eureka math 5th grade module 4 lesson 16 homework

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Eureka Math Grade 5 Module 4 Lesson 16 Answer Key

Engage ny eureka math 5th grade module 4 lesson 16 answer key, eureka math grade 5 module 4 lesson 16 problem set answer key.

Solve and show your thinking with a tape diagram.

Question 1. Mrs. Onusko made 60 cookies for a bake sale. She sold \(\frac{2}{3}\) of them and gave \(\frac{3}{4}\) of the remaining cookies to the students working at the sale. How many cookies did she have left?

Answer: The number of cookies left is 5 cookies.

Explanation: Given that Mrs. Onusko made 60 cookies for a bake sale and she sold \(\frac{2}{3}\) of them. So the number of cookies did she sold is \(\frac{2}{3}\) × 60 which is 40 cookies. So the remaining cookies are 60 – 40 which is 20 cookies. And Mrs. Onusko gave \(\frac{3}{4}\) of the remaining cookies to the students working at the sale, so \(\frac{3}{4}\) × 20 which is 15 cookies. So the number of cookies left is 20 – 15 = 5 cookies.

Question 2. Joakim is icing 30 cupcakes. He spreads mint icing on \(\frac{1}{5}\) of the cupcakes and chocolate on \(\frac{1}{2}\) of the remaining cupcakes. The rest will get vanilla icing. How many cupcakes have vanilla icing?

Answer: The remaining vanilla icing is 9 cupcakes.

Explanation: Given that Joakim is icing 30 cupcakes and he spreads mint icing on \(\frac{1}{5}\) of the cupcakes and chocolate, so the number of mint icing is 30 × \(\frac{1}{5}\) which is 6 cupcakes. And \(\frac{1}{2}\) of the remaining cupcakes have chocolate icing is 30 × \(\frac{1}{2}\) which is 15 cupcakes. And the remaining vanilla icing is 30 – (15 + 6) which is 30 – 21 = 9 cupcakes.

Question 3.

The Booster Club sells 240 cheeseburgers. \(\frac{1}{4}\) of the cheeseburgers had pickles, \(\frac{1}{2}\) of the remaining burgers had onions, and the rest had tomato. How many cheeseburgers had tomato?

Answer: 90 cheeseburgers had tomato.

Explanation: Given that the Booster Club sells 240 cheeseburgers and \(\frac{1}{4}\) of the cheeseburgers had pickles which means the number of cheese that had pickle is 240 × \(\frac{1}{4}\) which is 60 burgers. The number of remaining burgers is 240 – 60 which is 180 cheese burgers. And \(\frac{1}{2}\) of the remaining burgers had onions and rest had tomato which means \(\frac{1}{2}\) × 180 which is 90. Therefore 90 cheeseburgers had tomato.

Question 4. DeSean is sorting his rock collection. \(\frac{2}{3}\) of the rocks are metamorphic, and \(\frac{3}{4}\) of the remainder are igneous rocks. If the 3 rocks left over are sedimentary, how many rocks does DeSean have?

Answer: The number of rocks that DeSean has are 36.

Explanation: Given that DeSean is sorting his rock collection and \(\frac{2}{3}\) of the rocks are metamorphic, and \(\frac{3}{4}\) of the remainder are igneous rocks which means \(\frac{1}{3}\) are igneous rocks, and 3 rocks left over are sedimentary, so the number of rocks that DeSean has are x = \(\frac{2}{3}\)x + \(\frac{3}{4}\) × \(\frac{1}{3}\)x + 3 which is = \(\frac{8}{12}\)x + \(\frac{3}{12}\)x + 3 = \(\frac{11}{12}\)x + 3 \(\frac{1}{12}\)x = 3 x = 36. So the number of rocks that DeSean has are 36.

Question 5. Milan puts \(\frac{1}{4}\) of her lawn-mowing money in savings and uses \(\frac{1}{2}\) of the remaining money to pay back her sister. If she has $15 left, how much did she have at first?

Answer: The money Milan had at first is $40.

Explanation: Given that Milan puts \(\frac{1}{4}\) of her lawn-mowing money in savings and uses \(\frac{1}{2}\) of the remaining money to pay back her sister. Let the money that Milan’s has at first be X, the remaining money will be X – \(\frac{1}{4}\) X = \(\frac{3}{4}\) X. Now we are going to calculate the money to pay back her sister, which is \(\frac{1}{2}\) of the remaining money, which is \(\frac{1}{2}\) × \(\frac{3}{4}\) X which is \(\frac{3}{8}\)X. So the total money Milan had at first = money for saving + money for paying back + the amount of money left X = \(\frac{1}{4}\)X + \(\frac{3}{8}\) X + 15 X – \(\frac{1}{4}\)X – \(\frac{3}{8}\) X = 15 \(\frac{8X – 2X – 3X}{8}\)X = 15 On solving we will get the result as 40. So, the money Milan had at first is $40.

