Unknown Factors

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Answer Key & Explanations

Unknown Factors · Grade 3 · Worksheet 1

1. 8 × ? = 56 Answer: 7 Solution: We are solving: 8 × ? = 56 Let the unknown number be x. 8 × x = 56 To find x, we need to undo the multiplication by 8.
   Full step-by-step solution

   We are solving: 8 × ? = 56 Step 1: Let the unknown number be x. So the equation is: 8 × x = 56 Step 2: To find x, we need to undo the multiplication by 8. We do this by dividing both sides of the equation by 8. (8 × x) ÷ 8 = 56 ÷ 8 Step 3: On the left side, 8 ÷ 8 = 1, so we have: 1 × x = 56 ÷ 8 Step 4: Calculate 56 ÷ 8: 56 ÷ 8 = 7 Step 5: So x = 7 Step 6: Check: 8 × 7 = 56, which matches the original equation. Therefore, the correct answer is 7.

2. 8 × ? = 72 Answer: 9 Solution: The equation is 8 × ? = 72 To find the missing number, divide 72 by 8 72 ÷ 8 = 9 Check: 8 × 9 = 72 The answer is 9.
   Full step-by-step solution

   Step 1: The equation is 8 × ? = 72 Step 2: To find the missing number, divide 72 by 8 Step 3: 72 ÷ 8 = 9 Step 4: Check: 8 × 9 = 72 The answer is 9.

3. Liam is organizing his baseball card collection into 8 equal piles. He has 72 baseball cards in total. How many cards should be in each pile? Answer: 9 Solution: Liam has 72 baseball cards total. He wants to split them into 8 equal piles. To find how many cards are in each pile, divide the total number of cards by the number of piles: 72 ÷ 8.
   Full step-by-step solution

   Step 1: Liam has 72 baseball cards total. Step 2: He wants to split them into 8 equal piles. Step 3: To find how many cards are in each pile, divide the total number of cards by the number of piles: 72 ÷ 8. Step 4: 72 ÷ 8 = 9. Step 5: Therefore, there should be 9 cards in each pile.

4. Tom has 12 stickers to put in a sticker album. Each page can hold 2 stickers. How many pages will Tom fill completely? Answer: 6 Solution: We need to find how many groups of 2 are in 12. This is a missing factor problem: ? × 2 = 12 Divide the total stickers by stickers per page: 12 ÷ 2 = 6 Check: 6 × 2 = 12 ✓ The answer is 6 pages.
   Full step-by-step solution

   Step 1: We need to find how many groups of 2 are in 12. Step 2: This is a missing factor problem: ? × 2 = 12 Step 3: Divide the total stickers by stickers per page: 12 ÷ 2 = 6 Step 4: Check: 6 × 2 = 12 ✓ The answer is 6 pages.

5. ? × 8 = 64 Answer: 8 Solution: The equation is ? × 8 = 64 To find the missing factor, divide the product (64) by the known factor (8) 64 ÷ 8 = 8 Check: 8 × 8 = 64 ✓ The answer is 8.
   Full step-by-step solution

   Step 1: The equation is ? × 8 = 64 Step 2: To find the missing factor, divide the product (64) by the known factor (8) Step 3: 64 ÷ 8 = 8 Step 4: Check: 8 × 8 = 64 ✓ The answer is 8.

6. ? × 9 = 108 Answer: 12 Solution: We need to find the unknown factor in ? × 9 = 108 To find the unknown factor, we can divide the product (108) by the known factor (9) 108 ÷ 9 = 12 Check: 12 × 9 = 108 The answer is 12.
   Full step-by-step solution

   Step 1: We need to find the unknown factor in ? × 9 = 108 Step 2: To find the unknown factor, we can divide the product (108) by the known factor (9) Step 3: 108 ÷ 9 = 12 Step 4: Check: 12 × 9 = 108 The answer is 12.

7. Aroha is putting cookies into bags for a bake sale. Each bag holds 3 cookies. Aroha has 18 cookies in total. How many bags can Aroha fill? Answer: 6 Solution: Understand that we need to find how many groups of 3 fit into 18. This is a missing factor problem: ? × 3 = 18 Divide the total by the number in each group: 18 ÷ 3 = 6 Check: 6 × 3 = 18 ✓ The answer is 6 bags.
   Full step-by-step solution

   Step 1: Understand that we need to find how many groups of 3 fit into 18. Step 2: This is a missing factor problem: ? × 3 = 18 Step 3: Divide the total by the number in each group: 18 ÷ 3 = 6 Step 4: Check: 6 × 3 = 18 ✓ The answer is 6 bags.

8. Sarah is arranging chairs for a school assembly. There are 20 chairs in total, and Sarah puts them into 10 equal rows. How many chairs are in each row? Answer: 2 Solution: We know the total number of chairs (20) and the number of rows (10). This is a missing factor problem: 10 × ?
   Full step-by-step solution

   Step 1: We know the total number of chairs (20) and the number of rows (10). Step 2: This is a missing factor problem: 10 × ? = 20 Step 3: Divide the total by the number of rows: 20 ÷ 10 = 2 Step 4: Check: 10 × 2 = 20 ✓ The answer is 2 chairs in each row.

9. ? × 8 = 88 Answer: 11 Solution: The equation is ? × 8 = 88 To find the missing factor, divide the product (88) by the known factor (8) 88 ÷ 8 = 11 Check: 11 × 8 = 88 ✓ The answer is 11.
   Full step-by-step solution

   Step 1: The equation is ? × 8 = 88 Step 2: To find the missing factor, divide the product (88) by the known factor (8) Step 3: 88 ÷ 8 = 11 Step 4: Check: 11 × 8 = 88 ✓ The answer is 11.

10. 8 × ? = 96 Answer: 12 Solution: The equation is 8 × ? = 96 To find the unknown factor, divide 96 by 8 96 ÷ 8 = 12 Check: 8 × 12 = 96 ✓ The answer is 12.
    Full step-by-step solution

    Step 1: The equation is 8 × ? = 96 Step 2: To find the unknown factor, divide 96 by 8 Step 3: 96 ÷ 8 = 12 Step 4: Check: 8 × 12 = 96 ✓ The answer is 12.