Checking One-Digit Division
Grade 4 students learn to verify division answers by multiplying in Saxon Math Intermediate 4. Because multiplication and division are inverse operations, the check formula is: quotient times divisor = dividend. For 63 divided by 9 = 7, verify with 7 times 9 = 63. When a division has a remainder, the check becomes (quotient times divisor) plus remainder = dividend: 7 times 6 = 42, plus 5 remainder = 47. This Chapter 6 skill builds accuracy and number sense by requiring students to confirm their work using the relationship between the two operations.
Key Concepts
Property To check a division problem, you multiply the quotient, which is the answer you found, by the divisor, which is the number you are dividing by. The result of this multiplication should equal the dividend, the number that was originally being divided. This confirms your division is correct because multiplication and division are inverse operations.
Example Example 1: First, divide $24$ by $4$ to get $6$. $\frac{6}{4) \overline{24}}$. Then check the answer by multiplying: $6 \times 4 = 24$. The product matches. Example 2: First, divide $49$ by $7$ to get $7$. $\frac{7}{7) \overline{49}}$. Then check the answer by multiplying: $7 \times 7 = 49$. The product matches.
Explanation Division and multiplication are a team with opposite powers! Division breaks numbers apart, and multiplication puts them back together. If you can use multiplication to perfectly rebuild the original number, you know your division mission was a success!
Common Questions
How do you check a division answer?
Multiply the quotient by the divisor. If the product equals the original dividend, the answer is correct. For 42 divided by 6 = 7, check with 7 times 6 = 42. It matches, so the answer is right.
How do you check a division problem that has a remainder?
Use the formula: (quotient times divisor) plus remainder = dividend. For 47 divided by 6 = 7 remainder 5, check: 7 times 6 = 42, plus 5 = 47. The original dividend matches.
Why does multiplying check a division answer?
Division and multiplication are inverse operations — one undoes the other. Division breaks a number apart; multiplication rebuilds it. If you can use multiplication to perfectly reconstruct the original dividend, the division is correct.
What is the most common mistake when checking division?
Forgetting to add the remainder when checking. If there is a remainder, only multiplying quotient times divisor gives a number smaller than the dividend. Always add the remainder back in to complete the check.
What Saxon Math chapter covers checking one-digit division?
Checking one-digit division is taught in Saxon Math Intermediate 4, Chapter 6 (Lessons 51-60), reinforcing both division accuracy and the inverse relationship between multiplication and division.