Multiplication using place value understanding

The Multiplication using place value understanding exercise appears under the 4th grade (U.S.) Math Mission. This exercise uses place value and properties of multiplication to discover some multiplication techniques.

Types of Problems

There are three types of problems in this exercise:

1. Use the associativity property: This problem asks the user to multiply two numbers together. The user uses the associative property to fill in the blanks and arrive at the answer.

   

   Use the associative property

2. Use the distributive property: This problem asks the user to perform a multiplication property by using the distributive property on it's individual place values.

   

   Use the distributive property

3. Use several multiplication properties: This problem provides a multiplication problem that can be viewed as using all of the "big three" multiplication properties.

   

   Use several multiplication properties

Strategies

It is not necessary to know the names of the multiplication properties, but some familiarity could increase efficiency on this exercise.

1. The three problem types repeat the same pattern with different numbers, so it is possible to develop an algorithm to recognize the numbers that need to be inserted quickly.
2. The associative property of multiplication says that when multiplying numbers associate with each other, i.e., grouping does not matter. ${a\times (b\times c)=(a\times b)\times c}$.
3. The commutative property says order does not matter, i.e.,${a\times b=b\times a}$.
4. The distributive property says that ${a(b+c)=ab+ac}$.

Real-life applications

1. Efficiency in multiplication will increase the ability to work confidently in fractions which occur in real-life often.
2. By learning multiplication and memorizing the times tables, users provide themselves with essential building blocks to do higher learning math, like division, fractions and even algebra.
3. Multiplication is necessary for a career in the stock market.
4. Place value is used for writing checks.
5. A common example of place value is money (example: $1.69 means that there is 1 whole (dollar), 6 tenths (dimes), and 9 hundredths (pennies)).