Guided Practice #1
Practice Problem #1
Solve the proportion. Round decimals to the nearest tenth.
Start by using the cross product property If a/b = c/d, then ab = cd to set up an equation without fractions.
___ = (8)( ___ )
Answer: 5x , 4
Now, multiply the terms in parentheses on the right side to simplify.
5x = ___
Answer: 32
Now, isolate the x term.
Answer: 5
Finally, reduce the fraction to a number in decimal form.
x = ___
Answer: 6.4
Practice Problem #2
Solve the proportion. Round decimals to the nearest tenth.
Start by using the cross product property If a/b = c/d, then ab = cd to set up an equation without fractions.
___ = ___(y + 1)
Answer: 2y, 6
Use the distributive property to simplify the expression on the right.
2y = ___ + ___
Answer: 6y, 6
Subtract 2y from both sides to combine all of the y-terms on one side of the equation.
___ = ___ + 6
Answer: 0, 4y
Now, make the y-term the only term on the right side of the equation.
___ = 4y
Answer: -6
Isolate the y-term
___ = y
Answer: -6/4
Simplify the fraction and enter your answer as a decimal.
___ = y
Answer: -1.5
Practice Problem #3
Simplify the ratio.
Start by selecting the conversion factors you can use to help solve this problem.
- 12 inches = 1 foot
- 3 feet = 1 yard
- 16 ounces = 1 pound
- 5280 feet = 1 mile
Answer: 12 inches = 1 foot, 3 feet = 1 yard; There is not a conversion directly from yards to inches, so you will have to convert from yards to feet and then from feet to inches. You need both conversion factors!
The first thing you will need to do is change yards to feet, then feet to inches. So, 3 yd = ___ ft.
Answer: 9
Now that you know how many feet are in 3 yards, convert to inches.
3yd = 9 ft
9 ft = ___ in
Answer: 108; Remember, 1 foot = 12 in. So you can set this up as a proportion. 1 ft/12in = 9ft/x in. By the cross product property, x = (12)(9). Multiply for your answer.
Now, substitute 108 inches for 3 yd.
Answer: 108
Finally, reduce to simplify.
Answer: 1, 6
