Choose numbers with a particular sum, difference, product, or quotient

Key notes :

➕ Sum (Addition)

  • Sum means the total you get when you add numbers.
  • To choose numbers with a particular sum, find two numbers that add up to the target.
  • Example: If the sum must be 20, you can choose 12 and 8.
  • 🔢 Check: 12 + 8 = 20 ✔️

➖ Difference (Subtraction)

Difference is the answer when one number is taken away from another.

To choose numbers with a given difference, think:

  • Bigger number – smaller number = difference

Example: If the difference must be 7, you can choose 15 and 8.

🔢 Check: 15 − 8 = 7 ✔️

✖️ Product (Multiplication)

Product means the result of multiplying two numbers.

To choose numbers with a particular product, find two factors that multiply to the target.

Example: If the product must be 24, you can choose:

  • 6 × 4
  • 8 × 3

🔢 Check: 6 × 4 = 24 ✔️

➗ Quotient (Division)

Quotient is the answer you get when one number is divided by another.

To choose numbers with a particular quotient, think:

  • Dividend ÷ Divisor = Quotient

Example: If the quotient must be 5, you can choose 20 ÷ 4.

🔢 Check: 20 ÷ 4 = 5 ✔️

🎯 Use Backward Thinking

Start from the required total (sum/difference/product/quotient).

Think:

  • Which two numbers can make this result?

Try different combinations if needed.

🧠 Estimate Before Choosing

  • Use simple mental math to guess which numbers will work.
  • Helps avoid wrong combinations quickly.

🔍 Check Your Answer Always

  • After choosing numbers, add, subtract, multiply or divide to confirm.
  • If the answer doesn’t match the requirement, choose new numbers.

🎨 Quick Examples

  • Target sum = 30 → 12 + 18 ✔️
  • Target difference = 9 → 20 − 11 ✔️
  • Target product = 36 → 9 × 4 ✔️
  • Target quotient = 3 → 15 ÷ 5 ✔️

Learn with an example

👉 Choose two numbers from the box to complete the division number sentence.
3,4,24,95


___÷____ = 6

  • Look for numbers in the box that have 6 as a factor.
  • 24 has 6 as a factor. What number can you divide 24 by to get 6?
  • 24 ÷ 4 = 6
  • 4 is in the box.
  • The division number sentence is 24 ÷ 4 = 6.

👉 Choose two numbers from the box to complete the addition number sentence.
1,5,7,8


____+____= 9

  • Try 1. What number can you add to 1 to get 9?
  • 1 + 8 = 9
  • 8 is in the box.
  • The addition number sentence is 1 + 8 = 9.

👉 Choose two numbers from the box to complete the sentence.
3,5,9,10


​____and ____​ have a product of 45.

  • Look for numbers in the box that are factors of 45.
  • 3 is a factor of 45. What number can you multiply by 3 to get 45?
  • 3 × 15 = 45
  • 15 is not in the box.
  • 5 is a factor of 45. What number can you multiply by 5 to get 45?
  • 5 × 9 = 45
  • 9 is in the box.
  • The numbers 5 and 9 have a product of 45.

Let’s practice!🖊️