Mathematics
Grade 11
15 min
Add three or more numbers with four or more digits - word problems
Add three or more numbers with four or more digits - word problems
What you'll learn
- Solve word problems that involve adding three or more numbers with four or more digits, showing your work clearly with addition strategies.
- Explain the steps you took to solve an addition word problem with three or more numbers, using math words like 'addend', 'sum', and 'regrouping'.
- Identify the important information in a word problem needed to add three or more numbers with four or more digits.
- Apply different addition strategies, such as using base-ten blocks (drawing), or column addition, to solve addition word problems with four-digit numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate a multi-step word problem into an expression involving the sum of three or more complex numbers.
Accurately add the real and imaginary components of complex numbers, where each component is a number with four or more digits.
Calculate the total impedance of a series AC circuit by summing the complex impedances of its components.
Determine the resultant vector by summing multiple vectors represented as complex numbers.
Interpret the real and imaginary parts of a final complex number sum in the context of a given real-world scenario.
Verify the solution to a complex number addition problem by checking the sums of the real and imaginary parts independently.
How do engineers calculate the total electrical effect of multiple large industrial machines...
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Key Concepts & Vocabulary
TermDefinitionExample
Complex NumberA number of the form z = a + bi, where 'a' is the real part, 'b' is the imaginary part, and 'i' is the imaginary unit (i² = -1).The complex number z = 4500 + 2150i has a real part of 4500 and an imaginary part of 2150.
Real Part (Re(z))The component of a complex number that does not have 'i' as a coefficient. It is represented on the horizontal axis of the complex plane.For z = 8910 - 3456i, the real part is Re(z) = 8910.
Imaginary Part (Im(z))The real number coefficient of the imaginary unit 'i'. It is represented on the vertical axis of the complex plane.For z = 8910 - 3456i, the imaginary part is Im(z) = -3456.
Complex Plane (Argand Diagram)A two-dimensional coordinate plane where the horizontal axis...
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Core Formulas
Addition of Complex Numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
To add two complex numbers, add the real parts together and add the imaginary parts together separately. The structure of the complex number is maintained.
Summation of Multiple Complex Numbers
\sum_{k=1}^{n} (a_k + b_k i) = (\sum_{k=1}^{n} a_k) + (\sum_{k=1}^{n} b_k)i
To add three or more complex numbers, sum all the real parts to get the final real part, and sum all the imaginary parts to get the final imaginary part.
4 more steps in this tutorial
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Challenging
A drone's final position is given by the vector sum D_final = 8250 + 3150i. This was the result of four displacements. Three of the displacements were d₁ = 2100 + 1500i, d₂ = 4500 - 1200i, and d₄ = 1250 + 850i. What was the third displacement, d₃?
A.400 + 2000i
B.400 + 2000i
C.16100 + 4300i
D.-400 - 2000i
Challenging
Three impedances in a circuit are Z₁ = 2500 + 4000j, Z₂ = 3500 + 1500j, and Z₃ = k - 2500j, where k is a real number. For what value of k will the total impedance have an imaginary part of exactly 5000j?
A.k can be any real number.
B.k = 5000
C.k = 3000
D.k = -2000
Challenging
A student adds three impedances Z₁=2000+3000j, Z₂=4000+5000j, and Z₃=1000+2000j. They report a total of Z_total = 11000 + 8000j. They made the common pitfall error of adding the real part of one number to the imaginary part of another. Which specific error leads to their result?
A.They calculated (2000+4000+1000) + (3000+5000+2000)j, but swapped the final totals.
B.They calculated (2000+5000+1000) + (3000+4000+2000)j.
C.They calculated (2000+3000) + (4000+5000) + (1000+2000)j.
D.They added Z₁'s real part to Z₂'s imaginary part, and Z₂'s real part to Z₃'s imaginary part.
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Frequently asked questions
What grade level is "Add three or more numbers with four or more digits - word problems"?
Add three or more numbers with four or more digits - word problems is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Add three or more numbers with four or more digits - word problems?
You'll be able to: Solve word problems that involve adding three or more numbers with four or more digits, showing your work clearly with addition strategies; Explain the steps you took to solve an addition word problem with three or more numbers….
Is "Add three or more numbers with four or more digits - word problems" free to practice?
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How many practice questions are included with Add three or more numbers with four or more digits - word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.