Unknown Factors

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Unknown Factors · Grade 3 · Worksheet 2

1. Liam is organizing his trading cards into albums. He has 72 cards total and wants to put the same number of cards in each of his 8 albums. How many cards should Liam put in each album? Answer: 9 Solution: Liam has 72 cards total He wants to divide them equally among 8 albums To find how many cards go in each album, divide 72 by 8 72 ÷ 8 = 9 Check: 8 albums × 9 cards each = 72 cards total The answer is 9.
   Full step-by-step solution

   Step 1: Liam has 72 cards total Step 2: He wants to divide them equally among 8 albums Step 3: To find how many cards go in each album, divide 72 by 8 Step 4: 72 ÷ 8 = 9 Step 5: Check: 8 albums × 9 cards each = 72 cards total The answer is 9.

2. Liam is organizing his baseball card collection into albums. Each album page holds 8 cards. If Liam has 72 cards total, how many full pages will he fill? Answer: 9 Solution: Identify the total number of cards: 72 Identify how many cards fit on one page: 8 To find the number of full pages, divide the total cards by the cards per page: 72 ÷ 8 Calculate the division: 8 × 9 = 72 Therefore, 72 ÷ 8 = 9 Liam will fill 9 full pages.
   Full step-by-step solution

   Step 1: Identify the total number of cards: 72 Step 2: Identify how many cards fit on one page: 8 Step 3: To find the number of full pages, divide the total cards by the cards per page: 72 ÷ 8 Step 4: Calculate the division: 8 × 9 = 72 Step 5: Therefore, 72 ÷ 8 = 9 Liam will fill 9 full pages.

3. 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.

4. 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.

5. ? × 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.

6. 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.

7. Mere is arranging apples into a rectangular array on a table. She puts 9 apples in each row. The total number of apples is 63. The array has ? rows of apples. How many rows are there? Answer: 7 Solution: The apples are arranged in rows, and each row has 9 apples. The total is 63 apples. This is a missing factor problem: ?
   Full step-by-step solution

   Step 1: The apples are arranged in rows, and each row has 9 apples. The total is 63 apples. This is a missing factor problem: ? rows x 9 apples per row = 63 apples. Step 2: To find the missing factor, think: what number times 9 equals 63? Step 3: Skip-count by 9s: 9, 18, 27, 36, 45, 54, 63. That is 7 steps. Step 4: So, 7 x 9 = 63. Step 5: Therefore, the number of rows is 7. The answer is 7.