All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 8 Multiplication as Scaling** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 8 Multiplication as Scaling

Scaling is the process of resizing a number when you multiply by a fraction that is greater than or less than 1.

**Draw It**

Multiply the number 2 by three fractions greater than 1.

1. Multiply the number 2 by three different fractions greater than 1, such as 1\(\frac{1}{5}\), 1\(\frac{1}{2}\), and 1\(\frac{3}{4}\).

2 × 1\(\frac{1}{5}\) = 2 × 1\(\frac{1}{2}\) = 2 × 1\(\frac{3}{4}\) =

Answer:

The above-given equations:

2 x 1 1/5

1 1/5 is a mixed fraction. convert it into an improper fraction.

1 1/5 = 6/5

Now multiply:

2 x 6/5 = 12/5

Converting to a mixed number using long division with remainders for 12 ÷ 5

12 ÷ 5 = 2 R2

Therefore,

2. Plot 2 on the number line. Then plot the products on the number line.

Answer:

Representing fractions on a number line means that we can plot fractions on a number line, which is similar to plotting whole numbers and integers. Fractions represent parts of a whole. So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction.

Mixed fractions on the number line:

Mixed fractions have two parts, one whole number and one proper fraction. To represent mixed fractions on a number line, first, we have to mark two points: the whole number part on the left and its successor on the right.

3. Compare the products. Circle whether the products are greater than, less than, or equal to 2.

greater than 2 less than 2 equal to 2

Multiplying a number by a fraction greater than one results in a product that is ____ than the number.

Answer:

Now we have to compare the products.

Multiplying a number by a fraction greater than one results in a product that is greater than the number.

**Try It**

**Multiply the number 2 by three fractions less than 1.**

1. Multiply 2 by three different fractions less than 1 such as \(\frac{1}{4}\), \(\frac{1}{2}\), and \(\frac{5}{8}\).

2 × \(\frac{1}{4}\) = 2 × \(\frac{1}{2}\) = 2 × \(\frac{5}{8}\) =

Answer:

2. Plot 2 on the number line. Then plot the products on the number line.

Answer:

Representing fractions on a number line means that we can plot fractions on a number line, which is similar to plotting whole numbers and integers. Fractions represent parts of a whole. So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction.

Mixed fractions on the number line:

Mixed fractions have two parts, one whole number and one proper fraction. To represent mixed fractions on a number line, first, we have to mark two points: the whole number part on the left and its successor on the right.

3. Compare the products. Circle whether the products are greater than, less than, or equal to 2.

greater than 2 less than 2 equal to 2

Multiplying a number by a fraction less than one results in a product that is ____ than the number.

Answer:

Multiplying a number by a fraction less than one results in a product that is less than the number.

**Talk About it**

Question 1.

Predict whether the product of 3 and \(\frac{4}{5}\) is greater than, less than, or equal to 3. Explain.

Answer:

The above-given equation:

product of 3 and 4/5. This can be written as:

3 x 4/5 = 12/5 = 2 2/5.

12/5 = 2.4 which is less than 3

Therefore, the product is less than 3.

Question 2.

**Mathematical PRACTICE 3 Draw a Conclusion** Predict whether the product of 2 and 2\(\frac{1}{5}\) is greater than, less than, or equal to 2. Explain.

Answer:

The above-given equation:

product of 2 and 2 1/5

2 x 2 1/5

2 1/5 is a mixed fraction. Convert it into an improper fraction.

2 1/5 = 11/5

Now multiply:

2 x 11/5

= 22/5 = 4.4

Therefore, the product is greater than 2.

**Practice It**

**Without multiplying, circle whether each product is greater than, less than, or equal to the whole number.**

Question 3.

2 × \(\frac{1}{8}\)

greater than

less than

equal to

Answer:

without multiplying we need to circle the answer.

if we multiply we get the answer 1/4 which is less than 2. So we circled less than.

roughly we can do the problem

2 x 1/8 = 2/8 = 1/4

Question 4.

