Checking division with a remainder
Checking Division with a Remainder in Grade 4 Saxon Math Intermediate 4 teaches students to verify long division answers using the formula (Quotient x Divisor) + Remainder = Dividend. For example, to check 89 ÷ 7 = 12 R5, compute (12 x 7) + 5 = 84 + 5 = 89 — matching the original dividend confirms the answer. Students also learn where to place the first digit of a quotient based on place value: in 585 ÷ 5, the 5 is in the hundreds place and divides evenly by 5, so the first quotient digit goes above the hundreds column. Students practice writing a zero in the quotient when a brought-down digit is smaller than the divisor.
Key Concepts
Property: To check a division answer that has a remainder, we multiply the quotient (without the remainder) by the divisor and then add the remainder. The result should be the original number you started with, also known as the dividend. This confirms your calculation is correct. For example: (quotient $\times$ divisor) + remainder = dividend.
To check $137 \div 5 = 27 \text{ R } 2$, we calculate $(27 \times 5) + 2 = 135 + 2 = 137$. It matches! To check $240 \div 7 = 34 \text{ R } 2$, we calculate $(34 \times 7) + 2 = 238 + 2 = 240$. It matches! To check $95 \div 4 = 23 \text{ R } 3$, we calculate $(23 \times 4) + 3 = 92 + 3 = 95$. It matches!
How do you know you got it right? It's like reverse engineering your math! Multiply your main answer (the quotient) by the number you divided by (the divisor), then add the little leftover part (the remainder). If you get back to the number you started with, you've nailed it! It is the ultimate proof of your division skills.
Common Questions
How do you check a division answer with a remainder?
Use the formula (Quotient x Divisor) + Remainder = Dividend. Multiply the quotient by the divisor, then add the remainder. The result should match the original dividend.
How do you verify 89 ÷ 7 = 12 R5?
Compute (12 x 7) + 5 = 84 + 5 = 89. Since 89 matches the dividend, the answer is correct.
When do you write a zero in the middle of a quotient?
When you bring down a digit and the resulting number is still smaller than the divisor, you cannot make any groups, so you write 0 in the quotient and bring down the next digit.
Where do you place the first digit of the quotient?
Check whether the divisor goes into the first digit of the dividend. If yes, the first quotient digit goes above that column. If not, use the first two digits and place the first quotient digit above the second column.
What is the most common mistake when checking division?
Forgetting to add the remainder. After multiplying quotient by divisor, you must add the remainder before comparing to the dividend.