Fraction Word Problems with All Operations

Fraction Word Problems with All Operations
Fraction Word Problems with All Operations
Fraction Word Problems with All Operations
Fraction Word Problems with All Operations
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This one page worksheet contains short word problems that involve fractions and use addition, subtraction, multiplication, and division. I have students that cannot figure out which operation to use once fractions are involved, so I made this sheet in hopes that students can slow down to comprehend the words. Most of the problems use whole numbers first, and then have the exact same problem but with fractions. I feel like this sheet is challenging, but recently I have seen so many fractional word problems on standardized tests that students need all the practice they can get.

Students have to have mastered calculations with fractions before completing.

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Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) Γ· (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) Γ· (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (𝘒/𝘣) Γ· (𝘀/π˜₯) = 𝘒π˜₯/𝘣𝘀.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Total Pages
2 pages
Answer Key
Included
Teaching Duration
N/A
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