Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 19
Math
Unit 5
5th Grade
Lesson 19 of 25
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Divide a unit fraction by a whole number.
The core standards covered in this lesson
5.NF.B.7.A — Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
5.NF.B.7.C — 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?
The foundational standards covered in this lesson
3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
3.OA.B.6 — Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
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Nolan gives some Fruit-by-the-Foot to his $$3$$ friends to share equally.
a. If he has $$3$$ feet of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
b. If he has $$1$$ foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
c. If he has $${1\over2}$$ foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
d. If he has $${1\over3}$$ foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
Grade 5 Mathematics > Module 4 > Topic G > Lesson 26 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Priya and Mai used the diagrams below to find the value of $$\frac13 \div 4$$.
Priya’s diagram:
Mai’s diagram:
a. What is the same about the diagrams?
b. What is different?
c. Find the value that makes the equation true.
$$\frac13 \div 4 =$$ ____
Grade 4 Unit 3 Lesson 12 Activity 1, accessed on May 5, 2022, 10:44 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
a. Solve. Then check your work.
b. What do you notice in Part (a)? What do you wonder?
Problem Set
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Solve. Show or explain your work.
a. $${{1\over3} \div 2}$$
b. $${{1\over4} \div 9}$$
Zach spends half of his workday tutoring students. If he sees 5 students and spends the same amount of time with each student, what fraction of his workday does he spend tutoring each student?
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Lesson 18
Lesson 20
Topic A: Fractions as Division
Relate equal shares of objects to division expressions and visual representations of fractions.
5.NF.B.3
Write division expressions that represent fractions and vice versa.
Solve division problems when the quotient is a fraction or mixed number, including cases with larger values.
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Topic B: Multiplying a Fraction by a Whole Number
Multiply a fraction by a whole number where the product is a whole number.
5.NF.B.4.A 5.NF.B.6
Multiply a fraction by a whole number where the product is a whole number or a fraction.
Relate multiplication of a fraction by a whole number to multiplication of a whole number by a fraction and use this to develop a general method to multiply any fraction by any whole number (or vice versa).
5.NF.B.4.A 5.NF.B.5
Solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers.
5.NF.B.4 5.NF.B.6 5.OA.A.2
Topic C: Multiplying a Fraction by a Fraction
Multiply a fraction by a fraction without subdivisions using tape diagrams and number lines.
5.NF.B.4 5.NF.B.5 5.NF.B.6
Multiply a fraction by a fraction with subdivisions using tape diagrams and number lines.
Multiply a fraction by a fraction with more complicated subdivisions using an area model.
Develop a general method to multiply a fraction by a fraction.
Solve real-world problems involving multiplication of fractions with fractions and create real-world contexts for expressions involving multiplication of fractions with fractions.
Topic D: Multiplying with Mixed Numbers
Multiply mixed numbers by whole numbers.
Multiply mixed numbers by fractions.
Multiply mixed numbers by mixed numbers.
Develop a general method to multiply with mixed numbers.
Solve real-world problems involving multiplication with mixed numbers and create real-world contexts for expressions involving multiplication with mixed numbers.
Interpret multiplication as scaling.
5.NF.B.5 5.NF.B.5.A 5.NF.B.5.B
Topic E: Dividing with Fractions
5.NF.B.7.A 5.NF.B.7.C
Divide a whole number by a unit fraction.
5.NF.B.7.B 5.NF.B.7.C
Solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions.
5.NF.B.7.C 5.OA.A.2
Topic F: Fraction Expressions and Real-World Problems
Solve real-world problems involving multiplication and division with fractions.
5.NF.B.3 5.NF.B.6 5.NF.B.7
Write and evaluate numerical expressions involving operations with fractions.
5.NF.B.3 5.NF.B.4 5.NF.B.5 5.NF.B.6 5.NF.B.7 5.OA.A.1 5.OA.A.2
Topic G: Line Plots
Create line plots.
5.MD.B.2
Solve problems involving information presented in a line plot (dot plot).
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