Go Math! Practice Fluency Workbook Grade 6 Chapter 3 Rational Numbers Exercise 3.3 Answer Key

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Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 3 Rational Numbers

Page 15 Problem 1 Answer

Given:- 3/8

To Find:- To write each fraction as a decimal and to round to the nearest hundredth if necessary The given fraction is 3/8.

It can be converted into a decimal by dividing the numerator 3 by the denominator 8 using the long division method. The decimal value of 3/8 would be 0.375

The decimal value of the fraction 3/8 is0.375

Page 15 Problem 2 Answer

Given:- 7/5

To Find:- To write each fraction as a decimal and to round to the nearest hundredth if necessary The given fraction is 7/5.

Here, we can notice that the denominator is 5 , so we can easily convert the denominator in terms of 10 by multiplying both the numerator and denominator by 2.

Then, the fraction 7/5 would become 14/10. Therefore, the decimal value of the fraction 7/5 would be1.4

The decimal value of the fraction 7/5 is 1.4

Page 15 Problem 3 Answer

Given:- 21/7

To Find:- To write each fraction as a decimal and to round to the nearest hundredth if necessary The given fraction is 21/7.

Here, we can notice that the denominator is7 which cannot be easily converted in terms of 10,100,1000….

So, we divide the numerator by the denominator to get 3.0 or 3 as the numerator 21 is fully divisible by 7.

The fraction 21/7 can be written as 3.0 or 3

Go Math! Practice Fluency Workbook Grade 6 Chapter 3 Rational Numbers Exercise 3.3 Answer Key

Page 15 Problem 4 Answer

Given:- 5/3

To Find:- To write each fraction as a decimal and to round to the nearest hundredth if necessary The given fraction is 5/3.

Here, we can notice that the denominator is 3 which cannot be easily converted in terms of 10,100,1000….

So, we divide the numerator by the denominator to get 1.666which can be rounded to the nearest hundredth as 1.67.

The fraction 5/3 can be written in decimal form as 1.67

Page 15 Problem 5 Answer

Given:- 0.55

To Find:- To write each decimal as a fraction or mixed fraction in simplest form The given decimal is 0.55.

Since there are two digits after the decimal point, we can write 0.55 as 55/100.

Now, we can reduce the 55/100 in its simplest form by dividing both the numerator and denominator by 5 to get 11/20.

The decimal 0.55 can be written in the fractional form 11/20.

Page 15 Problem 6 Answer

Given:- 10.6

To Find:- To write each decimal as a fraction or mixed fraction in simplest form The given decimal is 10.6.

Since there is one digit after the decimal point, we can write 10.6 as 106/10

This can be further simplified by dividing the numerator and denominator by 2 to get 53/5.

The decimal 10.6 can be written in the fractional form as 53/5.

Page 15 Problem 7 Answer

Given:- −7.08

To Find:- To write each decimal as a fraction or mixed fraction in simplest form The given decimal is 7.08.

Since there are two digits after the decimal point, we can write 7.08 as 708/100

This can be further reduced by dividing the numerator and denominator by 4 to get 177/25.

The decimal−7.08can be written in the fractional form−177/25

Page 15 Problem 8 Answer

Given:- 0.5,0.05,5/8

To Find:- To write the numbers in order from least to greatest

To write the given numbers in order from the least to the greatest, we should first change all the numbers into similar terms such as all the numbers into fractions or all the numbers into decimals.

Here, we can convert 5/8 into a decimal by dividing the numerator by the denominator to get 0.625.

So, the numbers would be 0.5,0.05,0.625.

So, the order from the least to the greatest will be 0.05,0.5,0.625.

Rewriting 0.625 as a fraction and then writing the numbers in order from the least to the greatest will be 0.05,0.5,5/8.

The order of the numbers from the least to the greatest will be0.05,0.5,5/8.

Page 15 Problem 9 Answer

Given:- 1.3,1×1/3 ,1.34

To Find:- To write the numbers in order from least to greatest

To write the given numbers in order from the least to the greatest, we should first change all the numbers into similar terms such as all the numbers into fractions or all the numbers into decimals.

Here, we can rewrite 1×1/3 as 4/3 which can be converted into a decimal by dividing the numerator by the denominator to get 1.33.

So, the numbers would be 1.3,1.33,1.34 in order from the least to the greatest.

