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### Course: Arithmetic>Unit 16

Lesson 2: Multiplying decimals strategies

# Developing strategies for multiplying decimals

This video is all about understanding how to multiply decimals, specifically focusing on the strategy of converting decimals to fractions to make the multiplication process easier. Multiplying decimals can be made easier by thinking of the decimals as fractions. This helps understand what we are multiplying, and it also lays the groundwork for the standard method of decimal multiplication.

## Want to join the conversation?

• Why do you need multiple strategies can't ya just use one simple strategy?
• There are some advantages of using multiple strategies in mathematics.

1. This is a great way to check your work. If you use two different strategies and get the same answer, you can be much more confident that your answer is correct. If you get different answers, then that will let you know that something's wrong with one of the answers, giving you an opportunity to correct a mistake and make your two answers agree.

2. Even in math problems of a similar type, some problems are easier to solve with one strategy and some are easier to solve with another strategy. There are some beautiful arithmetic strategies. For example:

i) Multiplying a number by 5 is the same as multiplying the number by 10 and taking half (in either order).

ii) Multiplying a number by 99 is the same as multiplying by 100 and then subtracting the original number.

iii) Zeros at the end of a whole number cancel out decimal places in another number in multiplication problems (for example, 0.324 times 1600 is the same as 32.4 times 16).

You will also see this later on in algebra: there are multiple strategies for solving systems of equations, and multiple strategies for solving quadratic equations. The easiest strategy to use depends on the equation(s).

3. If you decide to teach math some day, you will see that not all students learn the same way. By teaching multiple strategies, you might be able to accommodate more students' learning styles.

4. Overall, understanding multiple strategies develops your mathematical intuition. Having a strong, accurate intuition will make it easier for you to remember material and to solve more challenging problems. The strongest math students are not the ones who memorize the most facts, but instead are the ones who have the best intuition and conceptual understanding.

While this is slightly off topic, think of chess. If you know only one strategy or tactic, you're unlikely to beat a good player. However, if you know multiple strategies and/or tactics, you're much more likely to beat a good player. Having the attitude of thinking like a chess player can help you become stronger in math.
• I still am a little confused... I want to dig deeper into the meaning of doing this. I want to learn why do we multiply decimals and fractions across, like we do for multiplication. I wonder why we move the decimal like we do. I am in a pile of questions...
• The reason we move the decimal is because we changed the decimal at first so we hack to change it back
• what means conceptualize
• Conceptualize means to form a concept or idea of something.
• so can we think of this with money if we want to make this easier?
• Yes. Lots of people use decimals when talking about money because they think it's easier for them.

Other people like to use fractions. It's up to you.
• So if you do a problem like 5/10 x 6/10 would you after the whole problem turn it into a decimal or do you keep it as a fraction?
• Here in Khan Academy, when you click the place where you have to put your answer, they will tell you if they want a fraction or a decimal or any of those.

What you do in life, it's up to what's more comfortable to you.
• Wouldn't you do 75 hundreths x 3?
• No, because 75 hundredths is the answer. You're doing 0.25 x 3, so you're are basically doing 0.25 + 0.25 + 0.25.
• I do not understand how the strategie works i tried it but i still couldn't figure it out
• Let's do 5 * 0.25.
steps:
5 * 0.25 =
5 * 25 * 0.01 =
125 * 0.01 =
1.25
• what is the easiest way to multiply decimals
• Is it correct to think of this strategy as multiplying by 10, or 100, to work with whole numbers for the purpose of making the calculations easier (but then you have to divide back to get the accurate answer). But for division, when you multiply the numerator and denominator by 10/10 or 100/100 (essentially 1), the answer must actually remain in the new form to be correct? 6 x 0.2 = 6 x 2 / 10, but 6 / 0.2 = 60 / 2 (no reverting back)
• The reason they are different is in the case of division, you are multiplying by values that = 1.
10/10 = 1
100/100 = 1
And, the identity property of multiplication tells us that we can multiply any number by 1 and we don't change the value of the original number. So, you are basically changing the way the numbers look in the fraction, but you haven't changed their value.

But, when you try to use the same technique with multiplying by 10 or 100 to have whole number, the value you are multiplying by does not equal 1. So, you need to divide by the 10 or 100 to return to the number's original value.

Hope this helps.