Fractions Number Line

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Answer Key & Explanations

Fractions Number Line · Grade 3 · Worksheet 1

1. Lily is baking cookies and needs to measure 3/4 cup of flour. 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 flour? Answer: 1/4 Solution: 1. The measuring cup goes from 0 (empty) to 1 (full). If she fills the cup to the 3/4 mark, that means 3/4 of the cup is full.
   Full step-by-step solution

   Let's go step by step. 1. Understand the problem: Lily wants exactly 3/4 cup of flour. The measuring cup goes from 0 (empty) to 1 (full). If she fills the cup to the 3/4 mark, that means 3/4 of the cup is full. 2. The total capacity of the cup is 1 whole. If the cup is full, the amount of flour is 1. If the cup has 3/4 flour, then the empty part is the remaining fraction. 3. To find the empty part: Empty part = Total capacity − Filled part Empty part = 1 − 3/4 4. Write 1 as a fraction: 1 = 4/4 5. Subtract: 4/4 − 3/4 = 1/4 6. Conclusion: When she has exactly 3/4 cup of flour, the fraction of the cup that is empty is 1/4. Final answer: 1/4

2. Ava is baking a cake and needs to measure 1 1/6 cups of milk. She has a large measuring cup with marks from 0 to 2 cups, and each cup is divided into 6 equal parts. Ava pours milk until the level reaches exactly 1 1/6 on the number line. How many sixths (fractions with denominator 6) is 1 1/6 equal to? Answer: 7/6 Solution: One whole cup is equal to 6/6 (six sixths). Ava has 1 whole cup plus 1/6 more.
   Full step-by-step solution

   Step 1: One whole cup is equal to 6/6 (six sixths). Step 2: Ava has 1 whole cup plus 1/6 more. Step 3: So the total is 6/6 + 1/6 = 7/6. Step 4: On a number line from 0 to 2, 1 1/6 is the same as 7/6, which is greater than 1 but less than 2. The answer is 7/6.

3. Aroha is helping her uncle build a bookshelf that is 9 feet long. They need to attach a support bracket at exactly 2/3 of the total length from the left end of the shelf. On a number line from 0 to 9 feet, where should they mark the spot for the bracket? Answer: 6 Solution: The total length of the bookshelf is 9 feet. We need to find 2/3 of 9 feet. To find a fraction of a number, multiply the fraction by the number: 2/3 × 9 First, divide 9 by 3 (the denominator): 9 ÷ 3 = 3.
   Full step-by-step solution

   Step 1: The total length of the bookshelf is 9 feet. Step 2: We need to find 2/3 of 9 feet. Step 3: To find a fraction of a number, multiply the fraction by the number: 2/3 × 9 Step 4: First, divide 9 by 3 (the denominator): 9 ÷ 3 = 3. This tells us one-third of 9 is 3. Step 5: Then multiply by 2 (the numerator): 3 × 2 = 6. Step 6: So 2/3 of 9 feet is 6 feet. The answer is 6.

4. Kaia is helping her dad build a garden path that is 2 meters long. They are drawing a number line from 0 to 2 meters to plan where to place stepping stones. Kaia needs to place a special decorative stone at the point that represents 7/8 of the total path length. On the number line from 0 to 2, between which two whole numbers should Kaia place the stone? Answer: between 0 and 1 Solution: The fraction is 7/8. Step 2: Look at the denominator: 8 means each whole unit (from 0 to 1, and from 1 to 2) is divided into 8 equal parts. Step 3: The numerator is 7, so we need 7 of those 8 parts.
   Full step-by-step solution

   Step 1: The number line goes from 0 to 2. The fraction is 7/8. Step 2: Look at the denominator: 8 means each whole unit (from 0 to 1, and from 1 to 2) is divided into 8 equal parts. Step 3: The numerator is 7, so we need 7 of those 8 parts. Since 7/8 is less than 1 (because 8/8 = 1), it must be located between 0 and 1 on the number line. Step 4: So the decorative stone should be placed between 0 and 1. The answer is between 0 and 1.

5. A number line from 0 to 1 is divided into 6 equal parts. A frog jumps and lands on the mark that is 4 parts away from 0. What fraction represents the frog's position on the number line? Answer: 4/6 Solution: This means the whole is divided into 6 sections. The frog lands on the mark that is 4 parts away from 0. This means it has covered 4 out of the 6 sections.
   Full step-by-step solution

   Step 1: The number line from 0 to 1 is divided into 6 equal parts. This means the whole is divided into 6 sections. Step 2: The frog lands on the mark that is 4 parts away from 0. This means it has covered 4 out of the 6 sections. Step 3: A fraction representing parts of a whole is written as (number of parts covered) / (total number of parts). Step 4: So, the fraction is 4/6. The answer is 4/6.

6. Carlos 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 a number line from 0 to 16 kilometers. How many kilometers has Carlos walked when he reaches the bench? Answer: 12 Solution: The total trail length is 16 kilometers. Carlos stops at 3/4 of the trail.
   Full step-by-step solution

   Step 1: The total trail length is 16 kilometers. Step 2: Carlos stops at 3/4 of the trail. Step 3: To find 3/4 of 16, multiply the fraction by the whole number: 3/4 × 16 Step 4: First, divide 16 by 4: 16 ÷ 4 = 4 Step 5: Then multiply by 3: 4 × 3 = 12 Step 6: Carlos has walked 12 kilometers when he reaches the bench. The answer is 12.

7. Lily is baking cookies and needs to measure 3/4 cup of sugar. She has a 1-cup measuring cup that is divided into equal parts. If she fills the cup to the 3/4 mark, how many equal parts of the whole cup has she filled? Answer: 3 Solution: 1. She fills it to the 3/4 mark. We need to find how many equal parts of the whole cup she has filled.
   Full step-by-step solution

   Let's break this down step by step. 1. Understand the problem: Lily has a 1-cup measuring cup divided into equal parts. She fills it to the 3/4 mark. We need to find how many equal parts of the whole cup she has filled. 2. Interpret the cup markings: If the cup is divided into equal parts, and it's a 1-cup measure, the most common way is to divide it into 4 equal parts (quarters). Each part = 1/4 cup. 3. Relating 3/4 cup to the equal parts: 3/4 cup means 3 parts out of 4 equal parts of the whole cup. 4. Conclusion: She has filled 3 equal parts of the whole cup. Final answer: 3

8. A number line is marked from 0 to 1 and divided into 8 equal parts. A point is placed on the mark that is 3 parts from 0. What fraction represents the location of this point? Answer: 3/8 Solution: This means each part represents a fraction of 1/8 of the whole. Locate the point. The point is placed 3 parts from 0.
   Full step-by-step solution

   Step 1: Understand the number line division. The number line from 0 to 1 is divided into 8 equal parts. This means each part represents a fraction of 1/8 of the whole. Step 2: Locate the point. The point is placed 3 parts from 0. Since each part is 1/8, 3 parts means 3 times 1/8. Step 3: Calculate the fraction. 3 parts from 0 = 3 × (1/8) = 3/8. Step 4: Interpret the result. The fraction 3/8 represents the distance from 0 to the point on the number line. Final Answer: 3/8