Explain how dividing 720 by 9 is like dividing 72 by 9
The Correct Answer and Explanation is :
Dividing ( 720 \div 9 ) is like dividing ( 72 \div 9 ) because the division process and result rely on understanding place value. The correct answer to ( 720 \div 9 ) is 80, while ( 72 \div 9 ) equals 8.
Here’s why they are similar:
- Place Value in Multiples of Ten:
When you divide ( 720 \div 9 ), you are essentially dividing ( 72 \div 9 ) and then considering the additional power of ten in ( 720 ).
- ( 720 ) can be rewritten as ( 72 \times 10 ).
- So, ( 720 \div 9 = (72 \div 9) \times 10 = 8 \times 10 = 80 ).
- Shared Factors:
Both ( 720 ) and ( 72 ) are multiples of 9. Dividing by 9 in each case involves simplifying these numbers by the same divisor, ( 9 ). - Division Logic:
The same logic used for ( 72 \div 9 ) applies to ( 720 \div 9 ), but the latter accounts for the “extra zero,” or the factor of ten, in ( 720 ). - Pattern Recognition:
Recognizing the relationship between ( 720 ) and ( 72 ) simplifies the calculation. If you know ( 72 \div 9 = 8 ), you only need to multiply by ( 10 ) for ( 720 ).
This relationship highlights the importance of understanding basic math principles such as place value and factorization. The zero in ( 720 ) doesn’t change the essential division process; it only scales the result by ten. These patterns make mental math easier and help build strong foundational math skills.