Learn on PengiEureka Math, Grade 5Chapter 23: Multiplication of a Fraction by a Fraction

Lesson 7: Convert measures involving whole numbers, and solve multi-step word problems.

Grade 5 students learn how to convert measurements involving whole numbers — such as centimeters to meters, yards to feet, and cups to pints — by expressing smaller units as fractions of larger units and multiplying. The lesson is part of Eureka Math's Chapter 23 on fraction multiplication and also builds skills in solving multi-step word problems using unit conversions. Students practice both converting in both directions and applying these conversions in context.

Section 1

Convert Smaller Units to Larger Units Using Fractions

Property

To convert a measurement of nn smaller units to a larger unit, where 1 smaller unit=1k larger units1 \text{ smaller unit} = \frac{1}{k} \text{ larger units}, you multiply the quantity by the fractional equivalent:

n smaller units=n×1k larger units=nk larger unitsn \text{ smaller units} = n \times \frac{1}{k} \text{ larger units} = \frac{n}{k} \text{ larger units}

Examples

Section 2

Solve Multi-Step Measurement Word Problems

Property

To solve multi-step word problems involving different units of measure, first convert the measurements to a common, larger unit. Then, perform the necessary operations (such as addition or subtraction) to find the final answer.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Convert Smaller Units to Larger Units Using Fractions

Property

To convert a measurement of nn smaller units to a larger unit, where 1 smaller unit=1k larger units1 \text{ smaller unit} = \frac{1}{k} \text{ larger units}, you multiply the quantity by the fractional equivalent:

n smaller units=n×1k larger units=nk larger unitsn \text{ smaller units} = n \times \frac{1}{k} \text{ larger units} = \frac{n}{k} \text{ larger units}

Examples

Section 2

Solve Multi-Step Measurement Word Problems

Property

To solve multi-step word problems involving different units of measure, first convert the measurements to a common, larger unit. Then, perform the necessary operations (such as addition or subtraction) to find the final answer.

Examples