Explore detailed solutions and clear explanations for Grade 6 percent math questions. This interactive resource helps students, teachers, and parents master percentage problems, including increases, decreases, comparisons, and real-life applications. Expand the View Solution tab under each question to verify your answers and follow the step-by-step logic.
Evaluate: $30\% \text{ of } 30 =$
$30\% \text{ of } 30$ is written mathematically as:
$$30\% \times 30 = \dfrac{30}{100} \times 30$$
$$= \dfrac{900}{100} = 9$$
Correct Answer: C
Evaluate: $150\% \text{ of } 60 =$
$150\% \text{ of } 60$ is written mathematically as:
$$150\% \times 60 = \dfrac{150}{100} \times 60$$
$$= \dfrac{150 \times 60}{100} = \dfrac{9000}{100} = 90$$
Correct Answer: D
Write as a percentage: $\dfrac{1}{4} =$
To change the fraction $\dfrac{1}{4}$ into a percentage, we need to convert it to a fraction with a denominator of $100$. Multiply both the numerator and the denominator by $25$:
$$\dfrac{1}{4} = \dfrac{1 \times 25}{4 \times 25} = \dfrac{25}{100} = 25\%$$
Correct Answer: D
Write as a percentage: $0.05 =$
To change the decimal number $0.05$ into a percentage, we rewrite it as a fraction with a denominator of $100$:
$$0.05 = \dfrac{0.05}{1} = \dfrac{0.05 \times 100}{1 \times 100} = \dfrac{5}{100} = 5\%$$
Correct Answer: C
If $100\%$ of a number is $15$, what is $50\%$ of the number?
Let $n$ be the number. "$100\%$ of a number is $15$" is written as:
$$100\% \times n = 15$$
Since $100\% = \dfrac{100}{100} = 1$, we know the number itself is $15$. Now find $50\%$ of the number:
$$50\% \times 15 = \dfrac{50}{100} \times 15 = \dfrac{750}{100} = 7.5$$
Correct Answer: A
If $10\%$ of a number is $7$, what is $80\%$ of the number?
Note that $80\%$ is exactly $8 \text{ times}$ greater than $10\%$.
Since $10\%$ of the number equals $7$, we simply multiply that result by $8$:
$$8 \times 7 = 56$$
Correct Answer: B
Which is the greatest?
Evaluate each expression as a fraction:
The largest resulting value is $75$. Hence, $3\% \text{ of } 2500$ is the greatest.
Correct Answer: D
The original price of a toy was \( $15 \). If the price is reduced by $20\%$, what is the new price?
First, calculate the discount amount ($20\%$ of $15$):
$$20\% \times 15 = \dfrac{20}{100} \times 15 = \dfrac{300}{100} = 3$$
Now, subtract the discount from the original price to find the new price:
$$\text{New price} = 15 - 3 = 12$$
Correct Answer: A
George bought a car for \( $5000 \) and sold it for \( $5500 \). What benefit, in percent, did he make?
First, find the benefit in dollars:
$$5500 - 5000 = 500$$
Next, express this benefit as a percentage of his original investment ($5000):
$$\dfrac{500}{5000} = \dfrac{5}{50} = \dfrac{10}{100} = 10\%$$
Correct Answer: B
If $20\%$ of $n$ is equal to $40$, what is $n$?
Write the statement as an algebraic equation:
$$20\% \times n = 40$$
Convert the percentage into a fraction:
$$\dfrac{20}{100} \times n = 40$$
Multiply both sides by $100$ to remove the denominator:
$$20n = 4000$$
Divide both sides by $20$:
$$n = \dfrac{4000}{20} = 200$$
Correct Answer: A
The price of a T-shirt was \( $20 \). It was first increased by $20\%$. They did not sell well, so the shop owner then decreased the new price by $20\%$. What is the final price?
Step 1: Increase the price by $20\%$.
$$20\% \times 20 = \dfrac{20}{100} \times 20 = 4$$
New price after increase: $20 + 4 = 24$.
Step 2: Decrease the new price ($24) by $20\%$.
$$20\% \times 24 = \dfrac{20}{100} \times 24 = \dfrac{480}{100} = 4.8$$
Final price after decrease: $24 - 4.8 = 19.2$.
Therefore, the new price of the T-shirt is $19.20.
Correct Answer: D
What percent of $1$ hour is $15$ minutes?
Since $1$ hour = $60$ minutes, we are comparing $15$ minutes to $60$ minutes. Set this up as a fraction and multiply by $100\%$:
$$\dfrac{15}{60} \times 100\% = \dfrac{1500}{60}\% = 25\%$$
Therefore, $15$ minutes is exactly $25\%$ of $1$ hour.
Correct Answer: D