ESTIMATING QUOTIENTS

When we a divide a number by another number, the result what we get is called quotient. 

For example, 

If $250 is divided equally to four people, then the share of each person is $50. This $50 is called quotient.

Because, when we divide 250 by 50, we get the result 4. 

We can estimate quotient using the formula given below. 

In case, we use long division to divide a number by another a number, we can estimate quotient using the formula given below. 

Practice Problems

Problem 1 :

Estimate quotient when 200 is divided by 50. 

Solution : 

So, the estimation of quotient when 200 divided by 50 is 4.

Problem 2 :

Estimate quotient when 78 is divided by 13. 

Solution : 

78 ÷ 13  =  78/13  =  6 

Because 13 goes into 78 by 6 times. 

So, the estimation of quotient when 78 divided by 13 is 6.

Problem 3 :

A local zoo had a total of 98,464 visitors last year. The zoo was open every day except three holidays. On average, how many visitors did the zoo have each day ?

Solution : 

Total number of days in an ordinary year  =  365. 

The zoo was open every day except three holidays.

So, total number of days that zoo opened  =  362

Total number of visitors in the year  =  98646

Therefore, number of visitors visited the zoo each day is nothing but the quotient when we divide 98464 by 362. 

Let us use long division to estimate the quotient when we divide 98464 by 362.

Step 1 : 

362 is greater than 9 and 98, so divide 984 by 362. Place the first digit in the quotient in the hundreds place. Multiply 2 by 362 and place the product under 984. Subtract.

Step 2 : 

Bring down the tens digit. Divide 2,606 by 362. Multiply 7 by 362 and place the product under 2,606. Subtract.

Step 3 : 

Bring down the ones digit. Divide the ones.

When we divide 98464 by 362, we get the quotient 272. 

So, the average number of visitors per day last year was 272.

Problem 4 :

Marco paid $39 for 8 tubes of oil paint. About how much did each tube cost ?

Solution : 

Cost of each tube is nothing but the quotient when we divide 39 by 8. 

Let us use long division to estimate the quotient when we divide 39 by 8.

Since 39 is not evenly divisible by 8, place a decimal point in the quotient. Add zeros to the right of the decimal point as needed.

Round to the nearest hundredth to find the dollar amount.

Therefore, the cost of each tube is about $4.88.

Problem 5 :

A school track is 9.76 meters wide. It is divided into 8 lanes of equal width. How wide is each lane ?

Solution : 

The width of each lane is nothing but the quotient when we divide 9.76 by 8. 

Let us use long division to estimate the quotient when we divide 9.76 by 8.

When we use the digit which comes after the decimal point, place a decimal point in the quotient directly above the decimal point in the dividend.

Therefore, each lane is 1.22 meters wide.

Problem 6 :

Aerobics classes cost $153.86 for 14 sessions. What is the fee for one session ?

Solution : 

The fee for one session is nothing but the quotient when we divide 153.86 by 14. 

Let us use long division to estimate the quotient when we divide 153.86 by 14.

When we use the digit which comes after the decimal point, place a decimal point in the quotient directly above the decimal point in the dividend.

Therefore, the fee for one aerobics class is $10.99.

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