Learn on PengiEureka Math, Grade 5Chapter 17: Making Like Units Numerically

Lesson 1: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.

In this Grade 5 Eureka Math lesson from Chapter 17, students learn to add fractions to and subtract fractions from whole numbers using equivalence and number line strategies. The lesson focuses on decomposing mixed numbers into whole number and fraction parts, finding like units, and modeling problems such as 1 + 1¾ and 2 3/10 + 3 on an empty number line.

Section 1

Adding a Whole Number to a Mixed Number

Property

To add a whole number to a mixed number, add the whole numbers together and keep the fraction part.

W+Abc=(W+A)+bcW + A\frac{b}{c} = (W + A) + \frac{b}{c}

Examples

Section 2

Adding Whole Numbers and Mixed Numbers on a Number Line

Property

To model the addition of a whole number and a mixed number on a number line, start at one number and move to the right by the value of the other number.
Adding a whole number corresponds to making full unit jumps.

Examples

Section 3

Subtracting a Fraction from a Whole by Converting the Whole

Property

To subtract a fraction from a whole number, convert the whole number WW into an equivalent fraction with the same denominator dd as the fraction being subtracted:

W−ad=W×dd−ad=(W×d)−adW - \frac{a}{d} = \frac{W \times d}{d} - \frac{a}{d} = \frac{(W \times d) - a}{d}

Examples

Section 4

Subtracting Fractions and Mixed Numbers from Whole Numbers on a Number Line

Property

To subtract a fraction or mixed number from a whole number on a number line, start at the whole number and move to the left.
The distance moved is equal to the value of the number being subtracted, and the final position is the difference.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Adding a Whole Number to a Mixed Number

Property

To add a whole number to a mixed number, add the whole numbers together and keep the fraction part.

W+Abc=(W+A)+bcW + A\frac{b}{c} = (W + A) + \frac{b}{c}

Examples

Section 2

Adding Whole Numbers and Mixed Numbers on a Number Line

Property

To model the addition of a whole number and a mixed number on a number line, start at one number and move to the right by the value of the other number.
Adding a whole number corresponds to making full unit jumps.

Examples

Section 3

Subtracting a Fraction from a Whole by Converting the Whole

Property

To subtract a fraction from a whole number, convert the whole number WW into an equivalent fraction with the same denominator dd as the fraction being subtracted:

W−ad=W×dd−ad=(W×d)−adW - \frac{a}{d} = \frac{W \times d}{d} - \frac{a}{d} = \frac{(W \times d) - a}{d}

Examples

Section 4

Subtracting Fractions and Mixed Numbers from Whole Numbers on a Number Line

Property

To subtract a fraction or mixed number from a whole number on a number line, start at the whole number and move to the left.
The distance moved is equal to the value of the number being subtracted, and the final position is the difference.

Examples