๐ Topic Summary
Dividing decimals with decimal divisors involves transforming the problem into one with a whole number divisor. This is achieved by multiplying both the divisor and the dividend by a power of 10 (10, 100, 1000, etc.) that makes the divisor a whole number. Once you have a whole number divisor, you can perform long division as usual, placing the decimal point in the quotient directly above the decimal point in the dividend.
For example, to divide 4.25 by 0.5, we multiply both numbers by 10 to get 42.5 รท 5. Now, we can easily divide 42.5 by 5 to get 8.5. Remember to always check your work by multiplying the quotient by the original divisor to ensure it equals the original dividend.
๐งฎ Part A: Vocabulary
- โ Match the term with its correct definition:
- ๐ Term: Dividend
- ๐ Term: Divisor
- ๐ Term: Quotient
- โ Term: Decimal
- โ Term: Decimal Divisor
- ๐ก The number that divides another number.
- โ A number expressed in base-10 notation using digits 0-9 and a decimal point to separate the whole and fractional parts.
- โ The result of division.
- โ The number being divided.
- โ A divisor that contains a decimal.
| Term |
Definition |
| Dividend |
(4) |
| Divisor |
(1) |
| Quotient |
(3) |
| Decimal |
(2) |
| Decimal Divisor |
(5) |
โ๏ธ Part B: Fill in the Blanks
When dividing decimals with decimal divisors, the first step is to make the ______ a whole number. To do this, you must multiply both the divisor and the ______ by the same power of ______. This ensures that the value of the ______ remains the same. After adjusting the decimal places, you can perform ______ division as usual.
Answers: divisor, dividend, 10, quotient, long
๐ค Part C: Critical Thinking
Explain why it's necessary to multiply both the divisor and the dividend by the same power of 10 when dividing decimals. What mathematical principle does this rely on?