# Subtracting Big Numbers From Small Numbers

Jan 23, 2024 | Southland

Subtracting Big Numbers From Small Numbers By Mathnasium | Added Aug 2, 2023

Our expert team of math educators and enthusiasts has spent over 40 years developing and refining the most powerful teaching methods and materials into the comprehensive, industry-leading Mathnasium Method™.

Exploring Subtraction

You have five cookies and your friend eats four of them. How many cookies do you have left? One!

5 – 4 = 1

5 – 5 = 0

Now, what if your friend wants to eat yet another cookie? How many cookies do you have left? We cannot take away one cookie from ZERO cookies since there are not enough cookies. So, what happens to the cookie that the friend wants to eat?

Subtracting Large Numbers from Small Numbers in Real-World Scenarios

Clearly, when we try to subtract a big number from a small number, the cookie model doesn’t help us. But here is a model that does!

Consider this “carrot” scenario: Farmer Frank is growing carrots. The root of the carrot (the orange part) grows underground, and the stem and leaves (the green parts) grow above ground. The root of the carrot is 20 cm long and the stem and leaves are 25 cm long.

Let’s say an ant crawls from the top of the leaves down 35 centimetres (cm). We can describe the movement below ground (underground) as negative, and the movement above ground as positive:

The ant’s starting point is 25 cm above ground. The ant moves 35 cm downwards. The ant is now 10 cm below ground, and so, 25 – 35 = -10 cm.

Let’s practice this again: A worm wiggles its way from the top of the soil down 13 cm. Where is the worm now?

The worm starts at 0 cm. The worm moves 13 cm downwards, in a negative direction. The worm is now 13 cm underground, and so, 0 – 13 = -13 cm.

Practice