10 × 1\(\frac{3}{5}\)

greater than

less than

equal to

Answer:

If we do roughly the given problem:

10 x 1 3/5

1 3/5 is a mixed fraction. Convert it into an improper fraction.

1 3/5 = 8/5

Now multiply: 10 x 8/5

10 get cancelled in 5 table { 5 x 2 = 10}

2 x 8 = 16 which is greater than 10.

Therefore, we have to circle greater than.

Question 5.

1\(\frac{3}{4}\) × 4

greater than

less than

equal to

Answer:

The above-given: 1 3/4 x 4

1 3/4 is a mixed fraction. convert it into improper fractions.

1 3/4 = 7/4

Now multiply: 7/4 x 4 = 7

Hence 7 is greater than 4.

Question 6.

12 × \(\frac{5}{6}\)

greater than

less than

equal to

Answer:

The above-given:

12 x 5/6

If we do roughly the given problem.

given the whole number:12

The product we got 10

compare both 10 and 12

10 < 12.

Therefore, 10 is less than 12.

Question 7.

1\(\frac{1}{3}\) × 2

greater than

less than

equal to

Answer:

The above-given:

1 1/3 x 2

If we do roughly the given problem:

The given whole number is 2

The product we got is 2/3 which is less than 2.

Question 8.

\(\frac{3}{5}\) × 6

greater than

less than

equal to

Answer:

The above-given:

3/5 x 6

**Algebra Without multiplying, circle whether the unknown in each equation is greater than, less than, or equal to the whole number.**

Question 9.

1\(\frac{2}{3}\) × 4 = b

greater than

less than

equal to

Answer:

The above-given:

1 2/3 x 4 = b

Question 10.

8 × \(\frac{4}{5}\) = h

greater than

less than

equal to

Answer:

The above-given:

8 x 4/5 = h

Question 11.

1 × 5 = k

greater than

less than

equal to

Answer:

The above-given:

1 x 5 = k

k = 5

Question 12.

6 × \(\frac{1}{3}\) = n

greater than

less than

equal to

Answer:

The above-given:

6 x 1/3 = n

n = 2

**Apply It**

**For Exercises 13-15, analyze each product in the table.**

Question 13.

Why is the first product less than \(\frac{3}{4}\)?

Answer:

The above-given:

The first product and its factors are given in the table.

1/2 x 3/4 = 3/8

3/8 is smaller than 3/4

3/8 = 0.375

3/4 = 0.75

3/8 is 50% smaller than 3/4.

Question 14.

Why is the product of 1 and \(\frac{3}{4}\) equal to \(\frac{3}{4}\)?

Answer:

The above-given:

1 x 3/4 = 3/4

if we multiply anything by 1 we get the same product

So, they are equal.

Question 15.

Mathematical PRACTICE 6 Explain to a Friend Miranda spent \(\frac{1}{5}\) of her time cooking pasta. If she spent 2 hours cooking, did Miranda spend more than, less than, or equal to 2 hours cooking pasta? Explain.

Answer:

The above-given:

The time she spent on her time cooking pasta = 1/5

The number of hours she spent cooking = 2

2 x 1/5 = 2/5

Question 16.

**Mathematical PRACTICE 6 Explain to a Friend** Miranda spent \(\frac{1}{5}\) of her time cooking pasta. If she spent 2 hours cooking, did Miranda spend more than, less than, or equal to 2 hours cooking pasta? Explain.

Answer:

The above-given:

The time she spent on her time cooking pasta = 1/5

The number of hours she spent cooking = 2

2 x 1/5 = 2/5

Question 17.

**Mathematical Practice 3 Which One Doesn’t Belong?** Circle the multiplication expression that does not belong based on scaling. Explain.

Answer:

2/5 x 3 = 6/5 = 1.2

1 1/2 x 3 = 3/2 x 3 = 9/2 = 4.5

3 x 3/5 = 9/5 = 1.8

3 x 1/2 = 3/2 = 1.5

The three factors are having products that are less than 3.

