61 useful answers · Page 2 of 3
Work through fractions, percentages, measurements, shapes, and useful calculations with examples.
Search this topicPut the percentage over one hundred and simplify. For 32%, write 32/100 = 8/25. If the percentage includes a decimal, clear that decimal from numerator and denominator together: 2.5% = 2.5/100 = 25/1000 = 1/40. Do not assume every percentage can be written with a single-digit denominator.
Convert the percentage to a decimal and multiply it by the whole amount. For 18% of 250, calculate 0.18 × 250 = 45. Identify the correct base first: eighteen percent of a price, quantity, or area uses that original amount. A quick ten-percent estimate helps check whether the result is plausible.
Divide the part by the whole and multiply by one hundred. If 27 of 90 items are finished, 27 ÷ 90 × 100 = 30%. Keep the order clear; dividing ninety by twenty-seven answers something else. The reference whole must not be zero, and both quantities should use comparable units.
Subtract the original value from the new value, divide by the original, and multiply by one hundred. A rise from 80 to 92 is 12 ÷ 80 × 100 = 15%. A negative result indicates a decrease. The formula is undefined from a zero starting value; report the actual change instead.
Subtract the discount percentage from one hundred, then multiply the original price by that remaining fraction. At 30% off a $70 item, you pay 70%: 70 × 0.70 = $49 before any applicable tax or fees. The discount is $21, which is different from the final amount paid.
Divide the sale price by the fraction of the original price still being paid. If $63 is the price after 30% off, calculate 63 ÷ 0.70 = $90. Adding thirty percent to the sale price does not reverse the discount, because that uses a different base. Use the price before additional taxes or fees.
Write equivalent ratios in the same order and cross-multiply. For 3/5 = x/20, the equation is 5x = 60, so x = 12. Check by simplifying 12/20 back to 3/5. Denominators cannot be zero, and matching units must occupy corresponding positions on both sides.
Use the stated scale as a proportion, keeping units consistent. If one centimeter represents half a meter, a seven-centimeter line represents 3.5 meters. Measure the drawing only at its intended printed scale; resizing it changes that relationship. Check a known labeled dimension before using a printed plan for a project.
Divide each price by its quantity in the same unit. A 750-gram pack at $6 costs $0.008 per gram, while a 500-gram pack at $4.50 costs $0.009 per gram. The first has the lower unit price. Compare equivalent products and consider whether you can use the larger amount without waste.
First express the quantities in the same units, then divide both parts by their greatest common factor. A 30:45 ratio becomes 2:3. Preserve the order and labels: two parts of the first material correspond to three parts of the second. A part-to-part ratio is not the same as the first part’s fraction of the total.
Divide total distance by total elapsed time in compatible units. Traveling 135 miles over three hours gives 45 miles per hour. Include stops if you mean the entire trip’s average. Do not simply average two speed readings unless the time spent at each speed is equal.
Add all the values and divide by how many values there are. For 8, 11, 11, and 14, the sum is 44 and the mean is 11. Count repeated values separately. This is the ordinary arithmetic average; it differs from the middle value and from the most frequent value.
Put the values in numerical order. With an odd count, choose the middle value; with an even count, average the two middle values. For 3, 6, 8, and 15, the median is (6 + 8)/2 = 7. Sorting comes first; the middle of an unsorted list is not necessarily the median.
Count how often each value appears and identify the most frequent. In 4, 4, 6, 9, and 9, both four and nine are modes. A set can have more than one mode, or no uniquely most frequent value. Do not confuse frequency with size: the largest number is not automatically the mode.
Divide the inches by twelve and add the feet. For 5 feet 9 inches, calculate 5 + 9/12 = 5.75 feet. Writing 5.9 feet means something different because feet use twelve inches, not ten. For the reverse conversion, multiply only the fractional part of the feet by twelve.
Divide the minutes by sixty and add the whole hours. Two hours forty-five minutes becomes 2 + 45/60 = 2.75 hours. It is not 2.45 hours. To convert back, multiply the decimal portion by sixty; for example, 0.2 hour is twelve minutes, not twenty.
Write a conversion fraction so the unwanted unit cancels. For 2.4 meters to centimeters, use 2.4 m × 100 cm/1 m = 240 cm. The fraction represents the same length on top and bottom. Check the direction: a measurement expressed in smaller units should have a larger numerical count.
Measure its length and width in feet and multiply. A room twelve feet long and nine feet wide has 108 square feet. Convert inches to fractions or decimals of a foot before multiplying. This gives floor area, not wall area; buying flooring also requires a separate allowance for the layout and cutting waste.
Multiply a base by its perpendicular height, then divide by two. A triangle with a ten-inch base and a six-inch perpendicular height has thirty square inches of area. A sloping side is not automatically the height. Keep base and height in the same units before applying the formula.
Add the two parallel side lengths, divide by two, and multiply by the perpendicular distance between them. For parallel sides of four and eight feet with a five-foot height, calculate (4 + 8)/2 × 5 = 30 square feet. Do not substitute a sloping side for the perpendicular height.
Multiply its diameter by pi, or multiply its radius by two and then by pi. A circle ten inches across has a circumference of 10π, approximately 31.42 inches. Radius is half the diameter. Use the calculator’s pi key and round at the end; circumference is a length, not an area.
Multiply the radius by itself, then by pi. A circle with a four-foot radius has area 16π, approximately 50.27 square feet. If you measured across the entire circle, halve that diameter first. Squaring the diameter instead of the radius makes the answer four times too large.
Sketch the floor and divide it into nonoverlapping rectangles, calculate each area, and add them. For sections measuring eight by ten feet and four by six feet, the total is 80 + 24 = 104 square feet. Make sure the sections neither overlap nor leave a gap; label measurements on the sketch.
Multiply length, width, and height using the same units. A box with internal dimensions forty by thirty by twenty centimeters holds 24,000 cubic centimeters before anything is placed inside. Use internal measurements for capacity, since wall thickness reduces usable space. Volume uses cubic units, unlike the square units used for area.
Source checks for these answers: September 22, 2026. Product instructions and local requirements can vary.