Fractions Number Line

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Fractions Number Line · Grade 3 · Worksheet 2

1. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with carrots and the rest with lettuce, what fraction of the garden has lettuce? Show your answer on a number line from 0 to 1. Answer: 5/8 Solution: The garden is divided into 8 equal sections. Find how many sections have carrots. The problem says 3 sections are planted with carrots.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. So, the whole garden is represented by 8/8. Step 2: Find how many sections have carrots. The problem says 3 sections are planted with carrots. Step 3: Find how many sections have lettuce. Total sections = 8 Carrot sections = 3 Lettuce sections = 8 - 3 = 5 Step 4: Write the fraction for lettuce. Lettuce sections = 5 Total sections = 8 So, fraction of garden with lettuce = 5/8 Step 5: Represent on a number line from 0 to 1. The number line from 0 to 1 is divided into 8 equal parts. 0 is 0/8, 1 is 8/8. Lettuce occupies 5 parts out of 8, so on the number line, it goes from 0 to 5/8 if we consider the portion with lettuce starting from 0, but the question asks for the fraction of the garden that has lettuce, which is 5/8, so we mark the point at 5/8 on the number line as the end of the lettuce portion when starting from 0. Number line: 0 --- 1/8 --- 2/8 --- 3/8 --- 4/8 --- 5/8 --- 6/8 --- 7/8 --- 1 The lettuce portion is from 0 to 5/8. Final answer: 5/8

2. Liam is walking on a nature trail that is 16 kilometers long. He stops to rest at a bench that is located at the 3/4 point of the trail on the trail map's number line. How many kilometers has Liam walked when he reaches the bench? Answer: 12 Solution: Step 1: The total trail length is 16 kilometers Step 2: We need to find 3/4 of 16 kilometers Step 3: To find a fraction of a number, multiply the number by the fraction Step 4: 16 × 3/4 = (16 × 3)/4 = 48/4 = 12 Step 5: Liam has walked 12 kilometers when he reaches the bench Step 6: We can verify…
   Full step-by-step solution

   Step 1: The total trail length is 16 kilometers Step 2: We need to find 3/4 of 16 kilometers Step 3: To find a fraction of a number, multiply the number by the fraction Step 4: 16 × 3/4 = (16 × 3)/4 = 48/4 = 12 Step 5: Liam has walked 12 kilometers when he reaches the bench Step 6: We can verify this makes sense because 3/4 means the trail is divided into 4 equal parts, and 16 ÷ 4 = 4, so each part is 4 kilometers, and 3 parts would be 3 × 4 = 12 kilometers The answer is 12.

3. Liam is walking on a nature trail that is 16 kilometers long. He stops to rest when he has completed 3/4 of the trail. On a number line that shows the trail from 0 to 16 kilometers, how many kilometers from the start is Liam's resting point? Answer: 12 Solution: The total trail length is 16 kilometers. Liam has completed 3/4 of the trail. To find 3/4 of 16, multiply 16 by 3/4.
   Full step-by-step solution

   Step 1: The total trail length is 16 kilometers. Step 2: Liam has completed 3/4 of the trail. Step 3: To find 3/4 of 16, multiply 16 by 3/4. Step 4: 16 × 3/4 = (16 × 3) / 4 = 48 / 4 = 12 Step 5: So Liam's resting point is 12 kilometers from the start. The answer is 12.

4. Lily is baking cookies and needs to measure 3/4 cup of sugar. She has a measuring cup that shows fractions from 0 to 1. If she starts at 0 and fills the cup, what fraction of the cup will be empty when she has exactly 3/4 cup of sugar? Answer: 1/4 Solution: 1. The measuring cup goes from 0 (empty) to 1 (full). When the cup is full, it contains 1 whole cup.
   Full step-by-step solution

   Let's think through this step by step. 1. The measuring cup goes from 0 (empty) to 1 (full). When the cup is full, it contains 1 whole cup. 2. Lily needs 3/4 cup of sugar. If she fills the cup to the 3/4 mark, that means the cup is 3/4 full. 3. The amount of empty space in the cup is the part from the current fill level (3/4) to the top (1). 4. To find the empty part, subtract the filled part from the whole cup: Empty space = 1 - 3/4 5. Write 1 as a fraction: 1 = 4/4 So: 4/4 - 3/4 = 1/4 6. Therefore, when she has exactly 3/4 cup of sugar, the fraction of the cup that is empty is 1/4. Final answer: 1/4

