ISEE Upper Level

Unit Conversions

Converting between units of length, weight, capacity, and time — unit arithmetic only

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Imagine trying to trade 10 pieces of candy for a new video game. Your friend says, "No way, this game costs 20 dollars!" How do you know if it's a fair trade? You have to convert candy to dollars! 🍬

Unit conversions are just like translating languages, but for numbers. On the ISEE, you might need to change inches to feet, minutes to hours, or meters to centimeters. It's like knowing that 4 quarters equal 1 dollar. If you have 12 quarters, you can easily trade them in for 3 dollars! 🎮

The ISEE Mathematics Achievement section loves to test if you can switch between units. Sometimes the test makers are nice and give you the conversion rule (like 1 mile = 5,280 feet). But for the basics, you are the boss! You should memorize everyday facts like 12 inches in a foot, 60 seconds in a minute, and 100 centimeters in a meter. 📏

You will also see these pop up in the Quantitative Reasoning section, where you might have to compare two columns. For example, Column A might be '2 hours' and Column B might be '100 minutes.' By converting hours to minutes, you instantly know Column A is bigger! Always write down your units like they are part of the math problem. If you set it up right, the old units will magically vanish, leaving you with exactly what you need.

Key Formula

Starting Amount \times \frac{Unit You Want}{Unit You Have} = New Amount

Practice Questions

4 practice questions for ISEE Upper Level

Q1 Hard

A hose is filling a pool at a rate of 12 gallons per minute. There are 128 fluid ounces in 1 gallon. Which expression has a value equal to the hose's flow rate in fluid ounces per second?

\frac{12 \times 128}{60}

\frac{12 \times 60}{128}

\frac{128 \times 60}{12}

\frac{12}{128 \times 60}

Show Solution

Using unit analysis, set up the conversion to cancel out gallons and minutes: $12 \frac{gallons}{minute} \times \frac{128 ounces}{1 gallon} \times \frac{1 minute}{60 seconds}$ . Multiplying across the numerators and denominators gives $\frac{12 \times 128}{60}$ fluid ounces per second.

Answer: A

Q2 Hard

There are approximately 3,280 feet in 1 kilometer. A train is traveling at a speed of 120 kilometers per hour. Which expression represents the train's speed in feet per second?

\frac{120 \times 60 \times 60}{3 , 280}

\frac{120 \times 3 , 280}{60 \times 60}

\frac{3 , 280 \times 60}{120 \times 60}

\frac{120}{3 , 280 \times 60 \times 60}

Show Solution

Set up the conversion using unit analysis to cancel out kilometers and hours: $120 \frac{km}{hour} \times \frac{3 , 280 feet}{1 km} \times \frac{1 hour}{60 minutes} \times \frac{1 minute}{60 seconds}$ . Multiplying the numerators and denominators gives $\frac{120 \times 3 , 280}{60 \times 60}$ feet per second.

Answer: B

Q3 Hard

Which is the most reasonable unit to use when measuring the mass of a standard pencil?

A milligrams

B grams

C kilograms

D liters

Show Solution

A standard pencil weighs about 5 to 10 grams. Milligrams are too small (used for very light things like medicine doses), kilograms are too large (used for human body weight or heavier objects), and liters measure volume, not mass. Therefore, grams are the most reasonable unit.

Answer: B

Q4 Hard

A machine produces 450 candies per hour. Each candy weighs 5 grams. There are 1,000 grams in 1 kilogram. Which expression represents the machine's production rate in kilograms per day?

\frac{450 \times 5 \times 24}{1 , 000}

\frac{450 \times 5}{1 , 000 \times 24}

\frac{450 \times 24}{5 \times 1 , 000}

\frac{450 \times 1 , 000}{5 \times 24}

Show Solution

Use unit analysis to convert candies per hour to kilograms per day: $450 \frac{candies}{hour} \times \frac{5 grams}{1 candy} \times \frac{1 kg}{1 , 000 grams} \times \frac{24 hours}{1 day}$ . Multiplying across the numerators and denominators yields $\frac{450 \times 5 \times 24}{1 , 000}$ kilograms per day.

Answer: A

Tips & Strategies

📝 Write out the words! If you put 'miles' on top and 'miles' on the bottom of your fractions, you can cross them out just like numbers. This proves you set the math up correctly.
🧠 Memorize the 'everyday' units before test day. The ISEE will usually tell you how many feet are in a mile, but they expect you to know that there are 60 minutes in an hour, 12 inches in a foot, and 16 ounces in a pound!
🐘 Use the 'Big to Small' trick. Going from a Big unit (like hours) to a Small unit (like minutes)? Multiply! Going from Small to Big? Divide!

Common Mistakes

🛑 Watch out for converting only halfway! If a question asks for feet per second, don't stop at feet per minute. Always re-read the final sentence of the question to check what unit they want.
🏃 Don't forget to line up your decimal points when multiplying or dividing by 10, 100, or 1,000 in the metric system. Moving the decimal the wrong way is a super common trap!

Frequently Asked Questions

Do I need to memorize every single unit conversion? 🤔

Nope! The ISEE usually gives you the weird ones (like how many feet are in a mile). Just memorize the basics: time (seconds/minutes/hours), basic length (inches/feet/yards), and the metric system prefixes (milli, centi, kilo).

What if I forget if I should multiply or divide?

Use the fraction trick! Write your numbers as fractions with the words attached. If you want to get rid of inches and change to feet, put inches on the bottom of your fraction so they cross out. The math will naturally tell you whether to multiply or divide.

Are unit conversions on both math sections of the ISEE? ⚖️

Yes! You might see them as regular word problems in the Mathematics Achievement section, or as tricky comparisons in the Quantitative Reasoning section where you have to decide if Column A or Column B is bigger.

What if I get totally stuck on a conversion? 🎯

Since the ISEE has absolutely no penalty for guessing, you should never leave a question blank! Use your common sense to eliminate answers that are way too big or way too small, pick your favorite letter from what's left, and move on.

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