Mental Strategies for Multi-Digit Division
Partial Quotients and Multi-Digit Division
Partial Quotients and Multi-Digit Decimal Division
Word problems
100
32÷8=
4
100
Divide, and then check your work using multiplication. This problem is allowed to have a remainder.
41÷30=
1 R11
30 X 1=30
30+11=41
100
Divide and show your work.
1.2÷ 6=
1.2÷ 60=
0.2
0.02
100
Ms. Arnold had 12 oranges to distribute evenly to 3 of her friends. How many oranges did each friend get?
Each friend got 4 oranges.
200
12,000÷400=
30
200
Divide.Then check with multiplication.
65÷17=
3 R14
17 X 3 =51
51+14=65
200
Estimate the quotients. Remember to put back the decimal.
3.24÷ 82
___________÷___________
=____________
=320 ÷ 80=4
=3.20 ÷ 80=0.04
Answer is 0.04
200
Wilson has 5.6 kilograms of takis to deliver equally to 16 stores. How many kilograms of takis will be delivered to each store? Show your work; no remainder.
Wilson will deliver 0.35 kilograms of takis to each store.
300
Estimate the quotients for the following problems. Round the divisor first and then the dividend (whole number).
141÷73=
______________÷____________
=_________________
____140__________÷ ____70
=__2___
300
Divide. Enter your answers in the boxes. Enter only numbers in the box.You are allowed to have a remainder for this problem.
337 ÷ 70=
The quotient is 5 with a remainder of 7.
300
Estimate the quotients.
7.15÷ 31=
6÷30=
6 ÷3=2
6÷30= 0.2
300
A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did each pair of socks cost?
Each pair of socks cost $6.75.
400
Which equation can be represented by the model shown? Show your work on a place value chart.
2,735 ÷ 10 = 27.35
2,735 ÷ 100 = 27.35
2,735 x 10 - 27.35
2,735 x 100 = 27.35
2,735 ÷ 100 = 27.35
400
Julio and Norah each estimate the quotient of 4,583 ÷ 52 . Julio estimates that the quotient is about 900. Norah estimates that the quotient is about 80 . Whose estimate is more reasonable? Julio or Norah?
Explain your answer with words using 1-2 sentences.
Norah's estimate is more reasonable because if I think about how many times 52 can fit into 4, 583, first I look at the two numbers of 4,583 and see that 52 can't fit into 45, then I look at 458 and estimate how many times 52 or 50, since I rounded down can fit into 458 or 400, which is 8 times. So I estimated that it would fit into 4,583 around 80 times.
400
Estimate the quotient.
27.97÷ 28=
27÷ 30
27÷ 3=9
27÷ 30=0.9
400
Mr. H buys crates to store 1,034 soccer balls. Each crate can hold 22 soccer balls. How many crates does Mr. H need to store all of the soccer balls?
Mr. H needs 47 crates.
500
2. Which equation can be represented by the model shown? Show your work on the place value chart.
5,200 ÷ 10 = 520
5,200 ÷ 100 = 520
5,200 x 10 = 520
5,200 x 100 = 520
5,200 ÷ 10 = 520
500
Divide. Show your work. Enter your answer in the box.
19.81
500
Use place value reasoning and the first quotient to compute the second quotient. Explain how you placed the decimal point in your answer with words. 1-2 sentences.
56.8 ÷ 40 = 1.42
56.8 ÷ 4 = _____________
a.0.142
b.142.0
c.1,420
d.14.2
d. 14.2.
Example: I knew where to place the decimal because in my first answer, the equation was 56.8 ÷ 40= 1.42. In the second equation it was
56.8 ÷ 4, which means the place value of 1.42 moved one number to the left making it 14.2.
I thought about it like taking away the zero and moving my answer to the left one time.
500
Angie sells 17 bracelets at a fair. She makes a total of $106.25 . Each bracelet is sold for the same price. What is the price of each bracelet?
The bracelets cost $6.25 each.