.
Width of the box = 10 3/6 inches
Inches John wants to leave on each side = 7 1/2 inches
To convert the mixed numbers to improper fractions:
10 3/6 inches = (10 * 6 + 3)/6 = 63/6 inches
7 1/2 inches = (7 * 2 + 1)/2 = 15/2 inches
Now we can subtract the inches John wants to leave on each side from the width of the box:
Width John needs = (63/6) - (15/2) inches
To subtract fractions, we need to find a common denominator:
Denominator of (63/6) = 6
Denominator of (15/2) = 2
The common denominator for 6 and 2 is 6.
Now, let's subtract the fractions:
Width John needs = (63/6) - (45/6) inches
Width John needs = (63 - 45)/6 inches
Width John needs = 18/6 inches
Simplifying the fraction:
Width John needs = 3 inches
Answer: John will need 3 inches across.
To find out how many inches across John will need, we need to subtract the space he wants to leave on each side of the box from the total width of the box.
First, let's convert the mixed fraction of 10 3/6 inches into an improper fraction. We multiply the whole number (10) by the denominator (6), then add the numerator (3). This gives us (10 * 6) + 3 = 63/6 inches.
Next, let's convert the mixed fraction of 7 1/2 inches into an improper fraction. We multiply the whole number (7) by the denominator (2), then add the numerator (1). This gives us (7 * 2) + 1 = 15/2 inches.
Now, let's subtract the spaces on each side of the box from the total width of the box. We have:
Total width of the box - Space on each side = Required width
63/6 inches - 15/2 inches = Required width
To subtract the fractions, we need to find a common denominator. The common denominator for 6 and 2 is 6. So we rewrite the fractions with a common denominator:
(63/6) - (15/2) = Required width
Multiplying the numerator and denominator of (63/6) by 2, we get:
126/12 - (15/2) = Required width
Now that we have a common denominator, we can subtract the fractions:
(126 - 90) / 12 = Required width
36/12 = Required width
Finally, we simplify the fraction 36/12 by dividing both the numerator and denominator by their greatest common divisor (which is 12):
36/12 = (36 ÷ 12) / (12 ÷ 12) = 3/1 = 3 inches
So John will need 3 inches across.