Guided Practice #2
Practice Problem #4
Simplify the ratio.
Let's start by identifying the target and numerator and denominator units.
Numerator: ___
Answer: kilogram
Denominator: ___
Answer: gram (base unit)
Great! You can convert either unit to the other to solve this problem, but it will be easier to change the kilograms to grams. Why? You usually go from larger units to smaller units to avoid the possibility of dealing with decimals.
To change kilo to base unit on the scale below, move ___ spaces to the ___.
Answer: 3, right
That's correct. You'll need to move the decimal place on 7kg three spaces to the right.
Answer: 7,000
Now just simplify the fraction.
Answer: 140, 1
Practice Problem #5
Simplify the ratio.
Ok, start by selecting the conversion 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: 16 ounces = 1 pound; oz stands for ounces and lb for pounds
16 ounces = 1 pound
That's right. The first thing you will need to do is change pounds to ounces. So,
4 lb = ____ oz
Answer: 64
Great. Now, substitute 64 oz for 4 lb.
Answer: 64
Now, reduce the fraction to simplify the ratio.
Answer: 5, 32
Practice Problem #6
The area of a rectangle is 125 ft2. The ratio of the width to length is 1:5. Find the length and width.
Ok, let's start by finding terms to represent the width and length. If the width (shorter side) is x, what is the length?
1 = ___
Answer: 5x
Great! Now that we have variables to represent the length and width, we can plug them into the equation for the area of a rectangle. Which is the proper equation?
- P = 2(l + w)
- A = lw
Answer: A = lw
That's correct. Let's start by solving. Plug in the values.
A = lw
125 = ( ___ )( ___ )
Answer: 5x, x
Good. Simplify the right side by multiplying the terms in parentheses.
125 = ___x2
Answer: 5
Nice job! Isolate the x-term now.
___ = x2
Answer: 25
Ok, now find x.
___ = x
Answer: 5
Great! Now that we know x = 5, plug that value in to find the length and width.
w = ___ft
l = ___ft
Answer: 5, 25
