Solving Problems Involving Missing Numbers in Addition and Subtraction
Primary 4 · Mathematics
Solving Problems Involving Missing Numbers in Addition and Subtraction
Lesson 3 of 4
20 min
Let's begin
Byiringiro's class had 40 exercise books in the cupboard. The teacher gave out some books. Then a parent brought 15 new books. Now there are 30 books.
How many books did the teacher give out? 40 − □ + 15 = 30. Two signs and one box!
Today you will solve number sentences that use both + and −.
A number sentence is like a journey. To find where it started, walk back from the end and undo each step. Adding is undone by subtracting. Subtracting is undone by adding.
Worked example 1
□ − 125 + 300 = 800
Step 1 The last step was + 300. Undo it: 800 − 300 = 500.
Step 2 The step before was − 125. Undo it: 500 + 125 = 625.
Step 3 Check: 625 − 125 + 300 = 500 + 300 = 800. So □ = 625.
Worked example 2
250 + □ − 100 = 600
Step 1 Undo the − 100: 600 + 100 = 700. So 250 + □ = 700.
Step 2 □ = 700 − 250 = 450. Check: 250 + 450 − 100 = 600.
Worked example 3
Byiringiro's books: 40 − □ + 15 = 30
Step 1 Undo the + 15: 30 − 15 = 15. So 40 − □ = 15.
Step 2 □ = 40 − 15 = 25. The teacher gave out 25 books. Check: 40 − 25 + 15 = 30.
Worked example 4
350 + □ = 500 + 150. Work out the right side first: 650. Then □ = 650 − 350 = 300.
Worked example 5
900 − □ = 400 + 200. The right side is 600. Then □ = 900 − 600 = 300.
Careful! When you walk backwards, every sign turns around: + becomes − and − becomes +. And undo the last step first.
Tip
Walk back and turn every sign around. Start from the answer. Undo the last step first, then the one before. + becomes −, and − becomes +.
Work each one in your exercise book first. Then tap Show answer to check.
120 + □ − 50 = 200
Answer: 130. Undo − 50: 200 + 50 = 250. Then 250 − 120 = 130. Check: 120 + 130 − 50 = 200.
□ − 60 + 25 = 90
Answer: 125. Undo + 25: 90 − 25 = 65. Undo − 60: 65 + 60 = 125.
75 − □ + 40 = 100
Answer: 15. Undo + 40: 100 − 40 = 60. Then 75 − □ = 60, so □ = 15.
480 + □ = 300 + 400
Answer: 220. The right side is 700, and 700 − 480 = 220.
1 000 − □ = 250 + 350
Answer: 400. The right side is 600, and 1 000 − 600 = 400.
What you learned today
Sources and credits
The work-backwards method, the stories, drawings and practice questions were written by Ganzaa.
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