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Math Practice Quiz

19 Questions 12 min
Math Practice Quiz focuses on Quz-style intermediate problems: fraction operations, percent change, one-variable linear equations, and multi-step word problems. You will practice setting up expressions from text, tracking units, and checking results with estimation. This skill set supports students, technicians, and analysts who make pricing, time, and quantity decisions.
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1You are scaling a recipe and need to simplify the fraction 6/8 before you multiply it. What is 6/8 in simplest form?
2A label says a solution is 15% salt. As a decimal, what is 15%?
3You estimate a bill using 3 + 4 × 2. What is the value of the expression?
4A job takes 2.5 hours. How many minutes is that?
5A store coupon takes 30% off an $80 item. How much is the discount amount?
6You are mixing solutions and need 1/3 of a bottle plus 1/6 of a bottle. What is 1/3 + 1/6?
7A technician records an offset error modeled by x − 5 = 12. What is x?
8A 10% increase means you add 10% of the new value to get the new value.

True / False

9You are simplifying an expression and need to expand 2(x − 3). What do you get?
10A $50 part is discounted 20%. What is the final price?
11A length is 3/4 of a meter, and you need 8 times that length. What is (3/4) × 8?
12A service fee rises from $50 to $60. What is the percent increase?
13You drive 150 miles in 2.5 hours. What is your average speed in miles per hour?
14The expression 3x + 2 simplifies to 5x.

True / False

15A shipping cost model is 2x + 3 = 15, where x is the number of boxes. What is x?
16A mixture ratio uses the expression (3/5) ÷ (2/3). What is the value?
17If 3 items cost $7.50, the unit price is $2.50 per item.

True / False

18A machine produces 120 parts in 3 minutes at a steady rate. How many parts per minute is that?
19A jacket costs $80. It is discounted 25%, then an 8% sales tax is applied to the discounted price. What is the final price?
20Solve for x: 4(2 − x) + 3 = 15.
21A pump fills 12 gallons in 15 minutes at a steady rate. About how many gallons will it fill in 2.5 hours?
22A tool costs $240. A sale takes 15% off, then you use a $20 coupon, then 7.5% tax is applied to the discounted price. What is the final price (nearest cent)?
23Your phone plan charges a $25 base fee plus $0.12 per text. If your bill is $43, how many texts did you send?

Frequent Setup Errors in Intermediate Quz-Style Math

1) Solving the right math for the wrong target

A common miss is answering a related quantity instead of the asked quantity. Example: you compute the discount amount ($12 off) when the question asks for the final price ($48). Before computing, write a one-line target with units, like final price ($) or rate (miles per hour).

2) Percent base confusion

“10% increase” and “10 percentage points” are different. Percent change uses the original as the base: (new − old) ÷ old. In word problems, label the base right next to the percent step, like “10% of old.”

3) Incorrectly stacking percents

Successive changes must be multiplied, not added. A 20% decrease then a 10% decrease is ×0.80 then ×0.90, which is an overall 28% decrease, not 30%.

4) Fraction rule mix-ups

  • Add/Subtract: using a common denominator is required. Do not add denominators.
  • Divide: multiply by the reciprocal of the second fraction. People often flip the wrong fraction.
  • Simplify: reduce before multiplying to avoid large numbers.

5) Distribution and sign slips in linear expressions

Errors often come from missing a negative: −(x − 3) = −x + 3. Show one operation per line and keep parentheses until distribution is finished.

6) Units and rounding mistakes

Convert minutes to hours (or vice versa) before forming an equation. Keep extra decimals through the last step, then round once to match the requested precision.

Printable Intermediate Math Quick Sheet: Fractions, Percents, and One-Variable Algebra

Printable note: You can print this page or save it as a PDF and keep this sheet next to you for timed practice.

Order of operations (PEMDAS)

  • Parentheses
  • Exponents
  • Multiplication and division (left to right)
  • Addition and subtraction (left to right)

Fractions and decimals

  • Simplify: divide numerator and denominator by the GCF.
  • Add/Subtract: convert to a common denominator, then add or subtract numerators.
  • Multiply: multiply numerators and denominators, then simplify. Cross-cancel first when possible.
  • Divide: a/b ÷ c/d = a/b × d/c.
  • Decimal to fraction: write as (integer)/(power of 10), then simplify. Example: 0.125 = 125/1000 = 1/8.

