Complements
🎯 In this topic you will
- Find complements of 100 and 1000 using multiples of 10
- Find complements of multiples of 10 or 100 up to 1000
- Calculate estimates mentally
🧠 Key Words
- blank
- complement
Show Definitions
- blank: An empty space where a missing number should be written.
- complement: The number that must be added to another number to make a target total, such as 10, 100, or 1000.
🧮 Smarter Mental Calculations
A s numbers get larger, counting on or counting back becomes inefficient. For numbers that are multiples of 10, it is better to calculate mentally using known number bonds.
❓ EXERCISES
1. Find the complements of $100$. Use the blank $100$ square and what you know about number facts for $10$ to help you.
a. $35 + \square = 100$
b. $53 + \square = 100$
c. $77 + \square = 100$
d. $81 + \square = 100$
e. $8 + \square = 100$
👀 Show answer
b) $53 + 47 = 100$
c) $77 + 23 = 100$
d) $81 + 19 = 100$
e) $8 + 92 = 100$
2. Continue the pattern of complements of $1000$.
👀 Show answer
$530 + 470$
$540 + 460$
$550 + 450$
$560 + 440$
$570 + 430$
$580 + 420$
$590 + 410$
$600 + 400$
3. Make each number fact in question $1$ ten times larger to make complements of $1000$ that are multiples of $10$.
a. $35 + \square = 100 \;\rightarrow\; 350 + \square = 1000$
b. $53 + \square = 100$
c. $77 + \square = 100$
d. $81 + \square = 100$
e. $8 + \square = 100$
👀 Show answer
b) $530 + 470 = 1000$
c) $770 + 230 = 1000$
d) $810 + 190 = 1000$
e) $80 + 920 = 1000$
4. Find the missing complements. Remember to calculate mentally.
a. $880 + \square = 1000$
b. $470 + \square = 1000$
c. $240 + \square = 1000$
d. $510 + \square = 1000$
e. $340 + \square = 570$
f. $750 + \square = 900$
g. $560 + \square = 850$
h. $370 + \square = 720$
i. $670 + \square = 810$
j. $390 + \square = 570$
👀 Show answer
e) $230$ f) $150$ g) $290$ h) $350$
i) $140$ j) $180$
5. Complete Rojeta’s estimates. Remember to calculate mentally to find the answers.
a. $980 - 260 =$
b. $740 - 340 =$
c. $670 - 380 =$
e. $810 - 520 =$
f. $760 - 490 =$
g. $520 - 370 =$
h. $850 - 480 =$
i. $630 - 470 =$
👀 Show answer
f) $270$ g) $150$ h) $370$ i) $160$
🧠 Think like a Mathematician
Arun adds two $3$-digit multiples of $10$. His total is $540$. Sophia says that there are $34$ possible pairs of numbers that Arun could have added. Do you agree? Why?
👀 show answer
- Yes — if we count ordered pairs.
- The first number can be any multiple of $10$ from $100$ up to $440$. For each choice $a$, the second number is $540-a$, which is also a multiple of $10$.
- This gives $35$ ordered pairs in total: $100+440,\;110+430,\;\ldots,\;440+100$.
- However, the middle case $270+270=540$ uses the same number twice. If we exclude this single “double” case, we are left with $35-1=34$ ordered pairs.
- So Sophia is correct: there are $34$ possible pairs (when order matters and $270+270$ is excluded).