QCM : Mastering Fractions, Decimals, and Ratios — 10 questions

Questions et réponses du QCM

1. What does converting a fraction into a decimal mean?

Adding the numerator and denominator to convert to decimal form
Subtracting the denominator from the numerator to find the decimal
Dividing the numerator by the denominator to get a decimal value
Multiplying the numerator by the denominator to find a decimal

Dividing the numerator by the denominator to get a decimal value

Explication

Converting a fraction into a decimal involves dividing the numerator by the denominator to obtain a decimal value, which can then be used for further calculations or conversions.

2. Which calculator function is used to simplify fractions derived from decimal amounts?

MODE button
LOG button
SHIFT button
SD button

SD button

Explication

The SD (simplify) button on the calculator is used to automatically reduce fractions to their simplest form after converting decimal amounts into fractions, as explicitly stated in the content.

3. What is the role of dividing the total by the denominator and then multiplying by the numerator when finding a fraction of a quantity?

To convert a fraction into a percentage
To calculate a specific part or portion of the total
To find the remaining part after subtraction
To determine the total amount from a part

To calculate a specific part or portion of the total

Explication

The process of dividing the total by the denominator and multiplying by the numerator is used to find a specific part or portion of the total quantity, which is the purpose of calculating a fraction of a quantity.

4. Arrange the following percentage calculation concepts in the order they were likely established or published: percentage of an amount, percentage increase/decrease, interest and GST calculations, standard form numbers.

Interest and GST calculations, percentage of an amount, percentage increase/decrease, standard form numbers
Percentage increase/decrease, percentage of an amount, interest and GST calculations, standard form numbers
Standard form numbers, interest and GST calculations, percentage of an amount, percentage increase/decrease
Percentage of an amount, percentage increase/decrease, interest and GST calculations, standard form numbers

Percentage of an amount, percentage increase/decrease, interest and GST calculations, standard form numbers

Explication

The most logical chronological order is: first, the basic concept of calculating a percentage of an amount; then, the development of percentage increase/decrease techniques; followed by interest and GST calculations, which are more advanced financial concepts; and finally, the standard form numbers, which are used for very large or small numbers and likely developed later for scientific and mathematical purposes.

5. How do the concepts of percentage increase and percentage decrease differ in their calculation methods?

Percentage increase involves multiplying the original amount by (1 + percentage), while percentage decrease involves multiplying by (1 - percentage).
Both percentage increase and decrease are calculated by dividing the difference between two amounts by the original amount and multiplying by 100.
Percentage increase is calculated by adding the percentage of the original to the original amount, whereas percentage decrease involves subtracting the percentage of the original from the original amount.
Both concepts involve multiplying the original amount by the percentage expressed as a decimal, but increase uses a positive decimal and decrease uses a negative decimal.

Percentage increase involves multiplying the original amount by (1 + percentage), while percentage decrease involves multiplying by (1 - percentage).

Explication

Percentage increase involves multiplying the original amount by (1 + percentage as a decimal), which increases the amount, while percentage decrease involves multiplying by (1 - percentage as a decimal), which decreases the amount. The key difference is in whether the percentage is added or subtracted from 1 in the multiplier.

6. Who is credited with establishing the standard formulas for calculating GST included and excluded amounts?

The International Accounting Standards Board (IASB)
The International Monetary Fund (IMF)
The World Trade Organization (WTO)
The Government of the country implementing GST

The Government of the country implementing GST

Explication

The standard formulas for calculating GST included and excluded amounts are established by the government of the country that implements GST, as it is a tax law enacted by government authority.

7. What is a key effect of simplifying ratios in mathematical calculations?

It makes ratios easier to interpret and work with.
It eliminates the need for common denominators.
It increases the size of the numbers in the ratio.
It converts ratios into decimals automatically.

It makes ratios easier to interpret and work with.

Explication

Simplifying ratios reduces them to their smallest whole-number form, making them easier to interpret and use in calculations, which is the primary effect of ratio simplification.

8. A total of $1800 is to be split between two people in the ratio 2:3. How much money does each person receive?

$900 and $900
$720 and $1080
$720 and $1080
$600 and $1200

$720 and $1080

Explication

The total ratio parts are 2 + 3 = 5. Divide the total amount, $1800, by 5 to find the value of one part: $1800 ÷ 5 = $360. Then multiply by each ratio part: first person gets 2 × $360 = $720, second person gets 3 × $360 = $1080. The correct split is $720 and $1080.

9. What is a key feature of rate calculations?

Subtracting the rate from the total quantity to determine the remaining amount
Adding the rate to the total quantity to find the overall amount
Finding the unit rate by dividing the total quantity by the number of units
Calculating the total amount by multiplying the rate by the number of units

Finding the unit rate by dividing the total quantity by the number of units

Explication

The key feature of rate calculations is finding the unit rate, which involves dividing the total quantity by the number of units to determine the amount per unit.

10. What is a standard form number?

A notation to express percentages as fractions
A way to write numbers as a product of a number between 1 and 10 and a power of 10
A method to convert fractions into decimals for easier calculations
A technique to simplify ratios by dividing all parts by their highest common factor

A way to write numbers as a product of a number between 1 and 10 and a power of 10

Explication

A standard form number is a way to express very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of 10, making them easier to read and work with.

Révisez avec les flashcards

Mémorisez les réponses avec 20 flashcards sur Mastering Fractions, Decimals, and Ratios.

Fractions in Decimals — conversion method?

Use calculator SD button to simplify fractions from decimals.

Subtracting fractions from whole — process?

Convert to common denominator or decimal, then subtract from 1.

Fraction of a quantity — formula?

(Total ÷ denominator) × numerator.

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