Ratios and Proportions Terms

Ratios and proportions 5

• Cross MultiplicationCross multiplication is a shortcut for solving a proportion: if a/b = c/d, then ad = bc. Multiply each numerator by the denominator on the other side and set the two products equal. To solve x/6 = 10/15, write 15x = 60, so x = 4. It works only when one fraction equals one fraction.Grade 7, Grade 8, Algebra 1
• ProportionA proportion is an equation that says two ratios are equal, such as 1/2 = 3/6. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Grade 6, Grade 7, Grade 8
• RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 3/5. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Grade 6, Grade 7, Grade 8
• Scale DrawingA scale drawing is a drawing of a real object in which every length is multiplied by the same number, so it has the same shape but a different size. Its scale, such as 1 cm = 2 m, links a length on the drawing to the actual length. Maps, floor plans and blueprints are scale drawings.Grade 7
• Scale FactorA scale factor is the number used to multiply side lengths when making a similar figure larger or smaller. A scale factor of 2 doubles every length, and a scale factor of 1/2 makes lengths half as large. Find it by dividing a new length by the matching original length. Areas change by the square of the scale factor.Grade 7, Grade 8, Algebra 1

Rates 4

• RateA rate is a ratio that compares two quantities measured in different units, such as 150 miles in 3 hours or 12 dollars for 4 pounds. The word "per" signals a rate. Dividing gives the unit rate, the amount for 1 unit: 150 miles in 3 hours is 50 miles per hour.Grade 6, Grade 7
• Simple InterestSimple interest is interest paid only on the original amount of money, called the principal, at a fixed yearly rate. Find it with I = Prt: multiply the principal by the rate written as a decimal and by the time in years. The interest is the same every year, so the balance grows in a straight line.Grade 7, Algebra 1
• Unit PriceA unit price is the cost of one unit of something, found by dividing the total price by the number of units. For example, 18 dollars for 6 pounds is 18 ÷ 6 = 3 dollars per pound. It is the fairest way to compare products sold in different package sizes: the lower unit price costs less per unit.Grade 6, Grade 7, Grade 8
• Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Grade 6, Grade 7, Grade 8

Proportional relationships 4

• Constant of ProportionalityThe constant of proportionality is the constant ratio between two proportional quantities, k = y/x. It is the k in y = kx and stays the same for every pair of values, which makes the graph a straight line through the origin. If 3 notebooks cost 9 dollars, k = 3 dollars per notebook.Grade 7, Grade 8, Algebra 1
• Directly ProportionalDirectly proportional describes two quantities whose ratio never changes: y = kx for a fixed nonzero number k, the constant of proportionality. If x doubles, y doubles; if x is cut in half, so is y. The graph is a straight line through the origin, and y/x = k for every pair.Grade 7, Grade 8, Algebra 1
• Inversely ProportionalInversely proportional describes two quantities whose product never changes: y = k/x, or xy = k, for a fixed nonzero number k. When one quantity doubles, the other is cut in half. On a 120-mile trip, speed and time are inversely proportional: 60 mph takes 2 hours and 30 mph takes 4 hours.Grade 8, Algebra 1, Algebra 2
• Proportional RelationshipA proportional relationship is a relationship between two quantities in which one is always the same multiple of the other, so y = kx for a fixed number k. The ratio y/x is the same for every pair, and the graph is a straight line through the origin. Example: at 3 dollars per pound, cost = 3 × pounds.Grade 7, Grade 8, Algebra 1

Percent change 3

• Percent ChangePercent change measures how much a value grew or shrank relative to where it started: the difference divided by the original amount, written as a percent. From 50 to 60 is a 20% increase; from 80 to 60 is a 25% decrease. The original value is always the base, which is the step people get wrong.Grade 7, Grade 8, Algebra 1
• Percent DecreasePercent decrease is how much a quantity went down, written as a percent of its original value. Subtract the new value from the original, divide by the original, and multiply by 100. A price that drops from 80 dollars to 60 dollars has a decrease of 20 dollars, and 20/80 = 25%.Grade 7, Grade 8, Algebra 1
• Percent IncreasePercent increase is how much a quantity grew, written as a percent of its original value. Subtract the original from the new value, divide by the original, and multiply by 100: from 80 to 100 is 20/80 = 25%. To increase a number by r%, multiply it by 1 + r/100, so 80 × 1.25 = 100.Grade 7, Grade 8, Algebra 1

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Updated November 2026·Reviewed by the Effortless Math team