Math / Numbers & Operations

Question9. Which One Doesn't Belong? Which expression does not have a two-digit quotient? $1,955 \div 85$ $6,701 \div 36$ $1,699 \div 54$ $2,754 \div 71$

Studdy Solution

STEP 1

What is this asking? Which of these division problems gives an answer less than $10$ ? Watch out! Don't just blindly divide, think about how big the answer should be before calculating it!

STEP 2

1. Estimate the Quotients
2. Calculate the Quotients
3. Identify the Odd One Out

STEP 3

Let's estimate each quotient to get a feel for which one might be smaller than the others.
We can do this by rounding the numbers to make the division easier.

STEP 4

For $1,955 \div 85$ , we can round $1,955$ to $2,000$ and $85$ to $100$ .
So, $2,000 \div 100$ is $20$ .

STEP 5

For $6,701 \div 36$ , let's round $6,701$ to $7,000$ and $36$ to $40$ . $7,000 \div 40$ is the same as $700 \div 4$ , which is a bit more than $100$ , since $4 \cdot 100 = 400$ and $4 \cdot 200 = 800$ .

STEP 6

For $1,699 \div 54$ , round $1,699$ to $1,700$ and $54$ to $50$ . $1,700 \div 50$ is the same as $170 \div 5$ , which is more than $30$ , since $5 \cdot 30 = 150$ .

STEP 7

Lastly, for $2,754 \div 71$ , round $2,754$ to $2,800$ and $71$ to $70$ . $2,800 \div 70$ is the same as $280 \div 7$ , which is exactly $40$ !

STEP 8

Now, let's calculate the actual quotients to be sure.

STEP 9

$1,955 \div 85 = 23$

STEP 10

$6,701 \div 36 = 186 \text{ R } 5$

STEP 11

$1,699 \div 54 = 31 \text{ R } 25$

STEP 12

$2,754 \div 71 = 38 \text{ R } 56$

STEP 13

We're looking for the expression that doesn't have a two-digit quotient.
That means we're looking for a quotient that's less than $10$ .

STEP 14

Looking at our calculated quotients, we see that $1,955 \div 85 = 23$ .
Since $10 \cdot 1 = 10$ and $10 \cdot 10 = 100$ , we know that $23$ is between $10$ and $100$ , so it is a two-digit number.

STEP 15

All the other quotients ( $186$ , $31$ , and $38$ ) are also two-digit numbers.
Oops! It looks like our estimations were a bit off.
But that's okay, because we did the full calculations to be absolutely sure!

STEP 16

None of the expressions have a quotient that isn't a two-digit number.
All the quotients are greater than $10$ .
There's no "odd one out"!

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Question9. Which One Doesn't Belong? Which expression does not have a two-digit quotient? $1,955 \div 85$ $6,701 \div 36$ $1,699 \div 54$ $2,754 \div 71$

Studdy Solution

STEP 1

What is this asking? Which of these division problems gives an answer less than $10$ ? Watch out! Don't just blindly divide, think about how big the answer should be before calculating it!

STEP 2

1. Estimate the Quotients
2. Calculate the Quotients
3. Identify the Odd One Out

STEP 3

Let's estimate each quotient to get a feel for which one might be smaller than the others.
We can do this by rounding the numbers to make the division easier.

STEP 4

For $1,955 \div 85$ , we can round $1,955$ to $2,000$ and $85$ to $100$ .
So, $2,000 \div 100$ is $20$ .

STEP 5

For $6,701 \div 36$ , let's round $6,701$ to $7,000$ and $36$ to $40$ . $7,000 \div 40$ is the same as $700 \div 4$ , which is a bit more than $100$ , since $4 \cdot 100 = 400$ and $4 \cdot 200 = 800$ .

STEP 6

For $1,699 \div 54$ , round $1,699$ to $1,700$ and $54$ to $50$ . $1,700 \div 50$ is the same as $170 \div 5$ , which is more than $30$ , since $5 \cdot 30 = 150$ .

STEP 7

Lastly, for $2,754 \div 71$ , round $2,754$ to $2,800$ and $71$ to $70$ . $2,800 \div 70$ is the same as $280 \div 7$ , which is exactly $40$ !

STEP 8

Now, let's calculate the actual quotients to be sure.

STEP 9

$1,955 \div 85 = 23$

STEP 10

$6,701 \div 36 = 186 \text{ R } 5$

STEP 11

$1,699 \div 54 = 31 \text{ R } 25$

STEP 12

$2,754 \div 71 = 38 \text{ R } 56$

STEP 13

We're looking for the expression that doesn't have a two-digit quotient.
That means we're looking for a quotient that's less than $10$ .

STEP 14

Looking at our calculated quotients, we see that $1,955 \div 85 = 23$ .
Since $10 \cdot 1 = 10$ and $10 \cdot 10 = 100$ , we know that $23$ is between $10$ and $100$ , so it is a two-digit number.

STEP 15

All the other quotients ( $186$ , $31$ , and $38$ ) are also two-digit numbers.
Oops! It looks like our estimations were a bit off.
But that's okay, because we did the full calculations to be absolutely sure!

