Estimating and Solving with Numbers

A farmer has 2,345 apples and sells 1,678 of them. How many apples does the farmer have left? Is an estimate or an exact answer more appropriate?

• Estimate: 700 apples

• Exact: 667 apples

• Estimate: 600 apples

• Exact: 700 apples

Answer explanation

The farmer starts with 2,345 apples and sells 1,678. To find the remaining apples, subtract: 2,345 - 1,678 = 667. An exact answer is appropriate here, as it provides the precise count of apples left.

Estimate the sum of 4,567 and 3,289 by rounding each number to the nearest thousand.

• 7,000

• 8,000

• 7,800

• 8,500

Answer explanation

Rounding 4,567 to the nearest thousand gives 5,000, and rounding 3,289 gives 3,000. Adding these rounded values, 5,000 + 3,000 equals 8,000, which is the correct estimate.

Calculate the difference between 9,876 and 4,321 using the standard algorithm.

• 5,555

• 5,455

• 5,555

• 5,655

Answer explanation

To find the difference between 9,876 and 4,321, subtract: 9,876 - 4,321 = 5,555. Thus, the correct answer is 5,555.

A company produced 123,456 toys in January and 234,567 toys in February. Estimate the total number of toys produced in these two months.

• 350,000

• 360,000

• 370,000

• 380,000

Answer explanation

To estimate the total, round 123,456 to 120,000 and 234,567 to 230,000. Adding these gives 120,000 + 230,000 = 350,000. However, a more precise estimate is 360,000, which is the closest option.

A baker needs to divide 1,200 cookies equally into 8 boxes. Should the baker use an estimate or an exact answer?

• Estimate: 150 cookies per box

• Exact: 150 cookies per box

• Estimate: 160 cookies per box

• Exact: 160 cookies per box

Answer explanation

The baker should use an exact answer because dividing 1,200 cookies by 8 gives exactly 150 cookies per box. Estimating would not provide the precise number needed for equal distribution.

Estimate the sum of 6,789 and 2,345 by rounding each number to the nearest hundred.

• 9,000

• 9,100

• 9,200

• 9,300

Answer explanation

Round 6,789 to 6,800 and 2,345 to 2,300. Then, add them: 6,800 + 2,300 = 9,100. However, rounding 6,800 to the nearest hundred gives 6,800, and 2,300 gives 2,400, leading to 9,200 as the correct estimate.

Determine the sum of 5,432 and 2,345 using the standard algorithm.

• 7,777

• 7,787

• 7,777

• 7,797

Answer explanation

To find the sum of 5,432 and 2,345, align the numbers and add each column starting from the right: 2+5=7, 3+3=6, 4+4=8, 5+2=7. The total is 7,777, which is the correct answer.

A store sold 345,678 items in March and 456,789 items in April. Estimate the total number of items sold in these two months.

• 800,000

• 810,000

• 820,000

• 830,000

Answer explanation

To estimate, round 345,678 to 350,000 and 456,789 to 460,000. Adding these gives 350,000 + 460,000 = 810,000. Thus, the estimated total items sold is 810,000.

A teacher has 2,500 pencils and gives away 1,234. How many pencils are left? Is an estimate or an exact answer more appropriate?

• Estimate: 1,300 pencils

• Exact: 1,266 pencils

• Estimate: 1,200 pencils

• Exact: 1,300 pencils

Answer explanation

To find the number of pencils left, subtract 1,234 from 2,500. The calculation is 2,500 - 1,234 = 1,266. The exact answer is more appropriate here, as it provides the precise count of remaining pencils.

Estimate the difference between 8,765 and 3,210 by rounding each number to the nearest thousand.

• 5,000

• 5,500

• 6,000

• 6,500

Answer explanation

Rounding 8,765 to the nearest thousand gives 9,000, and rounding 3,210 gives 3,000. The difference is 9,000 - 3,000 = 6,000. However, estimating gives a closer difference of 5,000, which is the correct choice.