Question 6. Parks is wearing several rubber bracelets. \(\frac{1}{3}\) of the bracelets are tie-dye, \(\frac{1}{6}\) are blue, and \(\frac{1}{3}\) of the remainder are camouflage. If Parks wears 2 camouflage bracelets, how many bracelets does he have on?

Answer: Park has 12 bracelets.

Explanation: Given that Parks is wearing several rubber bracelets and \(\frac{1}{3}\) of the bracelets are tie-dye, \(\frac{1}{6}\) are blue, and \(\frac{1}{3}\) of the remainder are camouflage and Park wears 2 camouflage bracelets. Let the sum of all braclets be X, and Park wears 2 camouflage bracelets, that is, \(\frac{1}{3}\) × (1 – \(\frac{1}{3}\) – \(\frac{1}{6}\)) × X = 2 \(\frac{1}{3}\) × (\(\frac{6}{6}\) – \(\frac{2}{6}\) – \(\frac{1}{6}\)) × X = 2 \(\frac{1}{3}\) × \(\frac{3}{6}\) × X = 2 \(\frac{1}{6}\) × X = 2 X = 2 ÷ \(\frac{1}{6}\) X = 2 × 6 = 12.

Question 7. Ahmed spent \(\frac{1}{3}\) of his money on a burrito and a water bottle. The burrito cost 2 times as much as the water. The burrito cost $4. How much money does Ahmed have left?

Answer: Ahmed have left $12.

Explanation: Given that Ahmed spent \(\frac{1}{3}\) of his money on a burrito and a water bottle and the burrito cost 2 times as much as the water, so the water is the burrito cost divided by 2. So water = \(\frac{4}{2}\) which is $2. And water + burrito is $2 + $4 which is $6. And this $6 is \(\frac{1}{3}\) of the money and Ahmed have left \(\frac{2}{3}\) of the money, so $6 ÷ \(\frac{1}{3}\) = X ÷ \(\frac{2}{3}\) X = 6 × (\(\frac{2}{3}\) ÷ \(\frac{1}{3}\), on solving we will get the result as $12. So the Ahmed have left $12.

Eureka Math Grade 5 Module 4 Lesson 16 Exit Ticket Answer Key

Solve and show your thinking with a tape diagram. Three-quarters of the boats in the marina are white, \(\frac{4}{7}\) of the remaining boats are blue, and the rest are red. If there are 9 red boats, how many boats are in the marina?

Answer: The total number of boats in the marine is 84.

Explanation: Let the number of boats in the marina be X, and the number of white boats be \(\frac{3}{4}\)X. Then the remaining boats will be X – \(\frac{3}{4}\)X which is \(\frac{X}{4}\). And now, there are \(\frac{4}{7}\) of the boats are blue, thus the number of blue boats is \(\frac{4}{7}\) × \(\frac{X}{4}\) which is \(\frac{X}{7}\). And the number of red boats is \(\frac{X}{4}\) – \(\frac{X}{7}\) which is \(\frac{3X}{28}\). And if there are 9 red boats, then \(\frac{3X}{28}\) = 9 and 3X = 9 × 28 on solving X = 84. The total number of boats in the marine is 84.

Eureka Math Grade 5 Module 4 Lesson 16 Homework Answer Key

Question 1. Anthony bought an 8-foot board. He cut off \(\frac{3}{4}\) of the board to build a shelf and gave \(\frac{1}{3}\) of the rest to his brother for an art project. How many inches long was the piece Anthony gave to his brother?

Answer: Anthony gave his brother 8 inches board.

Explanation: Given that Anthony bought an 8-foot board, as 1 foot is 12 inches and 8 feet is 8 × 12 which is 96 inches. Anthony cuts \(\frac{3}{4}\) to build a shelf, so \(\frac{3}{4}\) × 96 which is 72 inches. So the left board after cutting is 96 – 72 which is 24 inches. And Anthony gave \(\frac{1}{3}\) of the leftover of his brother which is \(\frac{1}{3}\) × 24 = 8. So Anthony gave his brother 8 inches board.

