Here are the necessary conversions:
1 ft = 12 in
1 in = 2.54 cm
1 m = 100 cm
When using conversions like these, you need to make sure that the units you start with get canceled out, so the units you started with need to be in the denominator (bottom of the fraction) in your conversion factor.
So we have the conversion factors*:
1 = 12 in/ft
1 = 2.54 cm/in
1 = 1/100 m/cm = .01 m/cm
(cm in denominator because previous step left us with cm)
Notice that conversion factors equal 1. So when we multiply what we were given by a conversion factor, we aren't changing the value, just the units.
4 ft 8 in = 4 ft * (12 in/ft) + 8 in = 4 * 12 in + 8 in = 48 in + 8 in = 56 in
56 in = 56 in * (2.54 cm/in) = 142.24 cm
142.24 cm = 142.24 cm * (.01 m/cm) = 1.4224 m
so,
4 ft 8 in = 1.4224 m
---- * NOTE: Using conversion factors in this problem was pretty straightforward but what if your conversion didn't have a 1 on one side? Or, what if you were converting in the other direction?
EX: 55 mi = 88 km (which I remember from speed limit signs in Canada)
If we divide both sides by 11, we get: 5 mi = 8 km
There 2 sets of conversion factors, depending on what units you're given:
If given mi: 1 = 8 km / 5 mi = 8/5 km/mi
If given km: 1 = 5 mi / 8 km = 5/8 mi/km
So now we can solve both types of questions:
How many kilometers in 15 miles?
15 mi = 15 mi * (8 km / 5 mi) = 3 * 8 km = 24 km
How many miles in 16 kilometers?
16 km = 16 km * (5 mi / 8 km) = 2 * 5 mi = 10 mi
This is a rectangle with length 5 units and width 3 units. The area = length x width = 5 x 3 = 15 sq units. The perimeter = 2 x (length + width) = 2 x 8 = 16 units.
12
11
5 * 3 * 2 = 30 cubic whatever units ==================
-3 to 2 is +5 units so move another +5 units to +7 -4 to -1 is +3 units so move another +3 units to +2 So the other end point is (7,2)
The two points are (2, -3) and (-4, 5). To start at the origin, O, which is (0, 0). Then, to find any point, such as (p, q), you move p units to the right (to the left if p is negative) and then q units up (down if q is negative). So, the first point is 2 units to the righ and 3 down. The second is 4 to the left and 5 up.
Pour the 5 into the 3, there is now two units left in the 5 container. Add these two units to the 8 container. Repeat the process, and you have four units in the 8.
This is a rectangle with length 5 units and width 3 units. The area = length x width = 5 x 3 = 15 sq units. The perimeter = 2 x (length + width) = 2 x 8 = 16 units.
That depends on the direction of the point in reference to the original coordinate. If the new point is 5 units to the right of (1,3), then the point is (6,3). If the point is 5 units left of (1,3), then the point is (-4,3). And so on.
12
length 5 units,width 3 units p=2(L+W) p=2(5+3) p=10+6 p=16 units
1. Fill 3 unit and pour into 5 2. Fill 3 unit again and then use it to fill up 5 (you will have 1 left over) 3. Empty 5 4. Pour the remaining 1 into the 5. 5. Fill the 3 and pour into 5 making 4 units in the 5 container.
5
We add only when numbers have the same sign. Since the numbers have different sings which means opposite signs, then we have to operate the opposite of addition which is subtraction. Why do we add numbers that have the same sign? Look at the real number line. As we decided to assign numbers with a positive sign if they go far from zero to the right, and with a negative sign if the go far from zero to the left, then we say there are to opposite directions of moving; we move to the right of any number, if the next number is a positive number, and we move to the left of any number, if the next number is a negative number. Let's try to plot the result of, say 5 + 3. The only possibility to do that is to go far from zero only to the right: first, 5 units, then 3 units more, so the total distance is 8 units to the right of zero. And we say 5 + 3 = 8. What about of -5 - 3? The only possibility to do that is to go far from zero only to the left: first, 5 units, then 3 units more, so the total distance is 8 units to the left of zero. And we say -5 - 3 = -8. What about of -5 + 3? There are two possibilities to do that. First, by moving to the left of zero 5 units, then from there, by moving back to the right 3 units. So the total distance from zero is 2 units to the left. And we say -5 + 3 = -2. Since the previous distance from zero became smaller, it means that we've subtracted those numbers (meaning their distances from zero), and we ploted their differnce (since the distance of -5 dominaned and it was on the left, then the remaining distance must be on the left).
11
The code works if you count the keys from left to right on the piano. First key on the left it #1, second from the left is #2 and so on. 5, 3, 2, 1, 2, 3, 5, 3, 2, 1, 2, 3, 5, 3, 5, 6, 3, 6, 5, 3, 2, 1
5 * 3 * 2 = 30 cubic whatever units ==================