Original explanations and practice in fractions, percentages, ratios, introductory algebra and geometry, with a fraction calculator that shows its reasoning.
Fraction steps & practice ↗Detailed explanations · Worked examples · Practical tools
An original illustration for CLEAR MATH. Start with a guide or explore the practical tools below.
20 complete guides.
A denominator names the size of a piece. Before combining fractions, make those pieces comparable. A short drawing and a careful equivalent-fraction step make the arithmetic easier to check.
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Multiplication can mean taking part of a quantity. Division can ask how many groups fit. Connect those meanings to the written rules before practicing with positive and negative fractions.
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A percentage describes a part relative to a stated whole. Identify what is known and what is missing before choosing a calculation. The same relationship solves three common kinds of question.
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A ratio compares quantities in a stated order. Sharing a total and scaling a known pair are related tasks, but they start with different information. Label the parts before calculating.
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An equation states that two expressions have the same value. Solve it by preserving that equality, then substitute your answer into the original statement to see whether it works.
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Perimeter measures a boundary. Area measures a surface. A labeled sketch, compatible units and a sensible estimate prevent many errors before any formula is used.
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Equivalent fractions describe the same number using different equal-sized parts. Learn why multiplying or dividing both parts by the same nonzero factor preserves the value, then use that idea to simplify.
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A mixed number combines a whole-number part and a proper fraction. Convert by counting equal fractional units, and pay particular attention to grouping when negative signs are involved.
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A larger denominator does not automatically mean a larger fraction. Compare equal units, use useful benchmarks and remember that negative numbers reverse some familiar intuitions about size.
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A decimal digit gets its value from its position. Read the places first, then use the next place to decide a rounding step. Zeros can preserve meaning even when they do not change the numerical value.
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A fraction and a decimal can name the same number. Some fractions end neatly in decimal form; others repeat. Keep an exact fraction when rounding would hide the relationship you need.
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Negative numbers extend the number line to the left of zero. Separate the sign of a value from the operation being performed, and use a consistent model to explain each step.
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Operation order makes a written expression unambiguous. Work inside grouping symbols first, handle powers, then perform multiplication and division together before addition and subtraction together.
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Distribution connects a product with a sum. Use a rectangular model and careful signs to understand expansion, then reverse the same relationship when factoring a common term.
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An inequality describes a range of possible values. Preserve the comparison while simplifying, and show whether the boundary itself belongs to the answer.
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An ordered pair describes a position relative to an origin and two axes. Its order, scale and signs matter. Build a consistent plotting routine before connecting points into a graph.
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An average helps only when its meaning is clear. Calculate three common summaries, see how they react to an unusual value, and keep the original observations and units available.
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The favorable-outcomes fraction requires equally likely outcomes. Define the experiment, list its possible results and check that assumption before converting counts into a probability.
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An angle measures turning between rays. Label the diagram and state the relationship before finding a missing value. A printed opening that looks nearly right is not a measurement.
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The relationship a² + b² = c² applies to a right triangle, with c opposite the right angle. Identify those roles before entering any lengths into the formula.
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