Before diving into the answers, let’s clarify the objective. Lesson 16 teaches students to solve word problems involving fraction-by-fraction multiplication.
By this point, students have moved beyond multiplying fractions by whole numbers. Now, they must tackle problems like: "Tom has 2/3 of a pound of cheese. He uses 1/4 of that cheese for a sandwich. How much cheese did he use?"
The key concept is the phrase "of" — in math, "of" usually means multiplication. The lesson also reinforces drawing tape diagrams (strip models) to visualize the problem.
Question: Kevin has 4/5 of a yard of fabric. He uses 3/4 of the fabric to make a pillow. How many yards of fabric did Kevin use?
Answer: 3/5 yard
Explanation: 4/5 × 3/4 = (4×3)/(5×4) = 12/20 = 3/5.
In Eureka Math Grade 5 Module 4 Lesson 16 , the goal is to solve multi-step word problems using tape diagrams and fraction-by-fraction multiplication. Below are the solutions and methods for the typical problems found in this lesson's homework. Problem 1: Anthony's Board Question: Anthony had an 8-foot board. He cut off 34three-fourths of it to build a shelf. He then gave 13one-third
of the remaining piece to his brother. How many inches long was the piece he gave to his brother? Answer: 8 inches Find the remaining length in feetIf Anthony cut off 34three-fourths of the 8-foot board, 14one-fourth of the board remains.
14×8 feet=2 feet remainingone-fourth cross 8 feet equals 2 feet remaining Calculate the brother's share in feetThe brother received 13one-third of that remaining 2-foot piece.
13×2 feet=23 footone-third cross 2 feet equals two-thirds foot
Convert the final length to inchesSince 1 foot = 12 inches, multiply the fraction of the foot by 12.
23×12 inches=243 inches=8 inchestwo-thirds cross 12 inches equals 24 over 3 end-fraction inches equals 8 inches Problem 2: General Fraction Multiplication
Objective: Multiply fractions and simplify where possible. These problems often involve "of" as the operation (e.g., 12one-half 34three-fourths Example A:
5×56×8=2548the fraction with numerator 5 cross 5 and denominator 6 cross 8 end-fraction equals 25 over 48 end-fraction Example B:
Simplify first by dividing 3 and 12 by their greatest common factor (3): Eureka Math Lesson 16 Homework 5.4 Answer Key
14×54=516one-fourth cross five-fourths equals 5 over 16 end-fraction Key Strategies for Lesson 16
Read-Draw-Write (RDW): Always read the problem carefully, draw a tape diagram to represent the "whole" and its "parts," and then write your equation and statement.
Identify the "New Whole": In multi-step problems, the second fraction often refers to a "remaining" amount rather than the original total.
Unit Conversions: Be prepared to convert your final fractional answer into a smaller unit (like feet to inches or hours to minutes) to finish the problem. Answer Summary
The primary answer for the core word problem in this lesson (Anthony’s board) is 8 inches. For other calculation-based problems, ensure you multiply the numerators and denominators across and simplify before or after multiplying.
For more detailed walkthroughs, you can check the G5-M4 Homework Solutions on Embarc Online or follow video guides from creators like Mrs. Setness and Math with Aubrey.
💡 Key Concept: Multiplying Fractions by Fractions In this lesson, the goal is to find a fraction of a fraction using area models and the standard algorithm (multiplying numerators and denominators). 📝 Homework Solutions Problem 1: Area Models Task: Draw an area model to solve the expressions. 1/3 of 1/4
Logic: Divide a square into 4 vertical columns; shade 1. Divide into 3 horizontal rows; shade 1. Result: 1 out of 12 squares are double-shaded. Answer: 1/12 1/2 of 3/5
Logic: Draw 5 vertical columns; shade 3. Split horizontally in half; shade 1 row. Result: 3 out of 10 squares are double-shaded. Answer: 3/10 Problem 2: Standard Algorithm Task: Solve using the multiplication rule ( 2/3 × 3/4 Multiply tops: Multiply bottoms: Simplify: 6/12 = 1/2 5/6 × 1/2 Multiply tops: Multiply bottoms: Answer: 5/12 Problem 3: Word Problem
Scenario: A fundraiser raised some money. 2/5 of the money goes to the school library. 1/3 of the library money is spent on new books. What fraction of the total money is spent on books? Equation: 1/3 of 2/5 →right arrow 1/3 × 2/5 Calculation: Statement: 2/15 of the total money is spent on new books. 🚀 Quick Tips for Success
"Of" means multiply: Whenever you see "1/2 of 1/4," replace "of" with "×."
Check units: Ensure your final answer is simplified to its lowest terms.
Overlap: In area models, the answer is always the part where the two shadings overlap. If you'd like to dive deeper into these problems: Specific question you're stuck on (e.g., Problem 4 or 5) Step-by-step visual for the area models Similar practice problems to test your skills Which part of the homework should we look at next?
