Finding Compatible Pairs for 100

What number goes with 37 to make 100?

Think about what the ones digit needs: $7 + ? = 10$, so we need $3$ in the ones place = Ones digit is 3

Think about what the tens digit needs: $3 + ? = 9$ (we carry 1 from the ones), so we need $6$ in the tens place = Tens digit is 6

Combine the digits: $37 + 63 = 100$ = The compatible number is 63

Answer: $37 + 63 = 100$, so 63 is compatible with 37

Using Compatible Numbers for Estimation

Estimate $52 \times 8$ using compatible numbers.

Find a compatible number close to 52: $52 \approx 50$ (50 is easy to multiply) = Use 50

Multiply using the compatible number: $50 \times 8 = 400$ = 400

Check if the estimate is reasonable: Since $52 > 50$, the actual answer is slightly more than 400 = Estimate: about 400

Answer: $52 \times 8 \approx 400$ (actual answer: 416)

Compatible Numbers for Division

Estimate $243 \div 6$ using compatible numbers.

Find a compatible number close to 243 that divides evenly by 6: $240$ is close to $243$ and divisible by $6$ = Use 240

Divide using the compatible number: $240 \div 6 = 40$ = 40

Verify the estimate makes sense: $6 \times 40 = 240$, which is close to $243$ = Estimate: about 40

Answer: $243 \div 6 \approx 40$ (actual answer: 40.5)

Mistake: Forgetting to account for the carry when finding complements to 100

Why: Students often think $37 + 73 = 100$, forgetting that $7 + 3 = 10$ creates a carry.

Correct: For 37: ones need $7 + 3 = 10$ (carry 1), tens need $3 + 6 = 9$ (plus carry = 10). Answer: $37 + 63 = 100$

Mistake: Choosing compatible numbers that are too far from the original

Why: Using $50$ to estimate $38 \times 4$ gives a rough estimate, but the error might be too large.

Correct: Choose $40$ instead of $50$ when estimating $38 \times 4$. Closer compatible numbers give better estimates.

Mistake: Thinking compatible numbers only work for addition

Why: Compatible numbers are useful for all operations, not just addition.

Correct: Use compatible numbers for estimation in multiplication ($48 \times 5 \approx 50 \times 5$) and division ($243 \div 6 \approx 240 \div 6$) too.

Shopping and Budgeting

Shoppers use compatible numbers to quickly add prices and stay within budget.

Items cost 23 dollars, 47 dollars, and 30 dollars. Think: $23 + 47 = 70$, then $70 + 30 = 100$ dollars total.

Cooking and Recipes

Cooks use compatible numbers when scaling recipes or measuring ingredients.

A recipe needs 375 grams of flour. You have 625 grams. Together that's 1000 grams (1 kg).

Sports Statistics

Sports fans use compatible numbers to quickly calculate scores, averages, and records.

A team scored 67 points in the first half. They need 33 more to reach 100 points.

Q: What makes numbers 'compatible'?

A: Numbers are compatible when they're easy to compute mentally. Usually this means they create round numbers (like 10, 100, or 1000) or are easy to multiply/divide (like 25, 50, or 100).

Q: How do I find the compatible number for any number up to 100?

A: To find what number adds to yours to make 100: First, find what adds to the ones digit to make 10. Then find what adds to the tens digit to make 9 (because you'll carry 1). Example: For 46, ones need 4 (6+4=10), tens need 5 (4+5+1=10). Answer: 54.

Q: When should I use compatible numbers instead of exact calculations?

A: Use compatible numbers when you need a quick estimate, want to check if an answer is reasonable, or are doing mental math. Use exact calculations when precision matters (like balancing a checkbook).