Solve proportions a/b = c/d for any unknown variable using cross multiplication. Get step-by-step solutions and verify your answer.
C =
9
Unknown value
Enter three values and select which variable to solve for:
The unknown value is:
c = 9
Left Side (a/b)
3/4 = 0.75
Right Side (c/d)
9/12 = 0.75
Verified!
Cross products: 36 = 36
Starting proportion: 3/4 = c/12
Cross multiply: 3 * 12 = 4 * c
Simplify left side: 36 = 4 * c
Divide both sides by 4: c = 36 / 4
Solution: c = 9
Verification: 3/4 = 0.750000 and 9/12 = 0.750000
Outer (a * d)
a * d
Inner (b * c)
b * c
The cross products are always equal: a*d = b*c
C =
9
Unknown value
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Practice with 3 problems to test your understanding.
To solve a proportion a/b = c/d, cross multiply: a * d = b * c. Then solve for the unknown. For example, to find x in 3/4 = x/12, cross multiply: 3 * 12 = 4 * x, so 36 = 4x, thus x = 9. You can verify by checking that 3/4 = 9/12 = 0.75.
A proportion is an equation stating that two ratios are equal. Written as a/b = c/d or a:b = c:d, it means the relationship between a and b is the same as between c and d. Proportions can be solved using cross multiplication, where you multiply the numerator of each fraction by the denominator of the other. This technique stems from the fundamental property that equal fractions have equal cross products.
A proportion is a mathematical statement that two ratios (or fractions) are equal. It can be written as a/b = c/d or a:b = c:d. For example, 1/2 = 3/6 is a proportion because both sides equal 0.5. Proportions express that the relationship between the first pair of numbers is identical to the relationship between the second pair.
Use cross multiplication: multiply the numerator of each fraction by the denominator of the other. For a/b = c/d, you get a*d = b*c. Then solve for the unknown. Example: Find x in 5/8 = x/24. Cross multiply: 5*24 = 8*x, so 120 = 8x, thus x = 15. Verify: 5/8 = 15/24 = 0.625.
Cross multiplication is a technique for solving proportions. In a/b = c/d, you multiply diagonally: a times d and b times c. These products are equal (a*d = b*c). This works because multiplying both sides of a/b = c/d by bd gives ad = bc. The name comes from the crossing pattern when you draw the multiplications.
In the proportion a:b = c:d, the extremes are the first and last terms (a and d), while the means are the middle terms (b and c). The fundamental property of proportions states that the product of the extremes equals the product of the means: a*d = b*c. This is what makes cross multiplication work.
Proportions are used everywhere: (1) Scaling recipes (if 2 cups serve 4, how many for 6?), (2) Map scales (1 inch = 10 miles), (3) Currency exchange rates, (4) Similar triangles in geometry, (5) Mixing ratios (paint, concrete), (6) Unit conversions, (7) Speed/distance/time problems, (8) Percentages and probability.
Cross multiply and see if the products are equal. For a/b and c/d to be proportional, a*d must equal b*c. Example: Are 3/4 and 9/12 proportional? Check: 3*12 = 36 and 4*9 = 36. Yes, they are equal, so 3/4 = 9/12 is a valid proportion.
In direct proportion, when one quantity increases, the other increases proportionally (y = kx). Example: more hours worked = more pay. In inverse proportion, when one increases, the other decreases (y = k/x). Example: more workers = less time to finish a job. This calculator solves direct proportions.
Yes, proportions work with any numbers: whole numbers, decimals, fractions, or mixed numbers. The cross multiplication method works the same way. For example, 0.5/1.5 = 2/6 is valid because 0.5*6 = 3 and 1.5*2 = 3. The calculator handles all number types.
Last updated: 2025-01-15
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C =
9
Unknown value