Term 1 Quiz 6&7

Answer explanation

To evaluate \( \frac{1}{4} \div \frac{6}{7} \), multiply by the reciprocal: \( \frac{1}{4} \times \frac{7}{6} = \frac{7}{24} \). Thus, the correct answer is \( \frac{7}{24} \).

Answer explanation

To evaluate \(2\frac{1}{2} \div \frac{7}{4}\), first convert \(2\frac{1}{2}\) to an improper fraction: \(\frac{5}{2}\). Then, divide by \(\frac{7}{4}\) by multiplying by its reciprocal: \(\frac{5}{2} \times \frac{4}{7} = \frac{20}{14} = \frac{10}{7}\). Thus, the correct answer is \(\frac{10}{7}\).

• -2.67

• 6

• 7.5

• 8

Answer explanation

First, calculate -15 × (2/15) = -2. Then, evaluate 4^2 ÷ 2 = 8. Finally, combine the results: -2 + 8 = 6. Thus, the correct answer is 6.

A $200 000 mortgage incurs $12 000 of interest each year. Write this as a percentage rate (e.g. write interest as a percentage of the principal).

• 5%

• 6%

• 7%

• 8%

Answer explanation

To find the interest rate, divide the annual interest ($12,000) by the principal ($200,000) and multiply by 100. This gives (12,000 / 200,000) * 100 = 6%. Therefore, the correct answer is 6%.

Calculate the interest paid on a 3 year loan of $65 000 with an interest rate of 7%.

Step 1: Convert the rate into a decimal

Step 2: Multiply the Principal by the decimal rate

Step 3: Multiply by the number of years

• $4 550

• $136 500

• $13 650

• $455 000

Answer explanation

To find the interest, convert 7% to 0.07. Then, multiply the principal ($65,000) by the rate (0.07) to get $4,550. Finally, multiply by 3 years: $4,550 x 3 = $13,650. Thus, the correct answer is $13,650.

A 3-year loan charges $900 interest. How much interest is charged each year?

• $600

• $900

• $300

• $100

Answer explanation

To find the annual interest, divide the total interest by the number of years. $900 ÷ 3 years = $300 per year. Thus, the correct answer is $300.

A loan lasts 4.5 years and requires monthly payments. How many payments must be made?

• 12

• 45

• 48

• 54

Answer explanation

A loan lasting 4.5 years requires monthly payments. To find the total payments, multiply 4.5 years by 12 months/year: 4.5 * 12 = 54. Therefore, the correct answer is 54.

Which of the following are equivalent ratios for 2:3?

• 4:6

  6:9

  8:12

• 3:4

  5:7

  7:10

• 5:8

  10:15

  15:20

• 2:5

  4:10

  6:15

Answer explanation

The ratios 4:6, 6:9, and 8:12 are equivalent to 2:3 because they can be simplified to the same ratio. For example, 4:6 simplifies to 2:3 by dividing both terms by 2.

Simplify the ratio 14:36.

• 7:36

• 14:18

• 7:18

• 14:72

Answer explanation

To simplify the ratio 14:36, divide both numbers by their greatest common divisor, which is 2. This gives 14 ÷ 2 = 7 and 36 ÷ 2 = 18, resulting in the simplified ratio 7:18.

Simplify the ratio 4:8:2.

• 1:2:0.5

• 2:4:1

• 1:2:1

• 2:1:0.5

Answer explanation

To simplify the ratio 4:8:2, divide each term by the greatest common divisor, which is 2. This gives 2:4:1, matching the answer choice 2:4:1.