5. Lily is measuring ribbon for a craft project. She has a ribbon that is 12 inches long. She needs to mark where 3/4 of the ribbon would be on a number line that goes from 0 to 12 inches. How many inches from the start of the ribbon is the 3/4 point? Answer: 9 Solution: We have a ribbon that is 12 inches long. We need to find 3/4 of the ribbon's length. Recall that "of" often means multiplication in math.
   Full step-by-step solution

   Step 1: Understand the problem. We have a ribbon that is 12 inches long. We need to find 3/4 of the ribbon's length. Step 2: Recall that "of" often means multiplication in math. So, 3/4 of 12 inches means: 3/4 × 12 Step 3: Multiply the fraction by the whole number. We can write 12 as 12/1: (3/4) × (12/1) = (3 × 12) / (4 × 1) = 36 / 4 Step 4: Simplify the fraction. 36 divided by 4 is 9. Step 5: Interpret the result. The 3/4 point along the ribbon is 9 inches from the start. Final Answer: 9

6. Noah is running a 12-kilometer race for charity. He wants to mark where he will be when he has completed 3/4 of the race on a number line from 0 to 12 kilometers. How many kilometers from the start should Noah mark to show 3/4 of the race distance? Answer: 9 Solution: The total race distance is 12 kilometers. Noah wants to find 3/4 of 12 kilometers.
   Full step-by-step solution

   Step 1: The total race distance is 12 kilometers. Step 2: Noah wants to find 3/4 of 12 kilometers. Step 3: To find a fraction of a number, multiply the fraction by the number: 3/4 × 12 Step 4: First, divide 12 by 4: 12 ÷ 4 = 3 Step 5: Then multiply by 3: 3 × 3 = 9 Step 6: So 3/4 of 12 kilometers is 9 kilometers. The answer is 9 kilometers from the start.

7. Place 5/6 on the number line between 0 and 2 = ? Answer: 5/6 Solution: The denominator is 6, so divide each whole unit into 6 equal parts. Starting from 0, count 5 of these 1/6 parts to the right. 5/6 is located 5/6 of the way between 0 and 1.
   Full step-by-step solution

   Step 1: The number line goes from 0 to 2, which is 2 whole units. Step 2: The denominator is 6, so divide each whole unit into 6 equal parts. Step 3: Starting from 0, count 5 of these 1/6 parts to the right. Step 4: 5/6 is located 5/6 of the way between 0 and 1. Step 5: The correct placement is at 5/6.

8. A baker is making a long loaf of bread that measures 100 centimeters from end to end. She needs to cut the loaf at the point that is 3/4 of the way from the left end. What fraction of the whole loaf will be to the right of the cut? Answer: 1/4 Solution: The loaf is 100 cm long. The cut is made 3/4 of the way from the left end. We need to find the fraction of the loaf to the right of the cut.
   Full step-by-step solution

   Step 1: Understand the problem. The loaf is 100 cm long. The cut is made 3/4 of the way from the left end. We need to find the fraction of the loaf to the right of the cut. Step 2: Visualize the loaf. Think of the loaf as a line from 0 (left end) to 100 (right end). The cut is placed at 3/4 of the total length from the left end. Step 3: Find the position of the cut. The total length is 100 cm. 3/4 of the total length is (3/4) * 100 = 75 cm. So the cut is 75 cm from the left end. Step 4: Determine the fraction to the right. The whole loaf is 100 cm. The part to the right of the cut is from 75 cm to 100 cm. This length is 100 - 75 = 25 cm. Step 5: Express the right part as a fraction of the whole. The fraction is (length of right part) / (total length) = 25 / 100. Simplify this fraction: 25/100 = 1/4. Step 6: Conclusion. Therefore, the fraction of the whole loaf to the right of the cut is 1/4. Answer: 1/4