The order of the numbers after rewriting 1.33 as a mixed fraction would be 1.3,1×1/3,1.34.

The order of the numbers from the least to the greatest would be 1.3,1×1/3,1.34.

Page 15 Problem 10 Answer

Given:- 2.07,2×7/10 10 ,2.67,−2.67

To Find:- To write the numbers in order from least to greatest

To write the given numbers in order from the least to the greatest, we should first change all the numbers into similar terms such as all the numbers into fractions or all the numbers into decimals.

Here, we can rewrite 2×7/10 as 2×7/10 which can be converted to decimal as 2.7.

So, the numbers would be2.07,2.7,2.67,−2.67.

Arranging them in the order from the least to the greatest will be −2.67,2.07,2.67,2.7.

Rearranging the numbers in the order from the least to the greatest after rewriting 2.7 as 2×7/10 will be −2.67,2.07,2.67,2×7/10.

The order of the numbers from the least to the greatest would be −2.67,2.07,2.67,2×7/10.

Page 15 Problem 11 Answer

Given:- Out of 45 times at bat, Raul got 19 hits.
To Find:- Raul’s batting average as a decimal It is given that out of 45 times while batting, Raul got 19 hits. So, the average can be represented as 19/45.

Converting it to a decimal, the numerator should be divided by the denominator to get0.4222.

Therefore, Raul’s batting average is0.422.

Raul’s batting average in decimal is0.422

Page 15 Problem 12 Answer

Given:- Karen’s batting average was 0.444. She was at bat 45 times

To Find:- To determine how many hits did Karen get

We know that the batting average is defined as the ratio of the number of hits to the number of times at the bat.

Substituting the given values in the formula of batting average, we get,

⇒ \(\text { Batting average }=\frac{\text { number of hits }}{\text { number of times at bat }}\)

⇒ \(0.444=\frac{\text { number of hits }}{45}\)

Multiplying both sides of the equation by 45, we get, the number of hits=0.444×45 =19.98  which can be rounded to the nearest whole number as20

The number of hits Karen got was 20.

Page 15 Problem 13 Answer

Given:- To have batting averages over 0.500 how many hits in 45 times at bat would Raul and Karen need?

To Find:- To determine the number of hits Raul and Karen would need to have batting averages over 0.500

We know that the batting average is defined as the ratio of the number of hits to the number of times at the bat. Substituting the given values in the formula of batting average, we get,

⇒ \(Batting average= \frac{\text { number of hits }}{\text { number of times at bat }}\)

⇒ \( 0.500=\frac{\text { number of hits }}{45}\)

Multiplying both sides of the equation by 45, we get,

the number of hits=0.500×45 =22.5 which can be rounded to the nearest whole number23

The number of hits Raul and Karen would need to have a batting average above 0.500 would be 23.

Page 15 Problem 14 Answer

we have to Solve the given question It is given that a car travels 65 miles per hour, but then travels 3/5 of this speed when going through construction. First, we need to write this fraction as a decimal.

When converting a fraction to a decimal: If the denominator is a factor of 10,100,1000,…, multiply the numerator and denominator by the same number to get a denominator that is a power of 10.

Then write the equivalent fraction as a decimal. If the denominator is not a factor of 10,100,1000,…, then divide the numerator by the denominator to find the decimal.

For3/5, the denominator of 5 is a factor of 10 so we can write an equivalent fraction to find the decimal:

⇒ \(\frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}\)

⇒ \(\frac{6}{10} in words is ” six tenths”.\)

Since tenths mean one decimal place, then 6/10 =0.6

To find the speed, we can either multiply 65 and 3/5 or multiply 65 and 0.6. It is easier to multiply 65 and 3/5 since 5 is a factor of 65.

From the above step, we get a fraction as a decimal is 0.6 and 3/5 of the given speed of 39 miles per hour.

⇒ Multiplying then gives:\(65 \times \frac{3}{5}=65 \times \frac{1}{5} \times 3=\frac{65}{5} \times 3=13 \times 3=39 miles per hour\)

Page 15 Problem 15 Answer

Given: A city’s sales tax is 0.07. Write this decimal as a fraction and tell how many cents of tax are on each dollar. 0.07 in words is ‘ ‘seven hundredths” so we can write it as a fraction with 7 as the numerator and 100 as the denominator.

