Learn on PengiEureka Math, Grade 5Chapter 18: Further Applications

Lesson 4: Explore part-to-whole relationships.

In this Grade 5 Eureka Math lesson from Chapter 18, students explore part-to-whole relationships by using fraction models to identify and draw a whole when given a fractional part, such as determining the full length of a ribbon when shown only 1/3 or 2/5 of it. Fluency activities build prerequisite skills including decomposing improper fractions, finding like units, and adding fractions with sums greater than 1. Students work collaboratively to solve multi-step ribbon and wire problems that require drawing, labeling, and writing equations to represent part-to-whole fraction situations.

Section 1

Finding the Whole from a Fractional Part

Property

If a given value VV represents a fraction ab\frac{a}{b} of an unknown whole WW, the whole can be found by first determining the value of one unit part (V÷aV \div a) and then multiplying by the total number of parts in the whole (bb).
The formula is:

W=(V÷a)×b=V÷abW = (V \div a) \times b = V \div \frac{a}{b}

Examples

Section 2

Solve Word Problems with Fractional Comparisons

Property

To solve problems where a fraction of one quantity equals a fraction of another (e.g., ab of X=cd of Y\frac{a}{b} \text{ of } X = \frac{c}{d} \text{ of } Y), find a common numerator for the fractions.
If km of X=kn of Y\frac{k}{m} \text{ of } X = \frac{k}{n} \text{ of } Y, the ratio of the wholes is X:Y=m:nX:Y = m:n.
A bar model can then be used to represent this relationship, with quantity XX having mm units and quantity YY having nn units.

Examples

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Chapter 18: Further Applications

  1. Lesson 1

    Lesson 1: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

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  2. Lesson 2

    Lesson 2: Strategize to solve multi-term problems.

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  3. Lesson 3

    Lesson 3: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

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  4. Lesson 4Current

    Lesson 4: Explore part-to-whole relationships.

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Lesson overview

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Section 1

Finding the Whole from a Fractional Part

Property

If a given value VV represents a fraction ab\frac{a}{b} of an unknown whole WW, the whole can be found by first determining the value of one unit part (V÷aV \div a) and then multiplying by the total number of parts in the whole (bb).
The formula is:

W=(V÷a)×b=V÷abW = (V \div a) \times b = V \div \frac{a}{b}

Examples

Section 2

Solve Word Problems with Fractional Comparisons

Property

To solve problems where a fraction of one quantity equals a fraction of another (e.g., ab of X=cd of Y\frac{a}{b} \text{ of } X = \frac{c}{d} \text{ of } Y), find a common numerator for the fractions.
If km of X=kn of Y\frac{k}{m} \text{ of } X = \frac{k}{n} \text{ of } Y, the ratio of the wholes is X:Y=m:nX:Y = m:n.
A bar model can then be used to represent this relationship, with quantity XX having mm units and quantity YY having nn units.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 18: Further Applications

  1. Lesson 1

    Lesson 1: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

    LearnPractice
  2. Lesson 2

    Lesson 2: Strategize to solve multi-term problems.

    LearnPractice
  3. Lesson 3

    Lesson 3: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Explore part-to-whole relationships.

    LearnPractice