Section D: Practice Problems Add and Subtract

Section Summary


In this section, we used our understanding of place value and expanded form to add and subtract large numbers using the standard algorithm.

We learned how to use the algorithm to keep track of addition of digits that results in a number greater than 9.

Whenever we have 10 in a unit, we make a new unit and record the new unit at the top of the column of numbers in the next place to the left.

When we subtract numbers it may be necessary to decompose tens, hundreds, thousands or ten-thousands before subtracting.

Finally, we learned that if the digit we are subtracting is a zero, we may need to decompose one unit of the digit in the next place to the left.

Sometimes, it is necessary to look two or more places to the left to find a unit to decompose. For example, here is one way to decompose a ten and a thousand to find .

Problem 1 (Lesson 18)

Clare took 11,243 steps on Saturday and 12,485 steps on Sunday.

  1. How many steps did Clare take altogether on Saturday and Sunday?

  2. How many more steps did Clare take on Sunday than on Saturday?

Problem 2 (Lesson 19)

  1. Find the value of the sum. Explain your calculations.


  2. Find the value of the difference. Explain your calculations.

Problem 3 (Lesson 20)

Find the value of each sum and difference using the standard algorithm.

Problem 4 (Lesson 21)

Here is how Han found

Subtract. Three hundred thousand, five hundred, twenty six, minus, four thousand, four hundred, seventy two, equals two hundred six thousand, fifty four.
  1. How can you tell by estimating that Han has made an error?

  2. What error did Han make?

  3. Find the value of .

Problem 5 (Lesson 22)

In 2018 the population of Boston is estimated as 694,583 and the population of Seattle is estimated as 744,995.

  1. Is the population difference between Boston and Seattle more or less than 100,000? Explain how you know.

  2. Is the population difference more or less than 50,000? Explain how you know.

  3. Find the difference in the populations of the two cities.

Problem 6 (Exploration)

Han says he has a method to find the value of without any carrying: “I just write 1,000,000 as .

  1. How might rewriting 1,000,000, as Han suggested, help with finding the difference of ?

  2. Try Han’s method to find .

Problem 7 (Exploration)

Use the information to determine when the airplane, telephone, printing press, and automobile were first invented.

  • The airplane was invented in 1903.

  • The printing press was invented 453 years before the most recent invention.

  • The automobile was invented 15 years before 1900.

  • It was 426 years after the invention of the printing press that the telephone was invented.

  • The automobile and telephone were invented the closest together in time with only 9 years between them.