What is the difference between point 𝐿 and point 𝑁?
We’ve been given a timeline with some of the labels filled in and we need to measure the distance between point 𝐿 and point 𝑁. When we see the word “difference,” it should immediately remind us that we’ll be using subtraction. We will be saying the value of point 𝑁 minus the value of point 𝐿 equals the difference.
But before we can do subtraction, we’ll need to find out the value of points 𝐿 and and 𝑁. And that means we need to know what we’re counting by. If we look from point 𝑀 to the next dash, we have the values for each of those points. It’s going from 870 to 886. If we subtract 870 from 886, we get 16. That tells us that we are counting up by 16 each time.
To find out the value of point 𝐿, we take the dash before 𝐿 — 806 — and add 16. Point 𝐿 is equal to 806 plus 16. Six plus six is 12. Write down our two, carry our one. One plus one is two and we bring down our eight. Point 𝐿 is located at 822.
Now, if we look at the distance between 𝑁 and 𝑂, it will also be plus 16. And if we wanted to go in the opposite direction — if we wanted to go from 𝑂 to 𝑁 — we would subtract 16. Point 𝑁 is equal to 950 minus 16. We can’t subtract six from zero. So we borrow from our five tens. We’ll have four tens and 10 ones. Then, we can say 10 minus six equals four and four minus one equals three. We bring down the nine. There’s nothing to subtract it from. So we know point 𝑁 is located at 934.
Back to our original problem, point 𝑁 minus point 𝐿 equals the difference. Since we found the value of point 𝑁 and point 𝐿, we’re ready to subtract: 934 minus 822. Starting in the units place, we have four minus two equals two. In the tens place, three minus two equals one. And in the hundreds place, nine minus eight equals one. The difference between point 𝑁 and point 𝐿 is 112 units.
The distance on the number line between 822 and 934 is 112 units.