Worksheet: Estimating Quotients with Decimals

In this worksheet, we will practice estimating the division of up to four-digit numbers by three-digit numbers by rounding or using compatible numbers.

Q1:

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 โˆ’ 1 2 = 8 7
  • B 9 9 + 1 2 = 1 1 1
  • C 1 2 รท 9 9 = 4 3 3
  • D 9 9 รท 1 2 = 8 ๐‘… 3
  • E 9 9 รท 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 she needs to wait another week to earn the remaining $3.
  • CBecause the remainder is less than $99.
  • DBecause she does not need to wait any further weeks.
  • EBecause the remainder is less than $5.

Q2:

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

What result do you expect?

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

The diagram below shows the first stage of the division algorithm. The digit ๐‘Ž (between 1 and 9) represents how many 241s there are in 602 tens. What is the place value of ๐‘Ž in the quotient?

  • Ahundreds
  • Bunits
  • Ctens
  • Dten thousands
  • Ethousands

What is the value of ๐‘Ž ?

  • A ๐‘Ž = 2
  • B ๐‘Ž = 1
  • C ๐‘Ž = 3
  • D ๐‘Ž = 5
  • E ๐‘Ž = 4

We have found that there are two 241s in 602 ( ๐‘Ž = 2 ) or 241 times 2 tens in 602 tens. The number ๐‘ is 2 times 241 tens. Which of the following is true?

  • A ๐‘ = 2 ร— 2 4 1
  • B ๐‘ = 2 ร— 2 4 1 ร— 1 0 0
  • C ๐‘ = 2 ร— 2 4 1 ร— 1 0
  • D ๐‘ = 2 ร— 2 4 1 + 1 0
  • E ๐‘ = 2 ร— 2 4 1 โˆ’ 1 0

The number ๐‘ is the remainder of the previous division. Which of the following is true?

  • A 6 0 2 5 = 2 0 ร— 2 4 1 โˆ’ ๐‘
  • B 6 0 2 5 = 2 ร— 2 4 1 + ๐‘
  • C 6 0 2 5 = 2 ร— 2 4 1 โˆ’ ๐‘
  • D 6 0 2 5 = 2 0 ร— 2 4 1 + ๐‘
  • E 6 0 2 5 = 2 0 0 ร— 2 4 1 + ๐‘

The diagram below shows the second stage of the division algorithm. The number ๐‘‘ is between 1 and 9 and represents the number of 241s in 1 2 0 5 . What are the values of ๐‘‘ , ๐‘’ , and ๐‘“ ?

  • A ๐‘‘ = 5 , ๐‘’ = 1 2 0 5 , ๐‘“ = 0
  • B ๐‘‘ = 5 , ๐‘’ = 0 , ๐‘“ = 2 4 1
  • C ๐‘‘ = 2 5 , ๐‘’ = 1 2 0 5 , ๐‘“ = 9 6 4
  • D ๐‘‘ = 4 , ๐‘’ = 9 6 4 , ๐‘“ = 0
  • E ๐‘‘ = 2 5 , ๐‘’ = 0 , ๐‘“ = 0

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?

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