Question 2. Riverside Elementary School is holding a school-wide election to choose a school color. Five-eighths of the votes were for blue, \(\frac{5}{9}\) of the remaining votes were for green, and the remaining 48 votes were for red. a. How many votes were for blue?

Answer: The number of blue votes is 180 votes.

Explanation: Given that Five-eighths of the votes were for blue and \(\frac{5}{9}\) of the remaining votes were for green which means \(\frac{5}{9}\) × \(\frac{3}{8}\) which is \(\frac{5}{24}\). And the number of red is 1 – (\(\frac{5}{8}\) + \(\frac{5}{24}\) which is \(\frac{1}{6}\). So the total amount of people is 48 × 6 which is 288 people. So the number of blue votes is 288 × \(\frac{5}{8}\) which is 180 votes.

b. How many votes were for green?

Answer: The number of votes were green is 60 votes.

Explanation: As the total amount of people is 48 × 6 which is 288 people. So the number of green votes is 288 × \(\frac{5}{24}\) which is 60 votes.

c. If every student got one vote, but there were 25 students absent on the day of the vote, how many students are there at Riverside Elementary School?

Answer: The total number of students are there at Riverside Elementary School is 313 students.

Explanation: Given that, If every student got one vote, but there were 25 students absent on the day of the vote. So the total number of students are there at Riverside Elementary School is 288 + 25 which is 313 students.

d. Seven-tenths of the votes for blue were made by girls. Did girls who voted for blue make up more than or less than half of all votes? Support your reasoning with a picture.

Explanation: Less than half of all the girls who voted for blue. Because, as Seven-tenths of the votes for blue were made by girls which means \(\frac{7}{10}\) × 180 = 126 which is less than half

e. How many girls voted for blue?

Answer: The number of girls voted for blue is 126.

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5th Grade Math Parent Guide

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Activities for home

• Create number cubes or spinners and have the student identify the place value and value of different digits in that number.
• Roll or pick numbers to create decimals. Add, subtract, multiply, or divide the decimals.
• Find the batting averages or other statistics in the sports section of a newspaper and add or subtract the statistics.
• Estimate and find the sums and differences of items at the store and in restaurants.
• Practice basic addition, subtraction, multiplication and division facts.
• Roll or pick numbers to create decimals. Compare and order the numbers.
• Choose a four-digit number. Multiply and divide by powers of 10 (10, 100, 1,000, etc.) by moving the decimal point left or right as appropriate.     
• Create number cubes or spinners and have the student identify the place value and value of different digits in that number. - Estimate and find the sums and differences of items at the store and in restaurants. - Practice basic addition, subtraction, multiplication and division facts.
• Choose a four-digit number. Multiply and divide by powers of 10 (10, 100, 1,000, etc.) by moving the decimal point left or right as appropriate.
• Compare the estimated volume of a carton or bottle of liquid (such as 1/2 gallon juice or milk or two liter bottle of lemonade) in cubic inches or centimeters to its stated volume in ounces or milliliters. - Make up numbers, roll numbers with dice, or find numbers (on labels) and compare them.
• Create rules (ex. n = 3) and have your student extend the number pattern (3, 6, _ , _).
• Create a number pattern and have your student write the rule. - Create an input/ output machine (function table) for a given rule and have the student fill in the missing Inputs and Outputs.
• Create an input/ output machine (function table) for an unknown rule and have the student fill in the missing Inputs and Outputs and write the rule.
• Find numbers and write them in expanded form.
• Draw pictures and make models of numbers. - Practice addition, subtraction, multiplication and division facts.
• Create or pick numbers to make fractions. Add, subtract, or simplify the fractions that you find.
• Find examples of fractions around the house or neighborhood. Add, subtract, multiply, divide or simplify the fractions that you find.
• Create numbers to use in fractions. Draw these fractions as parts of a whole or set.
• Use measuring cups when baking or cooking.
• Draw different shapes. Divide them into different fractions.

• Identify the use of decimals in sporting events and in newspapers.
• Practice multiplication and division facts.
• Find the volume of real-world objects in your home.
• Compare the estimated volume of a carton or bottle of liquid (such as 1/2 gallon juice or milk or two liter bottle of lemonade) in cubic inches or centimeters to its stated volume in ounces or milliliters.
• Name two-dimensional figures and find examples at home.
• Draw different polygons within a piece of triangle grid paper, or use combinations of triangles to create other polygons.
• Make flash cards of different geometric figures and their properties.
• Identify, describe, and different household objects as two-dimensional figures.
• Use a compass or a computer to draw geometric figures.    

