Number Sense - Math 7 Accelerated

1) A ___________ number is a number that can written as a ratio of two integers.

A rational number is a number that can be expressed as a ratio of two integers. In other words, it can be written in the form of a fraction, where the numerator and denominator are both integers. This includes whole numbers, integers, and fractions. The term "rational" is used to describe numbers that can be reasoned or expressed in a ratio, hence the name "rational number".

Explanation

A rational number is a number that can be expressed as a ratio of two integers. In other words, it can be written in the form of a fraction, where the numerator and denominator are both integers. This includes whole numbers, integers, and fractions. The term "rational" is used to describe numbers that can be reasoned or expressed in a ratio, hence the name "rational number".

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2) Which of the following numbers are irrational?

0.121121112...

The number 0.121121112... is irrational because it cannot be expressed as a fraction of two integers. It is a repeating decimal where the pattern of digits 121 repeats indefinitely. Since the pattern does not terminate or repeat in a predictable manner, it cannot be represented as a fraction and is therefore irrational.

Explanation

The number 0.121121112... is irrational because it cannot be expressed as a fraction of two integers. It is a repeating decimal where the pattern of digits 121 repeats indefinitely. Since the pattern does not terminate or repeat in a predictable manner, it cannot be represented as a fraction and is therefore irrational.

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3) Sally deposited $85 in her local bank which pays 4% interest. Select the equations that will help Sally calculate her bank balance after one year. Assume she doesn't make any new deposits during the year.

To calculate Sally's bank balance after one year, we need to consider the interest earned on her deposit. The equation that represents the interest earned is: Interest = Principal * Rate * Time. In this case, the principal is $85, the rate is 4% (or 0.04 as a decimal), and the time is 1 year. Therefore, the equation that will help Sally calculate her bank balance after one year is: Balance = Principal + Interest.

Explanation

To calculate Sally's bank balance after one year, we need to consider the interest earned on her deposit. The equation that represents the interest earned is: Interest = Principal * Rate * Time. In this case, the principal is $85, the rate is 4% (or 0.04 as a decimal), and the time is 1 year. Therefore, the equation that will help Sally calculate her bank balance after one year is: Balance = Principal + Interest.

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4) Which of the following numbers are irrational?

0.121121112...

The number 0.121121112... is irrational because it cannot be expressed as a fraction of two integers. It is a repeating decimal with a repeating pattern of 1211, which does not terminate or repeat in a predictable manner. Therefore, it falls into the category of irrational numbers.

Explanation

The number 0.121121112... is irrational because it cannot be expressed as a fraction of two integers. It is a repeating decimal with a repeating pattern of 1211, which does not terminate or repeat in a predictable manner. Therefore, it falls into the category of irrational numbers.

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5) Hank just finished his meal at a restaurant and received the $26 bill. He would like to leave a 10% tip to show his appreciation for the great service.Select all equations that would help Hank calculate his total bill including tip.

The correct answer is:
Total bill including tip = Bill + (Bill * 0.10)

This equation correctly calculates the total bill including a 10% tip. It takes the bill amount and adds 10% of the bill amount to calculate the tip. Then, it adds the tip to the bill amount to get the total bill including tip.

Explanation

The correct answer is:
Total bill including tip = Bill + (Bill * 0.10)

This equation correctly calculates the total bill including a 10% tip. It takes the bill amount and adds 10% of the bill amount to calculate the tip. Then, it adds the tip to the bill amount to get the total bill including tip.

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6) Which of the following numbers are rational?

0.121121112...

The number 0.121121112... is rational because it can be expressed as a fraction. To determine this, we can observe that the number has a repeating pattern, with the digits 1 and 2 repeating in a specific sequence. By representing this pattern as a fraction, we can express it as 121/999, which is a ratio of two integers. Therefore, 0.121121112... is rational.

Explanation

The number 0.121121112... is rational because it can be expressed as a fraction. To determine this, we can observe that the number has a repeating pattern, with the digits 1 and 2 repeating in a specific sequence. By representing this pattern as a fraction, we can express it as 121/999, which is a ratio of two integers. Therefore, 0.121121112... is rational.

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7) Hank just finished his meal at a restaurant and received the $28 bill. He would like to leave a 15% tip to show his appreciation for the great service.Select all equations that would help Hank calculate his total bill including tip.

None of these choices.

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Explanation

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10) 12 markers cost $9. Which fraction will complete the proportion to find the cost of 15 markers?

12 over 9 equals

None of these choices.

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Explanation

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11) Sally deposited $94 in her local bank which pays 5% interest. Select the equations that will help Sally calculate her bank balance after one year. Assume she doesn't make any new deposits during the year.

To calculate Sally's bank balance after one year, we need to use the equation for calculating compound interest. The equation is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal amount is $94, the interest rate is 5%, and since it is not mentioned how many times the interest is compounded, we cannot determine the value of n. Therefore, the equation that will help Sally calculate her bank balance after one year is A = 94(1 + 0.05)^t.

Explanation

To calculate Sally's bank balance after one year, we need to use the equation for calculating compound interest. The equation is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal amount is $94, the interest rate is 5%, and since it is not mentioned how many times the interest is compounded, we cannot determine the value of n. Therefore, the equation that will help Sally calculate her bank balance after one year is A = 94(1 + 0.05)^t.

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12) All rational numbers are also whole numbers.

True

False

This statement is false because not all rational numbers are whole numbers. Rational numbers include fractions and decimals that can be expressed as a ratio of two integers, while whole numbers include only positive integers and zero. Therefore, there are rational numbers that are not whole numbers, such as 1/2 or 3.14.

Explanation

This statement is false because not all rational numbers are whole numbers. Rational numbers include fractions and decimals that can be expressed as a ratio of two integers, while whole numbers include only positive integers and zero. Therefore, there are rational numbers that are not whole numbers, such as 1/2 or 3.14.