Knowledge Check: Chapters 1–6

Write 'six hundred thirteen' as a whole number using digits.

Write 'fifty-five thousand two hundred eight' as a whole number using digits.

Round 81,486 to the nearest hundred.

Simplify: $45 + 23$.

Translate the phrase to math notation and then simplify: the sum of 16 and 58.

Clayton walked 12 blocks to his mother's house, 6 blocks to the gym, and 9 blocks to the grocery store before walking the last 3 blocks home. What was the total number of blocks that Clayton walked?

Simplify: $145 - 79$.

Translate the phrase to math notation and then simplify: the difference of 32 and 18.

Last month, Stan's take-home pay was $3,816 and his expenses were $3,472. How much of his take-home pay did Stan have left after he paid his expenses?

Simplify: $7 \cdot 475$.

Simplify: $35(14)$.

Translate the phrase to math notation and then simplify: twice 524.

Simplify: $85 \div 5$.

Simplify: $0/9$.

Simplify: $495 \div 45$.

Write $n \cdot n \cdot n \cdot n \cdot n \cdot n$ in exponential form.

Simplify, using the order of operations: $(8 + 1) \cdot 4$.

Simplify, using the order of operations: $5[2 + 7(9 - 8)]$.

Evaluate $y^3$ when $y = 5$.

Evaluate $hw$ when $h = 12$ and $w = 3$.

Translate the phrase into an algebraic expression: three times the difference of $a$ and $b$.

Solve the equation: $n - 6 = 25$.

Translate the sentence into an algebraic equation and then solve it: 15 less than $y$ is 32. Enter the value of $y$.

List all the multiples of 4 that are less than 50, from smallest to largest, separated by commas.

Find all the factors of 30. Enter them from smallest to largest, separated by commas.

Find the prime factorization of 1080. Enter the answer in exponential form, e.g. $2^3 \cdot 5$.

Find the least common multiple of 9 and 15.

Find the least common multiple of 25 and 35.

Fill in < or > to make a true statement: $-6 \_\_ 3$. Enter the full inequality, e.g. $2>1$.

Fill in < or > to make a true statement: $-1 \_\_ -4$. Enter the full inequality, e.g. $2>1$.

Simplify: $|4 - 9|$

Simplify: $-15 + (-12)$

Early one morning, the temperature in Syracuse was -8°F. By noon, it had risen 12°. What was the temperature at noon (in °F)?

Simplify: $10 - (5 - 6)$

Evaluate $35 - a$ when $a = -4$.

Translate into an algebraic expression and simplify: the difference of $-7$ and $-4$. Give the simplified value.

Simplify: $-6(-9)$

Simplify: $(-2)^3$

Simplify: $16 - 3(5 - 7)$

Solve: $n + 6 = 5$

Solve: $-9r = -54$

Translate and solve: Eight less than $y$ is $-32$. Enter the value of $y$.

Convert the mixed number to an improper fraction: $3\tfrac{2}{7}$

Convert the improper fraction to a mixed number: $\tfrac{63}{11}$

Order using < or >. Enter the full inequality: $-2\tfrac{1}{2} \_\_ -3$

Simplify: $\tfrac{5}{20}$

Simplify: $\tfrac{1}{3} \cdot \tfrac{3}{4}$

Simplify: $-\tfrac{5}{6} \div \tfrac{5}{12}$

Simplify: $\left(-15\tfrac{5}{6}\right) \div \left(-3\tfrac{1}{6}\right)$

Simplify the complex fraction: $\tfrac{p/2}{q/5}$

Simplify: $\tfrac{9^2 - 4^2}{9 - 4}$

Simplify: $-\tfrac{3}{13} + \left(-\tfrac{4}{13}\right)$

Simplify: $\tfrac{2}{5} + \left(-\tfrac{7}{5}\right)$

Simplify: $-\tfrac{11}{36} - \tfrac{11}{20}$

Simplify: $-\tfrac{3}{4} \div \tfrac{x}{3}$

Simplify the complex fraction: $\tfrac{\left(\tfrac{5}{14} + \tfrac{1}{8}\right)}{\tfrac{9}{56}}$

