Dividing By a Decimal
Dividing by a decimal in Grade 8 Saxon Math Course 3 involves converting the divisor to a whole number by multiplying both the dividend and divisor by a power of 10, then performing standard long division. Students learn that this process does not change the value of the quotient and can be applied to any decimal divisor. This skill is essential for working with measurements, money, and algebraic expressions.
Key Concepts
Property To divide by a decimal, transform it into an equivalent problem where the divisor is a whole number. Multiply both the dividend and divisor by the same power of 10. $$ \frac{0.42}{0.6} \cdot \frac{10}{10} = \frac{4.2}{6} $$.
Examples $3.6 \div 0.6 = 36 \div 6 = 6$ $2.4 \div 0.08 = 240 \div 8 = 30$.
Explanation Dividing by a decimal is a no no. To fix it, slide the decimal in the divisor all the way to the right to make it whole. Just remember to slide the dividend's decimal the same number of spots!
Common Questions
How do you divide by a decimal?
Move the decimal point in the divisor to the right until it becomes a whole number. Move the decimal in the dividend the same number of places. Then divide as usual.
Why can you move the decimal point when dividing?
Multiplying both dividend and divisor by the same power of 10 does not change the quotient. This is equivalent to multiplying the division problem by 1.
How do you divide 4.5 by 0.3?
Move both decimal points one place right: 45 divided by 3 = 15. The answer is 15.
What if there are more decimal places in the divisor than the dividend?
Add zeros to the dividend as needed to match the number of decimal places you need to move. Then divide normally.
How is dividing by a decimal taught in Saxon Math Course 3?
Saxon Math Course 3 teaches this through the technique of multiplying both numbers by a power of 10 to eliminate the decimal in the divisor before dividing, reinforcing the equivalence principle.