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# Eureka Math Lesson 15 Homework Answers

Do you need some help with Eureka Math Lesson 15 Homework Answers for Grade 5? Do you want to learn how to find the area of rectangles with fractional side lengths and how to multiply fractions by mixed numbers? If so, you are in the right place. In this article, we will show you how to solve some of the problems from the Eureka Math curriculum for Grade 5 Module 5 and Module 4 Lesson 15. We will also share some tips and tricks to master Eureka Math and ace your homework.

## Eureka Math Lesson 15 Homework Answers

In this lesson, you will learn how to find the area of rectangles with fractional side lengths by multiplying fractions. You will also learn how to use rectangular fraction models to explain your thinking. Here are some examples of the problems you will encounter in this lesson:

• The length of a flowerbed is 4 times as long as its width. If the width is \$$\\frac38\$$ meter, what is the area?

• Mrs. Johnson grows herbs in square plots. Her basil plot measures \$$\\frac59\$$ yard on each side. Find the total area of the basil plot.

• Janet bought 5 yards of fabric \$$\\frac23\$$-feet wide to make curtains. She used \$$\\frac13\$$ of the fabric to make a long set of curtains and the rest to make 4 short sets. Find the area of the fabric she used for each of the short sets.

To solve these problems, you need to apply the formula for finding the area of a rectangle: Area = length x width. You also need to know how to multiply fractions by fractions. Here are some steps to follow:

• Write the fractions in simplest form.

• Multiply the numerators and denominators separately.

• Simplify the result if possible.

• Use a rectangular fraction model to show your work.

For example, to find the area of the flowerbed, you can do the following:

Step 1: Write the fractions in simplest form.

The width of the flowerbed is \$$\\frac38\$$ meter and the length is 4 times as long as the width, which means \$$\\frac38\$$ x 4 = \$$\\frac128\$$ or \$$\\frac32\$$ meter.

Step 2: Multiply the numerators and denominators separately.

The area of the flowerbed is \$$\\frac32\$$ x \$$\\frac38\$$ = \$$\\frac916\$$ square meter.

Step 3: Simplify the result if possible.

The fraction \$$\\frac916\$$ cannot be simplified further, so it is the final answer.

Step 4: Use a rectangular fraction model to show your work.

You can draw a rectangle with a width of \$$\\frac38\$$ and a length of \$$\\frac32\$$. Then, divide it into equal parts according to the denominators. You can shade \$$\\frac916\$$ of the rectangle to represent the area of the flowerbed.

In this lesson, you will learn how to multiply fractions by mixed numbers using fraction models or equations. You will also learn how to solve word problems involving multiplication of fractions by mixed numbers. Here are some examples of the problems you will encounter in this lesson:

Phillips family traveled \$$\\frac14\$$ of

the distance

to his grandmothers house on Saturday.

They traveled \$$\\frac13\$$

of

the remaining distance on Sunday.

What fraction

of

the total distance

• to his grandmothers house was traveled on Sunday?

Santino bought a \$$\\frac34\$$-pound bag

of chocolate chips.

He used \$$\\frac16\$$

of

the bag while baking.

How many pounds

• of chocolate chips did he use while baking?

Farmer Dave harvested his corn.

He stored \$$\\frac12\$$

of his corn in one large silo and \$$\\frac14\$$

of

the remaining corn in a small silo.

The rest was taken

to market

to be sold.

If he harvested 18 tons

of corn,

how many tons did he take

• to market?

To solve these problems,

you need

to apply

the rule for multiplying fractions by mixed numbers:

Convert

the mixed number

to an improper fraction

and then multiply as usual.

You also need

to know how

to convert an improper fraction

back

to a mixed number

if needed.

Here are some steps

to follow:

Write

the mixed number

as an improper fraction

by multiplying

the whole number

by

the denominator

to

• the numerator.

Multiply

• the numerators and denominators separately.

Simplify or reduce

• the result if possible.

If

the result is an improper fraction,

write it as a mixed number by dividing

the numerator by

the denominator and writing

• the remainder as a fraction.

For example,

to find how many pounds

of chocolate chips Santino used while baking,

you can do

the following:

Step 1: Write

the mixed number as an improper fraction.

Santino used latex]\\frac 1 6 [/latex]of

a latex]\\frac 3 4 [/latex]-pound bag

of chocolate chips,

which means latex]\\frac 1 6 [/latex]x latex]\\frac 3 4 [/latex].

To write latex]\\frac 3 4 [/latex]as an improper fraction,

we multiply latex]3[/latex]x latex]4[/latex]and add it

to latex]3[/latex],

which gives us latex]\\frac 15 4 [/latex].

So we have latex]\\frac 1 6 [/latex]x latex]\\frac 15 4 [/latex].

Step 2: Multiply

the numerators and denominators separately.