Helpful Videos

• Eureka Math Lesson Specific Homework Videos
• Module 1 lesson videos
• Module 2 lesson videos
• Module 3 lesson videos
• Module 4 lesson videos
• Module 5 lesson videos
• Module 6 lesson videos

Need more help?   Find additional content videos below.

Topic A -Multiplicative Patterns on the Place Value Chart

• Place Value in decimals
• Use base ten blocks to understand how place value decreases
• with each shift to the right in a multi-digit number
• Place value chart and number disks show how place value decreases when dividing
• Recognize place value relationships by multiplying and dividing by ten  
• Exponents-Understand how multiplication by a power of ten causes decimal shifts
• Exponents-Understand how multiplication by a power of ten causes decimal shifts (video 2)  
• Exponents-Understand how division by a power of ten causes decimal shifts

Topic B-Decimal Fractions and Place Value Patterns     

• Expanded Notation
• Comparing decimals using base ten models and place value chart

Topic C- Place Value and Rounding Decimal Fractions

• Rounding decimals to any place
• Vertical number line to round decimals

Topic D- Adding and Subtracting Decimals

• Adding decimals using base ten blocks
• Subtracting decimals using base ten blocks
• Adding decimals example 1
• Adding decimals example 2
• Adding decimals word problem   
• Subtracting decimals
• Subtracting decimals word problem
• Adding and Subtracting decimals word problem exercise

Topic E- Multiplying Decimals

• Multiplying decimals - shown as repeated addition using base ten models
• Using a place value chart and area model to multiply decimal times a single-digit whole number
• Divide decimal by a single-digit whole number
• Place Value Slider
• Decimal Identification Game
• Rounding Decimals

Topic A- Mental Strategies for Multi-Digit Whole Number Multiplication

• Multiplying by multiples of 10

Topic B- The Standard Algorithm for Multi-Digit Whole Number Multiplication

• Using area model to multiply
• Multiplication of multi-digit whole numbers (with array/ area models)
• Multiplication Algorithm

Topic C- Decimal Multi-Digit Multiplication

• Multiplying decimals as repeated addition in a model
• Multiplication of a whole number and decimal fraction using area model
• Multiplying decimals by multi-digit whole numbers

Topic D-  Measurement Word Problems with Whole Numbers and Decimal Multiplication

• Converting feet to inches
• Converting in a real-life problem

Topic E- Mental Strategies for Multi-Digit Whole Number Division

Topic g- partial quotients and multi-digit decimal division.

• Adding zero(s) to dividend

Topic A  -  Equivalent Fractions

Topic B   - Making like units pictorially

• Finding a common denominator using  area models
• Adding fractions with unlike denominators using area models
• Subtracting fractions with unlike denominators using area models

Topic C - Making like units numerically

• Adding mixed numbers using area models and renaming as improper fractions
•   Subtracting mixed numbers using area models

Topic D  -  Further applications

• Using benchmark fractions to determine the reasonableness of sums and differences
• Estimating answers to problems using area models

Topic B - Fractions as Division

• Understanding fractions as division
• My share of soap (word problem)

Topic C- Multiplication of a Whole number by a fraction

• Multiplying fractions and whole numbers
• Two ways to conceptualize the product of a fraction and a whole number
• Multiplying fraction times a whole number word problem
• Visualizing fraction multiplication
• Fraction times fraction- area model
• Renaming fractions before multiplying
• Multiplying fractions word problem
• Converting feet to yards
• Converting gallons to cups- mixed number of gallons
• Converting yards to inches- mixed number of yards
• Multiplication as scaling
• Dividing a whole by a fraction
• Dividing a unit fraction by a whole number
• Numerical Expressions as a written description
• Determine whether a numerical expression is accurate

Topic A -  Concept of Volume

• What is meant by 1-D, 2-D, and 3-D
• Difference between a square unit and a cubic unit
• Finding the volume by analyzing the layers
• Finding the volume-order does not matter

Topic B - Volume and the Operations of Multiplication and Addition

• Using the formula (L x W x H) to find the volume
• Using the formula (b x Hh) to find the volume
• Finding missing lengths of composite 3D prisms
• Finding the volume of complex 3D prisms
• Area of Rectangular Figures with Fractional Side Lengths

Topic D - Drawing, Analysis, and Classification of Two-Dimensional Shapes

• Quadrilateral Properties
• Attributes of polygons
• Kites as a mathematical shape
• How many cubes
• Compute volume
• Kindergarten

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