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Some ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.
Write the ratio of as a fraction.
| Write as a fraction. | |
| Convert the numerator and denominator to improper fractions. | |
| Rewrite as a division of fractions. | |
| Invert the divisor and multiply. | |
| Simplify. |
One real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person's overall health. A ratio of less than to is considered good.
Hector's total cholesterol is mg/dl and his HDL cholesterol is mg/dl. ⓐ Find the ratio of his total cholesterol to his HDL cholesterol. ⓑ Assuming that a ratio less than to is considered good, what would you suggest to Hector?
ⓐ First, write the words that express the ratio. We want to know the ratio of Hector's total cholesterol to his HDL cholesterol.
| Write as a fraction. | |
| Substitute the values. | |
| Simplify. |
ⓑ Is Hector's cholesterol ratio ok? If we divide by we obtain approximately so Hector's cholesterol ratio is high! Hector should either lower his total cholesterol or raise his HDL cholesterol.
Find the patient's ratio of total cholesterol to HDL cholesterol using the given information.
Total cholesterol is mg/dL and HDL cholesterol is mg/dL.
Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information.
Total cholesterol is mg/dL and HDL cholesterol is mg/dL.
To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units.
We know that to simplify a fraction, we divide out common factors. Similarly in a ratio of measurements, we divide out the common unit.
The Americans with Disabilities Act (ADA) Guidelines for wheel chair ramps require a maximum vertical rise of inch for every foot of horizontal run. What is the ratio of the rise to the run?
In a ratio, the measurements must be in the same units. We can change feet to inches, or inches to feet. It is usually easier to convert to the smaller unit, since this avoids introducing more fractions into the problem.
Write the words that express the ratio.
| Ratio of the rise to the run | |
| Write the ratio as a fraction. | |
| Substitute in the given values. | |
| Convert 1 foot to inches. | |
| Simplify, dividing out common factors and units. |
So the ratio of rise to run is to This means that the ramp should rise inch for every inches of horizontal run to comply with the guidelines.
Find the ratio of the first length to the second length: inches to foot.
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