The product

of latex]\\frac 1 6 [/latex]and latex]\\frac 15 4 [/latex]is latex]\\frac 15 24 [/latex],

because latex]1[/latex]x latex]15[/latex]= latex]15[/latex]and latex]6[/latex]x latex]4[/latex]= latex]24[/latex].

So we have latex]\\frac 15 24 [/latex].

Step 3: Simplify or reduce

the result if possible.

The fraction

latex]\\frac 15 24 [/latex]can be simplified by dividing both numerator and denominator by latex]3[/latex],

which gives us latex]\\frac 5 8 [/latex].

So we have latex]\\frac 5 8 [/latex].

Step 4: If

the result is an improper fraction,

write it as a mixed number by dividing

the numerator by

the denominator and writing

the remainder as a fraction.

The fraction

latex]\\frac 5 8 [/latex]is not an improper fraction,

so we do not need

to convert it

to a mixed number.

It is already in simplest form.

So we have latex]\\frac 5

In this lesson, you will learn how to use place value charts to multiply and divide decimals by powers of 10. You will also learn how to use exponents to write powers of 10 and how to use the metric system to convert units of measurement. Here are some examples of the problems you will encounter in this lesson:

• Write \$$3.2\$$ x \$$10^3\$$ in standard form.

• Write \$$0.005\$$ x \$$10^-2\$$ in standard form.

• Write \$$4,500\$$ in unit form using exponents.

• Convert 5 kilometers to meters.

• Convert 300 centimeters to meters.

To solve these problems, you need to know how to use place value charts to multiply and divide decimals by powers of 10. You also need to know how to use exponents to write powers of 10 and how to use the metric system to convert units of measurement. Here are some steps to follow:

• Use a place value chart to show the value of each digit in a decimal number.

• To multiply a decimal by a power of 10, move the decimal point to the right as many places as the exponent.

• To divide a decimal by a power of 10, move the decimal point to the left as many places as the exponent.

• To write a power of 10 using exponents, write 10 as the base and the number of zeros as the exponent.

• To convert units of measurement in the metric system, use the prefixes kilo-, hecto-, deka-, deci-, centi-, and milli- to indicate powers of 10.

For example, to write \$$3.2\$$ x \$$10^3\$$ in standard form, you can do the following:

Step 1: Use a place value chart to show the value of each digit in \$$3.2\$$.

You can write \$$3.2\$$ as \$$3 + \\frac210\$$ or \$$3 + 0.2\$$. You can use a place value chart to show that 3 is in the ones place and 2 is in the tenths place.

Ones Decimal point Tenths

--- --- ---

3 . 2

Step 2: To multiply \$$3.2\$$ by \$$10^3\$$, move the decimal point to the right as many places as the exponent.

The exponent of \$$10^3\$$ is 3, which means there are 3 zeros in \$$10^3\$$. To multiply \$$3.2\$$ by \$$10^3\$$, we need to move the decimal point 3 places to the right. We can add zeros as placeholders if needed.

Ones Decimal point Tenths Hundreds Thousands

--- --- --- --- ---

3 . 2 0 0

The result is \$$3200\$$.

Step 3: Write \$$3200\$$ in standard form.

Standard form is when we write a number without using exponents or fractions. To write \$$3200\$$ in standard form, we just write it as it is: \$$3200\$$.

Therefore, \$$3.2\$$ x \$$10^3\$$ = \$$3200\$$ in standard form.

## Tips and Tricks for Eureka Math Lesson 15 Homework Answers for Grade 5

Now that you have learned how to solve some of the problems from Eureka Math Lesson 15 Homework Answers for Grade 5, here are some tips and tricks to help you master Eureka Math and ace your homework:

• Practice using place value charts and exponents to multiply and divide decimals by powers of 10. This will help you understand how decimals and powers of 10 are related and how they affect the value of a number.

• Use estimation and mental math to check your answers. For example, if you are multiplying \$$4.5\$$ by \$$10^2\$$, you can estimate that the answer should be close to \$$450\$$, because you are moving the decimal point two places to the right. If you get an answer that is very different from your estimate, you may have made a mistake.

• Review the metric system and its prefixes. The metric system is based on powers of 10, which makes it easy to convert units of measurement by moving the decimal point. The prefixes kilo-, hecto-, deka-, deci-, centi-, and milli- indicate how many places you need to move the decimal point when converting units. For example, kilo- means \$$10^3\$$, so to convert kilometers to meters, you need to move the decimal point three places to the right.

## Conclusion

In this article, we have shown you how to solve some of the problems from Eureka Math Lesson 15 Homework Answers for Grade 5. We have also shared some tips and tricks to help you master Eureka Math and ace your homework. We hope you have learned something new and useful from this article. Remember, practice makes perfect, so keep practicing and reviewing the concepts and skills you have learned. Eureka Math is a great way to learn math and prepare for the future. We wish you all the best in your math journey! 6c859133af