FRACTION MULTIPLICATION AND THE PRODUCTS OF

DECIMALSLesson 6.2.11

ROUNDING DECIMALS - TENTHS

Round each number to the nearest tenth

310.2866.805118.380815.755877.7112.261

answers

ROUNDING DECIMALS - HUNDREDTHS

Round each number to the nearest hundredth.487.36222.700 159.4102.19058.13910.886

answers

APPLICATION PROBLEM

A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable.

APPLICATION PROBLEM SOLUTION 1

A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable.9.5

in

?

9.5 in ÷ 2 = 4.75 in(9.5 x .5 = 4.75 in)9.5 (3) + 4.75

= 9 (3) + .5 (3) + 4.75 = 27 + 1.5 + 4.75 = 33.25 inches

Estimation:10 x 4 = 40 (over estimate)or10 x 3.5 = 35

The tree will grow 33.25 inches in 3.5 years.

APPLICATION PROBLEM SOLUTION 2

A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable.

Year .5 1 1.5 2 2.5 3 3.5

Growth (in) 4.75 9.5 14.25 19.0 23.75 28.5 33.25

The tree will grow 33.25 inches in 3.5 years.

EXPLORATORY CHALLENGE

Work in small groups to complete the two given problems.

Show all of your work that supports your solutions and the placement of the decimal in the product.

After finding each product, use previous knowledge to prove your product has the decimal in the correct location. Be prepared to present your proof to the class.

EXPLORATORY CHALLENGE 1

Calculate the product: 34.62 x 12.8 Some possible proofs: 34.62 x 12.8 = 443.136

Using estimation: . If the decimal was located in a different place, the product would not be close to .

Using fractions: = 443.136.

The problem involves a hundredth x a tenth. . 443,136 x The digits shift 3 times to the right.

EXPLORATORY CHALLENGE 2

Xavier earns per hour working at the nearby grocery store. Last week, Xavier worked for hours. How much money did Xavier earn last week? Remember to round to the nearest penny.11.5 x 13.5 = 155.25

Some possible proofs:• Use estimation 12 x 14 = 168. If the decimal was located in a

different place, the product would not be close to 168.

• Use fractions: The decimal will be in the hundredths place: $155.25.

• The problem involves a tenth x a tenth. 15,525 x The digits shift 2 places to the right.

DISCUSSION

Do you see a connection between the number of decimal digits in the factors and the product? In the first problem, there are two decimal digits in the first factor and

one decimal digit in the second factor, which is a total of three decimal digits. The product has three decimal digits.

In the second problem, both factors have one decimal digit for a total of two decimal digits in the factors. The product also has two decimal digits.

PROBLEMS 1 - 4

1. Calculate the product. . × . 𝟑𝟐𝟒 𝟓𝟔 𝟓𝟒 𝟖𝟐

𝟑𝟐𝟒. × . = , . 𝟓𝟔 𝟓𝟒 𝟖𝟐 𝟏𝟕 𝟕𝟗𝟐 𝟑𝟕𝟗𝟐2. Kevin spends $ . on lunch every week during the school year. If there are . weeks 𝟏𝟏 𝟐𝟓 𝟑𝟓 𝟓

during the school year, how much does Kevin spend on lunch over the entire school year? Remember to round to the nearest penny. 𝟏𝟏. × . = . ≅ . Kevin would spend $ . on lunch over the entire school year. 𝟐𝟓 𝟑𝟓 𝟓 𝟑𝟗𝟗 𝟑𝟕𝟓 𝟑𝟗𝟗 𝟑𝟖 𝟑𝟗𝟗 𝟑𝟖

3. Gunnar’s car gets . miles per gallon, and his gas tank can hold . gallons of gas. How 𝟐𝟐 𝟒 𝟏𝟕 𝟖𝟐many miles can Gunnar travel if he uses all of the gas in the gas tank? 𝟐𝟐. × . = . Gunnar can drive . miles on an entire tank of gas.𝟒 𝟏𝟕 𝟖𝟐 𝟑𝟗𝟗 𝟏𝟔𝟖 𝟑𝟗𝟗 𝟏𝟔𝟖

4. The principal of East High School wants to buy a new cover for the sand pit used in the long jump competition. He measured the sand pit and found that the length is . feet and the 𝟐𝟗 𝟐width is . feet. What will the area of the new cover be? 𝟗 𝟖𝟐𝟗. × . = . The cover should have an area of . square feet.𝟐 𝟗 𝟖 𝟐𝟖𝟔 𝟏𝟔 𝟐𝟖𝟔 𝟏𝟔

MATH TALK

Do you see a connection between the number of decimal digits in the factors and the product?

How can we use information about the factors to determine the largest place value of the product and the number of decimal digits in the product?

EXIT TICKET

Use estimation or fraction multiplication to determine if your answer is reasonable.

Calculate the product.

 

 Paint costs for a gallon of paint. Nikki needs gallons to complete a painting project. How much will Nikki spend on paint? Remember to round to the nearest penny.

ROUNDING DECIMALS - TENTHS

Round each number to the nearest tenth

310.2866.805118.380815.755877.7112.261

≈ 310.3

≈ 6.8

≈ 118.4

≈ 815.8

≈ 877.7

≈ 12.3

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ROUNDING DECIMALS - HUNDREDTHS

487.36222.700 159.4102.19058.13910.886

≈ 487.36

≈ 2.19

≈ 159.41

≈ 22.70

≈ 58.14

≈ 10.89

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