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Worksheet: Estimating Quotients

Q1:

We want to divide 6 0 2 5 by 241 using the standard division algorithm.

What result do you expect?

  • Aaround 200
  • Baround 3
  • Caround 3 0 0 0
  • Daround 30
  • Earound 2

The diagram below shows the first stage of the division algorithm. The digit π‘Ž (between 1 and 9) represents how many 241s there are in 602 tens. What is the place value of π‘Ž in the quotient?

  • Atens
  • Bthousands
  • Cunits
  • Dhundreds
  • Eten thousands

What is the value of π‘Ž ?

  • A π‘Ž = 5
  • B π‘Ž = 1
  • C π‘Ž = 2
  • D π‘Ž = 3
  • E π‘Ž = 4

We have found that there are two 241s in 602 ( π‘Ž = 2 ) or 241 times 2 tens in 602 tens. The number 𝑏 is 2 times 241 tens. Which of the following is true?

  • A 𝑏 = 2 Γ— 2 4 1 Γ— 1 0
  • B 𝑏 = 2 Γ— 2 4 1 βˆ’ 1 0
  • C 𝑏 = 2 Γ— 2 4 1 + 1 0
  • D 𝑏 = 2 Γ— 2 4 1
  • E 𝑏 = 2 Γ— 2 4 1 Γ— 1 0 0

The number 𝑐 is the remainder of the previous division. Which of the following is true?

  • A 6 0 2 5 = 2 Γ— 2 4 1 βˆ’ 𝑐
  • B 6 0 2 5 = 2 0 0 Γ— 2 4 1 + 𝑐
  • C 6 0 2 5 = 2 Γ— 2 4 1 + 𝑐
  • D 6 0 2 5 = 2 0 Γ— 2 4 1 + 𝑐
  • E 6 0 2 5 = 2 0 Γ— 2 4 1 βˆ’ 𝑐

The diagram below shows the second stage of the division algorithm. The number 𝑑 is between 1 and 9 and represents the number of 241s in 1 2 0 5 . What are the values of 𝑑 , 𝑒 , and 𝑓 ?

  • A 𝑑 = 2 5 , 𝑒 = 1 2 0 5 , 𝑓 = 9 6 4
  • B 𝑑 = 4 , 𝑒 = 9 6 4 , 𝑓 = 0
  • C 𝑑 = 5 , 𝑒 = 0 , 𝑓 = 2 4 1
  • D 𝑑 = 5 , 𝑒 = 1 2 0 5 , 𝑓 = 0
  • E 𝑑 = 2 5 , 𝑒 = 0 , 𝑓 = 0

Q2:

Madison is saving up to buy a bike that costs $99. She gets $12 each week in pocket money. How many weeks will she have to wait until she has enough money to buy the bike?

Which calculation will help us answer this question?

  • A 9 9 βˆ’ 1 2 = 8 7
  • B 9 9 + 1 2 = 1 1 1
  • C 1 2 Γ· 9 9 = 4 3 3
  • D 9 9 Γ· 1 2 = 8 𝑅 3
  • E 9 9 Γ· 1 2 = 8

To find the number of weeks she has to wait, should we ignore the remainder or round it up?

  • Around it up
  • Bignore it

Why?

  • ADo NOT use the congruence symbol.
  • BBecause the remainder is less than $5.
  • CBecause she needs to wait another week to earn the remaining $3.
  • DBecause she does not need to wait any further weeks.
  • EBecause the remainder is less than $99.

Q3:

Mrs. Noah is arranging a field trip for her class of 32 students. She will be going herself along with three other teachers. She decides to use a company whose buses seat 15 people each. How many buses will she need to book?