9.1: Number Talk: Dividing by Powers of 10
Find the quotient mentally.
$30\div 10$
$34\div 10$
$3.4\div 10$
$34\div 100$
Let’s use ratios to work with how fast things move.
Find the quotient mentally.
$30\div 10$
$34\div 10$
$3.4\div 10$
$34\div 100$
Your teacher will set up a straight path with a 1-meter warm-up zone and a 10-meter measuring zone. Follow the following instructions to collect the data.
your slow moving time (seconds) | your fast moving time (seconds) | |
---|---|---|
row 1 |
After you finish collecting the data, use the double number line diagrams to answer the questions. Use the times your partner collected while you were moving.
Moving slowly:
Moving quickly:
Lin and Diego both ran for 10 seconds, each at a constant speed. Lin ran 40 meters and Diego ran 55 meters.
Lin and Diego want to run a race in which they will both finish when the timer reads exactly 30 seconds. Who should get a head start, and how long should the head start be?
Suppose a train traveled 100 meters in 5 seconds at a constant speed. To find its speed in meters per second, we can create a double number line:
The double number line shows that the train’s speed was 20 meters per second. We can also find the speed by dividing: $100 \div 5 = 20$.
Once we know the speed in meters per second, many questions about the situation become simpler to answer because we can multiply the amount of time an object travels by the speed to get the distance. For example, at this rate, how far would the train go in 30 seconds? Since $20 \boldcdot 30 = 600$, the train would go 600 meters in 30 seconds.
A unit to measure speed that tells you how many meters an object travels in one second.