Long Division with Multi-Digit Divisors — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To divide 480 by 12, I should first add 480 and 12 together to estimate.
Corrected: To divide 480 by 12, I should first estimate by thinking 480 divided by about 12 is around 40.
In Grade 5 long division, we estimate quotients by using compatible numbers, not by adding the dividend and divisor.
2. Fix the sentence:
In the problem 360 divided by 15, the number 15 is called the quotient.
Corrected: In the problem 360 divided by 15, the number 15 is called the divisor.
Grade 5 vocabulary: dividend (360) is divided by the divisor (15) to give the quotient (24).
3. Fix the sentence:
When I divide 720 by 24, I get a quotient of 30, so 24 times 30 should equals 720.
Corrected: When I divide 720 by 24, I get a quotient of 30, so 24 times 30 should equal 720.
After modal verbs like should, Grade 5 students use the base form equal, not equals, to keep subject-verb agreement correct.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The standard algorithm for long division follows the steps divide, multiply, subtract, bring down, and repeat.
In Grade 5, the long division algorithm cycles: divide, multiply, subtract, bring down, repeat until no digits remain.
2. When you divide 480 by 12 using the standard algorithm, the quotient is 40.
Because 12 multiplied by 40 equals 480, the Grade 5 quotient of 480 divided by 12 is exactly 40 with no remainder.
3. In the division problem 936 divided by 13, the dividend is 936.
Grade 5 vocabulary: the dividend is the total amount being split, the divisor is what we divide by, and the quotient is the result.
4. To estimate 612 divided by 18, I round 18 to 20 and 612 to 600, giving an estimate of 30.
Grade 5 estimation uses compatible numbers: 600 divided by 20 equals 30, a strong starting estimate before applying the standard algorithm.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain the steps of the long division standard algorithm using the example 525 divided by 15.
Sample answer: First I estimate: 525 divided by 15 is about 500 divided by 15, near 33. Then I divide 52 by 15, which is 3, write 3 above the 2. Multiply 3 times 15 equals 45, subtract from 52 to get 7. Bring down the 5 to make 75. Divide 75 by 15, which equals 5, write 5 in the quotient. Multiply 5 times 15 equals 75, subtract to get 0. The Grade 5 quotient is 35 with no remainder.
Grade 5 students master long division by following the standard algorithm steps in order until all digits are processed.
2. Why is estimating the quotient an important first step in long division?
Sample answer: Estimating the quotient gives me a benchmark answer before I start. If my final answer is far from the estimate, I know I made a mistake. For 480 divided by 12, I estimate 480 divided by 12 is about 40, since 12 times 40 equals 480. This Grade 5 strategy uses compatible numbers and helps me check whether my long division work is reasonable.
Grade 5 standard 5.NBT.6 emphasizes estimation as a tool to check the reasonableness of computed quotients.