kate is looking at a slide under a microscope. The insect on the slide is 7/15 inches long. he uses the microscope to magnify the object 3 3/4 times. How long does the insect appear to be now?
To find out how long the insect appears to be under the microscope, we need to multiply the original size of the insect by the magnification factor of the microscope.
First, let's convert the length of the insect to a mixed number. We have 7/15 inches. To convert this to a mixed number, divide the numerator (7) by the denominator (15).
7 ÷ 15 = 0.4666...
The quotient is approximately 0.4666. Now, let's convert this decimal to a mixed number. We can see that 0.4666 is close to 7/15, which means it can be simplified.
To find the fraction equivalent to 0.4666, we can set up an equation:
x / 1 = 0.4666 / 1
x ≈ 7 / 15
Therefore, the original length of the insect is approximately 7/15 inches.
Now, we need to multiply the original length of the insect by the magnification factor of the microscope, which is 3 3/4 times. To convert this mixed number to an improper fraction, we multiply the whole number (3) by the denominator (4), and add the numerator (3).
3 * 4 = 12
12 + 3 = 15
Therefore, the magnification factor is 15/4.
To find the final length of the insect, multiply the original length by the magnification factor:
7/15 * 15/4 = (7 * 15) / (15 * 4)
The common factor of 15 in the numerator and denominator cancels out, so we are left with:
7/4
Therefore, the insect appears to be 7/4 inches long under the microscope.