Checking Division with Multiplication
Checking division with multiplication uses the inverse relationship between the two operations to verify a quotient in Grade 6 math (Saxon Math, Course 1). The check formula: (quotient × divisor) + remainder = dividend. For example, 47 ÷ 5 = 9 remainder 2: check → 9 × 5 + 2 = 45 + 2 = 47 ✓. When there is no remainder, simply multiply quotient by divisor: 48 ÷ 6 = 8, check → 8 × 6 = 48 ✓. This verification step catches both computational errors and incorrect placement of the decimal point in long division. Building the habit of checking with multiplication is a powerful self-correction tool in arithmetic.
Key Concepts
Property To check a division problem, you multiply the quotient by the divisor and then add the remainder. The result should equal the dividend. $$ (\text{quotient} \times \text{divisor}) + \text{remainder} = \text{dividend} $$.
Examples To check if $245 \div 5 = 49$, multiply the quotient and divisor: $49 \times 5 = 245$. It matches!
To check if $368 \div 7 = 52$ R $4$, calculate $(52 \times 7) + 4$. This gives $364 + 4 = 368$, which is correct.
Common Questions
How do you check a division answer using multiplication?
Multiply quotient × divisor, then add any remainder. The result should equal the dividend.
Check: 63 ÷ 7 = 9
9 × 7 = 63. No remainder. 63 = 63. ✓
Check: 47 ÷ 5 = 9 remainder 2
(9 × 5) + 2 = 45 + 2 = 47. ✓
What formula summarizes checking division?
(quotient × divisor) + remainder = dividend.
Why is checking division with multiplication useful?
Division errors are common. Multiplication is the inverse operation and provides an independent verification. If the check fails, you know to recompute.