And the one factor which is circled is having a product greater than 3. It is different from the remaining so I circled it.

**Write About It**

Question 18.

How can I use scaling to help predict the product of a number and a fraction?

Answer:

I can predict the size of the product based on the size of the factors. For example fraction × fraction = smaller fraction, fraction × whole number = smaller number, whole number × mixed number = larger than the original whole number.

### McGraw Hill My Math Grade 5 Chapter 10 Lesson 8 My Homework Answer Key

**Without multiplying, circle whether each product is greater than, less than, or equal to the whole number.**

Question 1.

4 × \(\frac{1}{7}\)

greater than less than equal to

Answer:

The above-given:

4 x 1/7

if we do roughly the given fraction:

The above-given whole number is 4.

The product we got is 4/7

In decimals, 0.57 is less than the whole number. So we have rounded the less than.

Question 2.

12 × 2\(\frac{5}{6}\)

greater than less than equal to

Answer:

The above-given equation:

12 x 2 5/6

2 5/6 is a mixed fraction. So we have to convert it into an improper fraction.

The above-given whole number is 12

The product we got is 34

compare both the numbers

34 > 12 so we rounded greater than.

**Problem Solving**

Question 3.

Maresol spent \(\frac{4}{5}\) of her allowance on a pair of jeans. If she received $15 for allowance, did Maresol spend more than, less than, or equal to $15 on the jeans? Explain.

Answer:

The above-given:

A certain part of the amount spent by Marisol on a pair of jeans = 4/5

The allowances she received = $15

The equation is 15 x 4/5

she spent less than her allowances.

The actual allowance is $15

The amount she spent on jeans is $12

comparing both 12 < 15

so less than is rounded.

Question 4.

Dee used 2\(\frac{1}{3}\) cups of sugar for a cake recipe. If the amount of sugar the container holds is 3 times the amount she used, does the container hold more than, less than, or equal to 3 cups of sugar? Explain.

Answer:

The number of cups of sugar Dee used = 2 1/3

The number of cups a container can hold = 2 1/3 x 3

2 1/3 is a mixed fraction so convert it into an improper fraction.

The above-given whole number: 3

The container can hold 7 cups.

now compare both

7 > 3

So more than is rounded.

Question 5.

Derek ran \(\frac{3}{8}\) of a race before he had to stop for a break. If the race is 6 miles long, did Derek run more than, less than, or equal to 6 miles before he took a break? Explain.

Answer:

The number of races Derek ran before break = 3/8

The number of miles = 6

The equation is 3/8 x 6

9/4 < 6 so we rounded less than.

Question 6.

**Mathematical PRACTICE 3 Which One Doesn’t Belong?** Circle the multiplication expression that does not belong based on scaling. Explain.

6 × 2\(\frac{1}{2}\) 6 × 1\(\frac{3}{5}\) \(\frac{1}{2}\) × 6 2\(\frac{2}{5}\) × 6

Answer:

The above-given equations:

The circled one differs from the other three equations because all three equations are greater than the given whole number which is 6. And the one which is circled, the product we got is 3 which is less than 6.

**Vocabulary Check**

Question 7.

Fill in the blank with the correct term or number to complete the sentence. ____ is the process of resizing a number when you multiply by a fraction that is greater than or less than 1.

Answer: Scaling

– Scaling is the factor which is used to represent the object size. The size of the object can be shown by increasing or decreasing its original size. In general, the represented size of the object increased for the small object whereas it decreased for the bigger object. Scaling is used for better viewing of an object. The ratio by which an object’s size increases or decreases is called a scale factor.

– Scale factor is the ratio between the corresponding measurement of an object and the representation of that object. A scale factor is a whole number or greater than 1 to make a larger copy. The scale factor is a fraction or less than 1 to make a smaller copy. Therefore, the scale factor can be expressed by any number or fraction. Also, the scale factor can be expressed using the colon (:), such as

Original sized object: Representation-sized object

where, Representation sized object = Any number x Original sized object (in case of larger copy)

or, Representation sized object = 1/ any number