We then get 0.07=7/100.

Since there are 100 cents in a dollar, then the fraction means there are 7 cents of tax in each dollar. the tax is equal to 7 cents

Page 15 Problem 16 Answer

It is given that Norm has 373 sheets of paper left in a ream and each ream of paper initially has 500 sheets of paper. The portion of a ream that Norm has written as a fraction is then 373/500.

To find; A ream of paper contains 500 sheets of paper. Norm has 373 sheets of paper left from a dream. Express the portion of a ream Norm has as a fraction and as a decimal. _______________
When converting a fraction to a decimal:- If the denominator is a factor of 10,100,1000,…, multiply the numerator and denominator by the same number to get a denominator that is a power of 10. Then write the equivalent fraction as a decimal.

If the denominator is not a factor of 10,100,1000,…, then divide the numerator by the denominator to find the decimal.

⇒ \(For \frac{373}{500},\) the denominator of 500 is a factor of 1000 so we can write an equivalent fraction to find the decimal:

⇒ \(\frac{373}{500}=\frac{373 \times 2}{500 \times 2}=\frac{746}{1000}\)

⇒ \(\frac{746}{1000}\) in words is “seven hundred forty-six thousandths”.

Since thousandths mean three decimal places, then\( \frac{746}{1000}=0.746.\)

So, the portion written as a decimal number is 0.746

Page 16 Exercise 1 Answer

we have to write each decimal as a fraction or mixed number.0.61 in words is ” sixty-one hundredths” so we can write it as a fraction with 61 as the numerator and 100 as the denominator.

We then get 0.61=61/100

From the above step, we will get the answer 61/100

Page 16 Exercise 2 Answer

we have to write each decimal as a fraction or mixed number.3.43 in words is ‘ three and forty-three hundredths” so we can write it as a mixed number with 43 as the numerator and 100 as the denominator.

We then get

⇒  \(3.43=3 \frac{43}{100}\)

From the above step, we will get the answer 3×43/100

Page 16 Exercise 3 Answer

we have to write each decimal as a fraction or mixed number. 0.009 in words is “nine thousandths” so we can write it as a fraction with 9 as the numerator and 1000 as the denominator.

We then get\(0.009=\frac{9}{1000}\)

From the above step, we will get the answer 9/1000

Page 16 Exercise 4 Answer

we have to write each decimal as a fraction or mixed number.4.7 in words is ‘ ‘four and seven-tenths” so we can write it as a mixed number with 7 as the numerator and 10 as the denominator.

We then get \(4.7=4 \frac{7}{10}\)

From the above step, we will get the answer4x7/10

Page 16 Exercise 5 Answer

we have to write each decimal as a fraction or mixed number.1.5 in words is ” one and five tenths” so we can write it as a mixed number with 5 as the numerator and 10 as the denominator.

We then get \(1.5=1 \frac{5}{10}\)

Since 5 and 10 have a GCF of 5, we can reduce the fraction to:

⇒ \(1 \frac{5}{10}=1 \frac{5 \div 5}{10 \div 5}=11 \frac{1}{2}\)

From the above step, we will get the answer11x1/2

Page 16 Exercise 6 Answer

we have to write each decimal as a fraction or mixed number. 0.13 in words is ” thirteen hundredths” so we can write it as a fraction with 13 as the numerator and 100 as the denominator.

We then get \(0.13=\frac{13}{100}\)

From the above step, we will get the answer13/100

Page 16 Exercise 7 Answer

we have to write each decimal as a fraction or mixed number 5.0002 in words is ” five and two thousandths” so we can write it as a mixed number with 2 as the numerator and 1000 as the denominator.

We then get \(5.002=5 \frac{2}{1000} .\)

Since 5 and 10 have a GCF of 2, we can reduce the fraction to:

⇒ \(5 \frac{2}{1000}=5 \frac{2 \div 2}{1000 \div 2}=5 \frac{1}{500}\)

From the above step, we will get the answer5x1/500

Page 16 Exercise 8 Answer

we have to write each decimal as a fraction or mixed number.

0.021 in words is ‘ ‘twenty-one thousandths” so we can write it as a fraction with 21 as the numerator and 1000 as the denominator.

We then get \(0.021=\frac{21}{1000}\)

From the above step, we will get the answer 21/1000

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