STEP 16

None of the expressions have a quotient that isn't a two-digit number.
All the quotients are greater than $10$ .
There's no "odd one out"!

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Question9. Which One Doesn't Belong? Which expression does not have a two-digit quotient? 1,955÷851,955 \div 851,955÷85 6,701÷366,701 \div 366,701÷36 1,699÷541,699 \div 541,699÷54 2,754÷712,754 \div 712,754÷71

Studdy Solution

STEP 1

What is this asking? Which of these division problems gives an answer less than 101010? Watch out! Don't just blindly divide, think about how big the answer *should* be before calculating it!

STEP 2

1. Estimate the Quotients2. Calculate the Quotients3. Identify the Odd One Out

STEP 3

Let's **estimate** each quotient to get a feel for which one might be smaller than the others.We can do this by rounding the numbers to make the division easier.

STEP 4

For 1,955÷851,955 \div 851,955÷85, we can round 1,9551,9551,955 to 2,0002,0002,000 and 858585 to 100100100.So, 2,000÷1002,000 \div 1002,000÷100 is 202020.

STEP 5

STEP 6

For 1,699÷541,699 \div 541,699÷54, round 1,6991,6991,699 to 1,7001,7001,700 and 545454 to 505050. 1,700÷501,700 \div 501,700÷50 is the same as 170÷5170 \div 5170÷5, which is more than 303030, since 5⋅30=1505 \cdot 30 = 1505⋅30=150.

STEP 7

Lastly, for 2,754÷712,754 \div 712,754÷71, round 2,7542,7542,754 to 2,8002,8002,800 and 717171 to 707070. 2,800÷702,800 \div 702,800÷70 is the same as 280÷7280 \div 7280÷7, which is **exactly** 404040!

STEP 8

Now, let's **calculate** the actual quotients to be sure.

STEP 9

1,955÷85=231,955 \div 85 = 231,955÷85=23

STEP 10

6,701÷36=186 R 56,701 \div 36 = 186 \text{ R } 56,701÷36=186 R 5

STEP 11

1,699÷54=31 R 251,699 \div 54 = 31 \text{ R } 251,699÷54=31 R 25

STEP 12

2,754÷71=38 R 562,754 \div 71 = 38 \text{ R } 562,754÷71=38 R 56

STEP 13

We're looking for the expression that *doesn't* have a two-digit quotient.That means we're looking for a quotient that's less than 101010.

STEP 14

Looking at our calculated quotients, we see that 1,955÷85=231,955 \div 85 = 231,955÷85=23.Since 10⋅1=1010 \cdot 1 = 1010⋅1=10 and 10⋅10=10010 \cdot 10 = 10010⋅10=100, we know that 232323 is between 101010 and 100100100, so it *is* a two-digit number.

STEP 15

All the other quotients (186186186, 313131, and 383838) are also two-digit numbers.Oops! It looks like our estimations were a bit off.But that's okay, because we did the full calculations to be absolutely sure!

STEP 16

None of the expressions have a quotient that isn't a two-digit number.All the quotients are greater than 101010.There's no "odd one out"!

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Start learning now

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Question9. Which One Doesn't Belong? Which expression does not have a two-digit quotient? $1,955 \div 85$ $6,701 \div 36$ $1,699 \div 54$ $2,754 \div 71$

What is this asking? Which of these division problems gives an answer less than $10$ ? Watch out! Don't just blindly divide, think about how big the answer should be before calculating it!

1. Estimate the Quotients
2. Calculate the Quotients
3. Identify the Odd One Out

Let's estimate each quotient to get a feel for which one might be smaller than the others.
We can do this by rounding the numbers to make the division easier.

For $1,955 \div 85$ , we can round $1,955$ to $2,000$ and $85$ to $100$ .
So, $2,000 \div 100$ is $20$ .

For $1,699 \div 54$ , round $1,699$ to $1,700$ and $54$ to $50$ . $1,700 \div 50$ is the same as $170 \div 5$ , which is more than $30$ , since $5 \cdot 30 = 150$ .

Lastly, for $2,754 \div 71$ , round $2,754$ to $2,800$ and $71$ to $70$ . $2,800 \div 70$ is the same as $280 \div 7$ , which is exactly $40$ !

Now, let's calculate the actual quotients to be sure.

$1,955 \div 85 = 23$

$6,701 \div 36 = 186 \text{ R } 5$

$1,699 \div 54 = 31 \text{ R } 25$

$2,754 \div 71 = 38 \text{ R } 56$

We're looking for the expression that doesn't have a two-digit quotient.
That means we're looking for a quotient that's less than $10$ .

Looking at our calculated quotients, we see that $1,955 \div 85 = 23$ .
Since $10 \cdot 1 = 10$ and $10 \cdot 10 = 100$ , we know that $23$ is between $10$ and $100$ , so it is a two-digit number.

All the other quotients ( $186$ , $31$ , and $38$ ) are also two-digit numbers.
Oops! It looks like our estimations were a bit off.
But that's okay, because we did the full calculations to be absolutely sure!

None of the expressions have a quotient that isn't a two-digit number.
All the quotients are greater than $10$ .
There's no "odd one out"!