Rational to Decimal

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Answer Key & Explanations

Rational to Decimal · Grade 7 · Worksheet 2

1. Olivia is knitting a scarf and needs to use a specific stitch pattern. The pattern requires that for every 3 rows of a certain stitch, she uses 7 rows of a different stitch. She has completed a total of 33 rows. What fraction of the completed rows are the first type of stitch? Express your answer as a decimal. Answer: 0.3 Solution: The pattern has 3 rows of the first stitch and 7 rows of the second stitch, so one full cycle has 3 + 7 = 10 rows. The fraction of the first stitch in one cycle is 3/10. Olivia completed 33 rows total.
   Full step-by-step solution

   Step 1: The pattern has 3 rows of the first stitch and 7 rows of the second stitch, so one full cycle has 3 + 7 = 10 rows. Step 2: The fraction of the first stitch in one cycle is 3/10. Step 3: Olivia completed 33 rows total. Since each cycle is 10 rows, she completed 33/10 = 3.3 cycles. Step 4: The fraction of rows that are the first stitch remains the same regardless of how many cycles: 3/10. Step 5: Convert 3/10 to a decimal: 3 divided by 10 = 0.3. The answer is 0.3.

2. Emma is conducting a science experiment to create a saltwater solution. She needs to mix 0.6 kilograms of salt with 1.8 kilograms of water. What decimal represents the fraction of the total mixture that is salt? Answer: 0.25 Solution: Salt = 0.6 kg Water = 1.8 kg Total mixture = 0.6 + 1.8 = 2.4 kg Fraction = salt weight / total weight = 0.6 / 2.4 0.6 ÷ 2.4 = 6/24 = 1/4 1/4 = 0.25 The answer is 0.25.
   Full step-by-step solution

   Step 1: Find the total weight of the mixture Salt = 0.6 kg Water = 1.8 kg Total mixture = 0.6 + 1.8 = 2.4 kg Step 2: Find the fraction that is salt Fraction = salt weight / total weight = 0.6 / 2.4 Step 3: Simplify the fraction 0.6 ÷ 2.4 = 6/24 = 1/4 Step 4: Convert to decimal 1/4 = 0.25 The answer is 0.25.

3. Tane is drawing a large geometric design on a coordinate grid. He plots a square with vertices at (0, 0), (18, 0), (18, 18), and (0, 18). Inside the square, he draws a shaded rhombus (diamond) with vertices at (9, 3), (15, 9), (9, 15), and (3, 9). What is the area of the unshaded region inside the square? Express your answer as a decimal. Answer: 252 Solution: Find the area of the square. The side length of the square is 18 units. Area of square = side × side = 18 × 18 = 324 square units.
   Full step-by-step solution

   Step 1: Find the area of the square. The side length of the square is 18 units. Area of square = side × side = 18 × 18 = 324 square units. Step 2: Find the area of the rhombus. The vertices are at (9, 3), (15, 9), (9, 15), and (3, 9). This is a rhombus (a diamond shape) where the diagonals are horizontal and vertical. The horizontal diagonal goes from (3, 9) to (15, 9). Length = 15 - 3 = 12 units. The vertical diagonal goes from (9, 3) to (9, 15). Length = 15 - 3 = 12 units. Area of a rhombus = (diagonal1 × diagonal2) / 2 = (12 × 12) / 2 = 144 / 2 = 72 square units. Step 3: Find the unshaded area. Unshaded area = Area of square - Area of rhombus = 324 - 72 = 252 square units. The answer is 252.

4. Mason is building a wooden model of a bridge for his engineering class. The plans call for a support beam that is 11/16 of a meter long. He needs to cut this from a piece of wood that is measured in decimal meters on the ruler. What is the exact decimal equivalent of 11/16 of a meter? Answer: 0.6875 Solution: To convert the fraction 11/16 to a decimal, divide the numerator (11) by the denominator (16). Perform the division: 11 ÷ 16 = 0.6875. Since 16 × 0.6875 = 11 exactly, this is a terminating decimal.
   Full step-by-step solution

   Step 1: To convert the fraction 11/16 to a decimal, divide the numerator (11) by the denominator (16). Step 2: Perform the division: 11 ÷ 16 = 0.6875. Step 3: Since 16 × 0.6875 = 11 exactly, this is a terminating decimal. The exact decimal equivalent of 11/16 of a meter is 0.6875 meters.

5. Liam is designing a rectangular garden for his school's community project. The garden's length is 12.75 meters and its width is 8.4 meters. He needs to calculate the total area to determine how much soil to buy. What is the area of the garden in square meters? Answer: 107.1 Solution: To find the area of a rectangle, we use the formula: Area = length × width Here, length = 12.75 meters and width = 8.4 meters. Write the multiplication.
   Full step-by-step solution

   To find the area of a rectangle, we use the formula: Area = length × width Here, length = 12.75 meters and width = 8.4 meters. Step 1: Write the multiplication. Area = 12.75 × 8.4 Step 2: First, multiply 12.75 by 8.4 ignoring the decimals. That means compute 1275 × 84. Step 3: Break 1275 × 84 into parts. 1275 × 80 = 1275 × 8 × 10 = (10200) × 10 = 102000 1275 × 4 = 5100 Step 4: Add them. 102000 + 5100 = 107100 Step 5: Now place the decimal point. 12.75 has 2 decimal places, 8.4 has 1 decimal place, so total decimal places = 2 + 1 = 3. So, 107100 becomes 107.100 after moving the decimal 3 places left. Step 6: Simplify. 107.100 = 107.1 Thus, the area of the garden is 107.1 square meters.

6. 0.375 × 2.4 ÷ 0.6 = ? Answer: 1.5 Solution: Convert 0.375 to a fraction.
   Full step-by-step solution

   Step 1: Convert 0.375 to a fraction. 0.375 = 375/1000 = 3/8 Step 2: Write the expression as (3/8) × 2.4 ÷ 0.6 Step 3: Convert 2.4 to a fraction: 2.4 = 24/10 = 12/5 Step 4: Convert 0.6 to a fraction: 0.6 = 6/10 = 3/5 Step 5: Rewrite the expression: (3/8) × (12/5) ÷ (3/5) Step 6: Division by a fraction is multiplication by its reciprocal: (3/8) × (12/5) × (5/3) Step 7: Cancel common factors: (3/8) × (12/5) × (5/3) = (1/8) × (12/1) × (1/1) = 12/8 Step 8: Simplify 12/8 = 3/2 = 1.5 The answer is 1.5.