Mathematics Knowledge Practice Test 3

Correct answer: C — 36

First, find the number of cups needed per batch: 12 cups ÷ 4 batches = 3 cups per batch. Then, multiply this by the new number of batches: 3 cups/batch × 12 batches = 36 cups of flour. Alternatively, since 12 batches is exactly 3 times as many as 4 batches, you can just multiply $$12\text{ cups} \times 3 = 36$$

Correct answer: A — Any integer that is divisible by 2 without a remainder.

An even number is formally defined as any integer that can be divided exactly by 2, meaning it leaves a remainder of zero. For example, 2, 4, 6, and 8 are even numbers.

Correct answer: B — $13.00

To find 20% of a number, convert the percentage to a decimal by dividing by $$100 (20\% = 0.20)$$ and multiply it by the total amount. $65.00 × 0.20 = $13.00. Another quick way is to divide by 5, since 20% is equivalent to $$\frac{1}{5}$$

Correct answer: B — $$4:8$$

For 8 gardens, the ratio of mulch to paving stones is 16 to 32. Since you only need supplies for 2 gardens (which is exactly a quarter of 8), you must divide the original quantities by 4. Mulch: $$16 \div 4 = 4$$. Paving stones: $$32 \div 4 = 8$$. Therefore, the required proportion is $$4:8$$

Correct answer: B — $81.45

First, determine the discount amount by multiplying the original total by 10% (0.10). $90.50 × 0.10 = $9.05. Then, subtract the discount from the original total to find the final price: $90.50 - $9.05 = $81.45.

Correct answer: A — $20.79

To find the tip amount, convert the percentage to a decimal by dividing by $$100 (18\% = 0.18)$$ and multiply it by the total bill. $115.50 × 0.18 = $20.79.

Correct answer: A — 2,060

To divide by a decimal, move the decimal point in both the divisor and dividend to the right until the divisor is a whole number. Moving the decimal 3 places to the right changes the problem to $$8240 \div 4$$. 8240 divided by 4 is 2060.

Correct answer: A — 146

According to the order of operations (PEMDAS), first solve inside the parentheses: $$144 \div 12 = 12$$. Next, evaluate the exponent: $$12^2 = 144$$. Then perform multiplication and division from left to right: $$8 \times 5 = 40$$, and $$40 \div 20 = 2$$. Finally, add the results together: $$2 + 144 = 146$$

Correct answer: A — $$\frac{1}{2}$$

First, evaluate the exponent: $$(\frac{3}{2})^2$$ means $$(\frac{3}{2}) \times (\frac{3}{2}) = \frac{9}{4}$$. Next, perform the multiplication: $$\frac{1}{4} \times \frac{9}{4} = \frac{9}{16}$$. Finally, subtract the remaining fraction: $$\frac{9}{16} - \frac{1}{16} = \frac{8}{16}$$. Simplifying the fraction by dividing the top and bottom by 8 gives $$\frac{1}{2}$$

Correct answer: B — Any number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.

A rational number is any number that can be written as a simple fraction (a ratio) where both the numerator (p) and denominator (q) are integers, and the denominator is not equal to zero. This includes all integers, terminating decimals, and repeating decimals.