Perform the indicated operation: $4\tfrac{1}{3} + 9\tfrac{1}{3}$

Perform the indicated operation: $5\tfrac{8}{11} + 2\tfrac{4}{11}$

Perform the indicated operation: $9\tfrac{13}{20} - 4\tfrac{11}{20}$

Solve the equation: $y + \tfrac{3}{5} = \tfrac{7}{5}$

Solve the equation: $f + \left(-\tfrac{2}{3}\right) = \tfrac{5}{12}$

Solve the equation: $-\tfrac{2}{3} c = 18$

Write $1.73$ as a fraction.

Round $16.749$ to the nearest tenth.

Round $16.749$ to the nearest hundredth.

Simplify: $15.4 + 3.02$

Simplify: $(0.64)(0.3)$

Simplify: $0.96 \div (-12)$

Simplify: $24 \div (0.1 + 0.02)$

Simplify: $1.6 + \tfrac{3}{8}$

Solve: $m + 3.7 = 2.5$

Solve: $-6.5y = -57.2$

Three friends went out to dinner and agreed to split the bill evenly. The bill was $79.35. How much, in dollars, should each person pay?

The ages, in months, of 10 children in a preschool class are: 55, 55, 50, 51, 52, 50, 53, 51, 55, 49. Find the mean.

The ages, in months, of 10 children in a preschool class are: 55, 55, 50, 51, 52, 50, 53, 51, 55, 49. Find the median.

The ages, in months, of 10 children in a preschool class are: 55, 55, 50, 51, 52, 50, 53, 51, 55, 49. Find the mode.

Write the ratio $56$ to $32$ as a fraction. Simplify the answer if possible.

Laundry detergent comes in two sizes: 64 ounces for $10.99 or 48 ounces for $8.49. Find the unit price, in dollars per ounce, of the 64-ounce size. Round to the nearest thousandth of a dollar.

Laundry detergent comes in two sizes: 64 ounces for $10.99 or 48 ounces for $8.49. Find the unit price, in dollars per ounce, of the 48-ounce size. Round to the nearest thousandth of a dollar.

Simplify: $\sqrt{64 + 225}$

Simplify: $\sqrt{144n^2}$ (assume the variable is greater than or equal to zero)

Yanet wants a square patio in her backyard. She has 225 square feet of tile. How long, in feet, can a side of the patio be?

Convert $24\%$ to a decimal.

Convert $24\%$ to a simplified fraction.

Convert $\tfrac{1}{3}$ to a percent. Round to 3 decimal places if needed.

65 is what percent of 260?

When Aurelio and his family ate dinner at a restaurant, the bill was $83.50. Aurelio wants to leave 20% of the total bill as a tip. How much should the tip be?

Jorge got a raise in his hourly pay, from $19.00 to $19.76. Find the percent increase.

The total number of vehicles on one freeway dropped from 84,000 to 74,000. Find the percent decrease. Round to the nearest tenth of a percent.

Andy bought a piano for $4,600. The sales tax on the purchase was $333.50. Find the sales tax rate.

Mara received $31.80 commission when she sold a $795 suit. What was her rate of commission?

Aya bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $75. Find the sale price.

Oxana bought a dresser at a garage sale for $20. She refinished it, then added a 250% markup before advertising it for sale. What price did she ask for the dresser?

Find the principal invested if $660 interest was earned in 5 years at an interest rate of 3%.

Brenda borrowed $400 from her brother. Two years later, she repaid the $400 plus $50 interest. What was the rate of interest?

Solve the proportion: $\tfrac{x}{36} = \tfrac{5}{9}$.

An 8-ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get?

Solve for $a$: $\tfrac{12}{a} = -\tfrac{15}{65}$.