In this Grade 5 Eureka Math lesson from Chapter 23, students learn to relate decimal and fraction multiplication by converting between fraction and decimal notation for tenths and hundredths. Students practice multiplying fractions by fractions and multiplying whole numbers by decimals such as 0.1 and 0.01, building connections between the two representations. The lesson strengthens fluency with equivalent forms like 7/10 and 0.7 as a foundation for multiplying decimals and fractions interchangeably.
Section 1
Decimal Multiplication via Fraction Conversion
To multiply decimals, convert each decimal to its equivalent fraction. Then, multiply the fractions by multiplying the numerators and the denominators. Finally, convert the resulting fraction back to a decimal.
Section 2
Place Value Shifts in Decimal Multiplication
Multiplying a number by is the same as dividing by , which shifts each digit one place to the right on a place value chart. Multiplying by is the same as dividing by , which shifts each digit two places to the right.
Section 3
Solving Multi-Step Word Problems with Decimal Multiplication
To solve a multi-step word problem involving decimal multiplication, first break down the problem to identify all the necessary operations and their order. When a step requires multiplying decimals, apply the conversion method: change the decimals to fractions, multiply the fractions, and convert the product back to a decimal. Use this result to complete the remaining steps (like addition or subtraction) to find the final solution.
Expand to review the lesson summary and core properties.
Section 1
Decimal Multiplication via Fraction Conversion
To multiply decimals, convert each decimal to its equivalent fraction. Then, multiply the fractions by multiplying the numerators and the denominators. Finally, convert the resulting fraction back to a decimal.
Section 2
Place Value Shifts in Decimal Multiplication
Multiplying a number by is the same as dividing by , which shifts each digit one place to the right on a place value chart. Multiplying by is the same as dividing by , which shifts each digit two places to the right.
Section 3
Solving Multi-Step Word Problems with Decimal Multiplication
To solve a multi-step word problem involving decimal multiplication, first break down the problem to identify all the necessary operations and their order. When a step requires multiplying decimals, apply the conversion method: change the decimals to fractions, multiply the fractions, and convert the product back to a decimal. Use this result to complete the remaining steps (like addition or subtraction) to find the final solution.