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# Multiplying With Base 10

Oct 19, 2020 | Location Highlands

Sometimes, multiplying can be hard for students. Multiplication facts of bigger numbers are often difficult for kids to think of right off the top of their head.

8 x 12 can have students guessing, finger counting, or avoiding the work.

However, multiplying by 10’s first is especially easy as each product ends in 0.

##### What does it mean to multiply with base 10?

Multiplying by base 10 allows our students to split up the multiplicand (number being multiplied) into more manageable terms, 10 and another factor.

In 8 x 12, we teach students to split up 12 into 10 + 2. In 6 x 8, we remember that 8 + 2 = 10. We'll dissect both of these problems below!

Some prerequisites to Base 10 Multiplication are:

• Identify compliments of 10 (e.g. 9 + 1, 8 + 2, 7 + 3)
• Add 10 plus a single digit number
• Count by 10s
• Multiply single digit numbers by 10 (e.g. 7 x 10 = 70)
• Ability to double numbers (e.g. 7 x 2 = 14)
• Ability to add and subtract to and from numbers ending in 0
##### Multiplying with Base 10 for Double-Digit Numbers

8 x 12. Let's do it.

If a problem asks the student to multiply the multiplicand by a number larger than 10, they can split that number into 10 and whatever number added to 10 is equal to the original and then add the products of the multiplicand times 10 and the other number.

For example, 8 x 12 can be split up into 8 x 10 and 8 x 2. The sum of the products of 8 x 10 and 8 x 2 is 96 (80 + 16 = 96), the same value as the product of 8 x 12

##### Multiplying with Base 10 for Single-Digit Numbers

Students frequently have difficulty multiplying numbers by 6,7,8, and 9. Luckily, the Base 10 strategy also works well for these multipliers.

Let's go back to 6 x 8.

Knowing we need to use "10 is Our Friend," or Base 10, we remember that 8 is just 2 away from 10. Or, 10 - 2 = 8.

So, the expression, 6 x 8 can also be written as 6 x 10 - 6 x 2. The difference of 60 - 12 is equal to the product of 6 x 8, or 48.

Instead of relying on their fingers to multiply by 9s, students can remember that 9 groups of something is just one group less than 10 groups of something.

##### Using 5 to Multiply by 6 and 7

Students often can count by 5s and 2s fluently. They can often mentally add 2-digit numbers numbers accurately. To help with multiplication fats of 6 and 7, we ask students to tap into those foundational skills.

The expression 6 x 7 can be rewritten as 6 x 5 + 6 x 2. The sum of 30 and 12 has an identical value to the product of 6 x 7, which is 42

###### If this is what you want for your child - It's easy to get started!

Where are your child’s math skills?

Both you and your child can take our interactive quizzes to see how much you remember! What grade are they in?

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#160
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