The primary objective of Eureka Math Grade 5 Module 4 Lesson 16 Before diving into the answers, let’s clarify the
is to solve real-world word problems using tape diagrams and fraction-by-fraction multiplication. Homework Solutions and Explanations 1. Analyze the Anthony's Board Problem Anthony had an 8-foot board. He cut off three-fourths of the board. He gave
of the remaining piece to his brother. Find the length of the piece given to his brother in inches. Step 1: Find the length of the remaining piece. If Anthony cut off three-fourths one-fourth of the board remains. one-fourth cross 8 feet equals 2 feet Step 2: Find the fraction given to the brother. The brother received of that remaining 2-foot piece. one-third cross 2 feet equals two-thirds foot Step 3: Convert the final answer to inches. Since 1 foot = 12 inches:
two-thirds cross 12 equals 24 over 3 end-fraction equals 8 inches 2. Multi-Step Tape Diagram Application
In this lesson, problems typically follow a "fraction of a fraction" structure. For example, if a problem asks for " three-fourths of a total": Draw a tape diagram representing the whole.
Partition it into the first fraction's units (e.g., fourths).
Subdivide those units to find the second fraction (e.g., halves of the fourths). Key Takeaways for Lesson 16 Tape Diagrams
: Always start by modeling the "whole" and then "cutting" it according to the first fraction mentioned in the problem. "Of" means Multiply : When you see "
the remainder," it signifies a multiplication operation between those two values. Unit Conversions
: Many problems in this lesson require a final conversion from feet to inches or pounds to ounces to provide a complete answer. Explain with an Image Visualize the board problem Create visual
The length of the board piece Anthony gave to his brother is
In Eureka Math Grade 5 Module 4 Lesson 16, the objective is to solve word problems using tape diagrams and fraction-by-fraction multiplication. This lesson applies skills from previous lessons to multi-step real-world scenarios. Core Homework Problems & Answers The Board Problem: Anthony had an 8-foot board and cut off 34three-fourths of it to build a shelf. He gave 13one-third
of the remaining piece to his brother. How many inches was the piece he gave to his brother? Answer: 8 inches.
Relay Race Problem: Four track team members run a relay in 165 seconds. How many minutes did it take? Answer: minutes (or 2 minutes 45 seconds).
General Fraction Operations: Other problems typically involve converting mixed unit measurements (like months to years) and using tape diagrams to visualize "fractions of a remainder". Step-by-Step Guide to Solving Lesson 16 Problems 1. Draw a Tape Diagram Now, they must tackle problems like: "Tom has
Start by drawing a long rectangle (the tape) to represent the "whole" mentioned in the problem (e.g., the 8-foot board). Label the entire length. 2. Partition the Whole
Divide the tape into equal units based on the first fraction mentioned. For the board problem, divide the tape into 4 equal units because the denominator is 4. Shade the part that is "used" or "cut off". 3. Identify the Remainder
Look at the unshaded portion of your tape diagram. In the board example, if 34three-fourths is cut off, 14one-fourth of the board remains ( 4. Multiply Fraction by Fraction If the problem asks for a fraction of the remainder (e.g., 13one-third of the remaining 14one-fourth ), multiply the two fractions together:
13×14=112one-third cross one-fourth equals 1 over 12 end-fraction This tells you the brother received 1121 over 12 end-fraction of the original 8-foot board. 5. Convert Units if Necessary
Many Lesson 16 problems require a final unit conversion (e.g., feet to inches). To find 8 inches: 1121 over 12 end-fraction of 8 feet = 8128 over 12 end-fraction 8128 over 12 end-fraction 12 inches/foot = 8 inches. Final Results Summary Brother's piece: 8 inches. Relay time:
The Eureka Math Grade 5 Module 4 Lesson 16 homework focuses on solving complex word problems using tape diagrams and fraction-by-fraction multiplication. A key skill covered in this lesson is interpreting "fractions of a remainder" in multi-step scenarios. Core Problem Example
A typical problem from this lesson involves a multi-step reduction of a whole. For instance, if Anthony has an 8-foot board and cuts off 34three-fourths of it, and then gives 13one-third
of the remaining piece to his brother, you must find the final length in inches.
Find the first remainderSubtract the first portion from the whole. of the board remains.Length of remainder: .
Calculate the second portionTake the fraction of the remaining piece. .
Convert to the required unitMultiply by 12 to convert feet to inches. . Problem Set Highlights
Tape Diagrams: Students are required to draw visual models to represent the "whole" and partition it according to the problem's fractions.
Area Models: Some problems may use area models or vertical forms to visualize the multiplication of two fractions.
Reasoning: You must explain how you know a certain number of containers or units are necessary, especially when remainders are involved. Answer Key Reference
For the full detailed solutions, you can find the complete answer key for Module 4 on Scribd or follow step-by-step video walkthroughs on the Eureka Math Grade 5 playlist. Final Answer The brother received an 8-inch piece of the board.
Do you have a specific problem number from Lesson 16 that you need help solving? Eureka math grade 5 module 4 lesson 16 homework