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Unknown Factors

Grade 3 · Algebra · Worksheet 1

  1. ? × 7 = 84 Answer: ______________
  2. Max is arranging chairs for a school assembly. There are 36 chairs in total, and Max puts them into 6 equal rows. How many chairs are in each row? Answer: ______________
  3. Emma is baking cookies for her class party. She needs 72 cookies total. If each baking sheet holds 8 cookies, how many sheets does she need to bake all the cookies? Answer: ______________
  4. 8 × ? = 56 Answer: ______________
  5. Liam is organizing his baseball card collection into albums. Each album page holds 8 cards. If Liam has 72 cards total, how many pages will he need to display all his cards? Answer: ______________
  6. A rectangular garden has a length of 24 meters and a width of 18 meters. A fence is placed along the entire perimeter of the garden. What is the total length of the fence in meters?
    Answer: ______________
  7. Liam is organizing his baseball card collection into albums. Each album page holds 9 cards. If Liam has 72 baseball cards total, how many pages will he need to display all his cards? Answer: ______________
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Answer Key & Explanations

Unknown Factors · Grade 3 · Worksheet 1

  1. ? × 7 = 84 Answer: 12 Solution: The equation is ? × 7 = 84 To find the missing factor, divide 84 by 7 84 ÷ 7 = 12 Check: 12 × 7 = 84 ✓ The missing factor is 12.
    Full step-by-step solution

    Step 1: The equation is ? × 7 = 84 Step 2: To find the missing factor, divide 84 by 7 Step 3: 84 ÷ 7 = 12 Step 4: Check: 12 × 7 = 84 ✓ The missing factor is 12.

  2. Max is arranging chairs for a school assembly. There are 36 chairs in total, and Max puts them into 6 equal rows. How many chairs are in each row? Answer: 6 Solution: We know the total number of chairs (36) and the number of rows (6). This is a missing factor problem: 6 × ? = 36 Divide the total by the number of rows: 36 ÷ 6 = 6 Check: 6 × 6 = 36 ✓ The answer is 6 chairs in each row.
    Full step-by-step solution

    Step 1: We know the total number of chairs (36) and the number of rows (6). Step 2: This is a missing factor problem: 6 × ? = 36 Step 3: Divide the total by the number of rows: 36 ÷ 6 = 6 Step 4: Check: 6 × 6 = 36 ✓ The answer is 6 chairs in each row.

  3. Emma is baking cookies for her class party. She needs 72 cookies total. If each baking sheet holds 8 cookies, how many sheets does she need to bake all the cookies? Answer: 9 Solution: Emma needs 72 cookies total. Each baking sheet holds 8 cookies. To find how many sheets she needs, divide the total cookies by cookies per sheet: 72 ÷ 8 72 ÷ 8 = 9 Emma needs 9 baking sheets to make all the cookies.
    Full step-by-step solution

    Step 1: Emma needs 72 cookies total. Step 2: Each baking sheet holds 8 cookies. Step 3: To find how many sheets she needs, divide the total cookies by cookies per sheet: 72 ÷ 8 Step 4: 72 ÷ 8 = 9 Emma needs 9 baking sheets to make all the cookies.

  4. 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.

  5. Liam is organizing his baseball card collection into albums. Each album page holds 8 cards. If Liam has 72 cards total, how many pages will he need to display all his cards? Answer: 9 Solution: Identify what we know - total cards = 72, cards per page = 8 Set up the division problem: 72 ÷ 8 Calculate: 8 × 9 = 72 Since 8 × 9 = 72, Liam needs 9 pages The answer is 9.
    Full step-by-step solution

    Step 1: Identify what we know - total cards = 72, cards per page = 8 Step 2: Set up the division problem: 72 ÷ 8 Step 3: Calculate: 8 × 9 = 72 Step 4: Since 8 × 9 = 72, Liam needs 9 pages The answer is 9.

  6. A rectangular garden has a length of 24 meters and a width of 18 meters. A fence is placed along the entire perimeter of the garden. What is the total length of the fence in meters? Answer: 84 Solution: The perimeter of a rectangle is calculated by adding all four sides: length + width + length + width. This can also be written as 2 × length + 2 × width, or 2 × (length + width).
    Full step-by-step solution

    Step 1: The perimeter of a rectangle is calculated by adding all four sides: length + width + length + width. Step 2: This can also be written as 2 × length + 2 × width, or 2 × (length + width). Step 3: Using the formula 2 × (length + width): 2 × (24 + 18) Step 4: First add inside the parentheses: 24 + 18 = 42 Step 5: Then multiply by 2: 2 × 42 = 84 Step 6: The total length of the fence is 84 meters.

  7. Liam is organizing his baseball card collection into albums. Each album page holds 9 cards. If Liam has 72 baseball cards total, how many pages will he need to display all his cards? Answer: 8 Solution: Identify what we know - Liam has 72 cards total and each page holds 9 cards. Set up the division problem: 72 ÷ 9 Think: How many groups of 9 are in 72?
    Full step-by-step solution

    Step 1: Identify what we know - Liam has 72 cards total and each page holds 9 cards. Step 2: Set up the division problem: 72 ÷ 9 Step 3: Think: How many groups of 9 are in 72? Step 4: 9 × 8 = 72 Step 5: Since 9 × 8 = 72, then 72 ÷ 9 = 8 Step 6: Liam will need 8 pages to display all his baseball cards.