Percents and percent change

  • Percent to decimal: p% = p/100.
  • Part equation: part = (percent as decimal) × whole.
  • Percent change: (new − old) ÷ old, then convert to a percent.
  • Successive percent steps: multiply step factors in order. Example: 25% off then 8% tax is ×0.75 then ×1.08.
  • Reverse a percent change: if final = original × 0.80, then original = final ÷ 0.80.

One-variable linear equations

  • Goal: isolate the variable using inverse operations.
  • Keep balance: whatever you do to one side, do to the other side.
  • Distribute: a(b + c) = ab + ac.
  • Collect like terms: x-terms together, constants together.
  • Check: substitute your solution back into the original equation.

Word-problem setup checklist

  • Write what the question wants in one line with units.
  • Define the variable with units, like x = number of tickets.
  • Translate rate language: “per” means multiply, “total” means sum.
  • Do a quick estimate to catch impossible results (negative counts, wrong magnitude).

Step-by-Step Walkthroughs: Percent Chains and One-Variable Equations

Example 1: Successive percent steps (discount then tax)

Problem: A jacket costs $80. It is discounted 25%, then an 8% sales tax is applied to the discounted price. What is the final price?

  1. Translate percents to multipliers. 25% off means keep 75%: multiplier = 0.75. Tax adds 8%: multiplier = 1.08.
  2. Apply in order. Final = 80 × 0.75 × 1.08.
  3. Compute stepwise. 80 × 0.75 = 60. Then 60 × 1.08 = 64.8.
  4. Answer with money format. Final price = $64.80.
  5. Estimation check. 25% off takes it to about $60. Adding a bit of tax should land mid $60s, so $64.80 is reasonable.

Example 2: One-variable linear equation with units

Problem: A texting plan charges a $15 monthly fee plus $0.08 per text. Your bill is $27.80. How many texts did you send?

  1. Define the variable. Let x = number of texts (texts).
  2. Write the equation with units. 15 (dollars) + 0.08 (dollars/text) × x (texts) = 27.80 (dollars).
  3. Isolate the variable. 0.08x = 27.80 − 15 = 12.80.
  4. Divide. x = 12.80 ÷ 0.08 = 160.
  5. Check. 15 + 0.08(160) = 15 + 12.80 = 27.80, so 160 texts.

Math Practice Quiz FAQ: Fractions, Percent Change, and Word-Problem Setup

How do I decide what “of” means in percent problems?

In most word problems, “of” indicates multiplication: 30% of 50 is 0.30 × 50. The key is identifying the base, which is the “whole” the percent is taken from. Write a short label like “base = original price” before you calculate.

Why is 20% off then 10% off not a 30% discount?

The second percent applies to the already reduced price. Use multipliers: ×0.80 then ×0.90 gives ×0.72 overall, which is a 28% total reduction. If the problem asks for the final price, compute the final amount first, then convert to a percent change only if requested.

What is the fastest safe method for adding fractions?

Use a common denominator, but pick the least common denominator when it is easy. Example: 1/6 + 1/4, the LCD is 12, so 2/12 + 3/12 = 5/12. If fraction addition feels slow, practice the core mechanics on 5th Grade Fractions Skills Practice Quiz and then return to the intermediate mixed problems.

How can I stop making sign mistakes when distributing?

Attach the negative to the parentheses before you expand. Rewrite −(x − 3) as (−1)(x − 3), then distribute: −1·x + (−1)(−3) = −x + 3. If you tend to rush, keep parentheses until the final distribution step.

When should I round in percent and rate problems?

Round at the end unless the question forces rounding midstream (for example, “round each monthly payment to the nearest cent”). Early rounding can move the final percent change by a full percentage point. Keep extra digits during division, then round once to the requested precision.

What should I study next if these problems feel easy?

Move to harder multi-step algebra and mixed-operations items that punish setup errors. Use Hard Math Challenge With Answers to practice longer chains of reasoning and tighter distractors.

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