A carpenter has two pieces of oak trim One pioce of trim is 3 3/4 A long and other is 2 11/12 long Estimate how many of oak trim she has in all Then find the exact answer
The mark ≈ means approximately equal.
3 3/4 ≈ 4
2 11/12 ≈ 3
Estaminate 4 + 3 = 7
The exact answer :
3 3/4 = 3 3∙3/ 3∙ 4 = 3 9/12
2 11/12 + 3 3/4 = 2 11/12 + 3 9/12 = 2 + 3 + 11/12 + 9/12 = 5 + 20/12 =
5 + ( 12 + 8 )/12= 5 + 12/12 + 8/12= 5 + 1 + 8/12 = 6 + 4∙2/4∙3 = 6 2/3
To estimate how much oak trim the carpenter has in total, we can round the lengths of the two pieces and add them together.
First, let's round both lengths to the nearest whole number:
3 3/4 is approximately 4
2 11/12 is approximately 3
Now, let's add the rounded lengths:
4 + 3 = 7
So, the estimated total length of oak trim is 7.
To find the exact answer, we need to add the exact lengths of the two pieces of trim.
The first piece is 3 3/4, which is already in an exact form.
The second piece is 2 11/12, which we can convert to improper form for easier addition.
2 11/12 = (2 * 12 + 11) / 12 = 35/12
Now, let's add the exact lengths:
3 3/4 + 35/12
To add the fractions, we need to find a common denominator, which is 12:
3 3/4 = (3 * 4 + 3) / 4 = 15/4
Now, we have:
15/4 + 35/12
To add the fractions, we need to have the same denominator, which is 12:
15/4 = (15 * 3) / (4 * 3) = 45/12
Now we have:
45/12 + 35/12 = (45 + 35) / 12 = 80/12
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
80/12 = (80 / 4) / (12 / 4) = 20/3
So, the exact total length of oak trim is 20/3.
To estimate how much oak trim the carpenter has in total, we can round the lengths to the nearest whole number and add them together.
The first piece of trim is approximately 4 feet long (since 3 3/4 is close to 4).
The second piece of trim is approximately 3 feet long (since 2 11/12 is close to 3).
So, the estimated total length of oak trim is 4 + 3 = 7 feet.
To find the exact answer, we need to convert the lengths to the same unit. Let's convert both lengths to twelfths of a foot, since it will make it easier to add them.
The first piece of trim, 3 3/4, can be converted to 3 * 12 + 3 = 39 twelfths of a foot.
The second piece of trim, 2 11/12, can be converted to 2 * 12 + 11 = 35 twelfths of a foot.
Now, we can add the lengths together:
39 twelfths of a foot + 35 twelfths of a foot = 74 twelfths of a foot.
To get the exact answer, we need to convert this back to a mixed number:
74 twelfths of a foot = 6 2/12.
So, the exact answer is 6 2/12 feet of oak trim.