# Connections Between Adding and Subtracting, Multiplying and Dividing 03:57 minutes

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**Connections Between Adding and Subtracting, Multiplying and Dividing **

Jerome the Gnome sits in his home, with dreams of vacationing in Boca Raton. To confirm this fact, you should ask someone. Do gnomes turn to stone when kissed by the sun? In order for Jerome to elude this plight, he must do well to avoid the sunlight. Jerome'll visit a witch he can trust, he receives ingredients for a special pixie dust. He must collect all the items on the list to help him avoid this metamorphosis.

### Connections Between Adding and Subtracting, Multiplying and Dividing

What a wonderful idea, it's got some traction! Use **opposite operations** like **addition and subtraction**! Also, though it may be difficult to envision, another pair of opposites are **multiplication and division**. Jerome needs to collect sunflower seeds, ladybugs and forget-me-not petals.

### Sunflower seeds - The additive inverse property

While riding Dale the Snail through the forest, Jerome notices a hole in his napsack! After fixing the hole in his napsack Jerome needs to collect the same number of sunflower seeds he lost. Jerome had 200 sunflower seeds in his napsack, but lost 40 on the way leaving Jerome with 160 sunflower seeds. Jerome comes back with 40 sunflower seeds to replace the ones he lost. So 200 seeds minus the 40 seeds Jerome lost, PLUS the 40 seeds he collected gives him back the 200 seeds he needed. Whenever you add a number to its opposite, the result is always zero. This the **Inverse Property of Addition**.

### Ladybugs - Multiplication

The next item on the list is 12 ladybugs. Jerome can only catch 4 ladybugs at a time. So how many times does Jerome have to hunt ladybugs in order to reach his goal of 12? Adding 4 three times gives you 12. Another way to write this is to use the **definition of multiplication**, giving us 4 times 3. When adding a number to itself multiple times, it may be easier to write it as a multiplication problem. Here, we see that 'a' is added n' times, giving us 'n' times 'a'.

### Forget-me-not petals - The multiplication inverse property

The last items on the list are the forget-me-not petals. Each flower Jerome shakes yields 5 forget-me-not petals. Like before, this can be written with addition like this. Or since all the addends are the same, we can write this as a multiplication problem as well. Just like **addition and subtraction** are **opposite operations**, **multiplication and division** are also opposite operations. Since Jerome has 15 petals that he needs to **divide** into three jars Jerome puts an equal number of petals into each of the three jars. This process of splitting a number into equal parts is called **division**. Each flower yielded Jerome 5 forget-me-not petals and Jerome shook three flowers which he then needs to divide into three jars. This is the **Inverse Property of Multiplication**. If you **multiply** and then divide by the same number you get back your original number.

With the list now done, Jerome dreams of the sun. The witch keeps her promise and sprinkles the glitter, then Jerome celebrates with a twinkle and a flitter. Jerome planned to lie down just for a brief respite, no shade was welcome only sunlight. But all the day under the sun, Jerome willl learn quickly, sunburns just aren't fun.

**All Video Lessons & Practice Problems in Topic**Connections between Operations »

2 commentsHi @Hunter B.,

we are so happy that you enjoy our videos!

Let us know if you have any questions. We're always glad to help.

cool video, I learned a lot