SSAT Upper Level

Unit Conversions

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

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Imagine you are baking the ultimate, gooey, chocolate chip monster cookie. 🍪 The recipe says you need 24 teaspoons of sugar, but you only have a tablespoon! Uh oh. How do you measure it? Welcome to the magical world of Unit Conversions!

Unit conversion is just a fancy way of translating one math language into another. It’s like trading 10 dimes for 1 dollar bill. You still have the exact same amount of money, it just looks different! 💵 On the SSAT, you will act as a math translator. You might need to turn feet into inches to measure a treehouse, or change hours into minutes to see how long a soccer game lasts. ⚽

The trick is knowing your basic measurements and figuring out if you need to multiply or divide. If you are going from a BIG unit (like a gallon) to a SMALL unit (like a cup), you will have more pieces, so you multiply. If you are going from a SMALL unit (like inches) to a BIG unit (like miles), you will have fewer pieces, so you divide. Get ready to level up your measuring skills and crush those SSAT word problems! 🚀

Key Formula

To convert units, multiply your starting number by a fraction where the top and bottom are equal amounts:

Start \times \frac{Wanted Unit}{Starting Unit} = New Unit

. For time, always remember

1 hour = 60 minutes

, so

45 minutes = \frac{45}{60} hours = \frac{3}{4} hours

Practice Questions

4 practice questions for SSAT Upper Level

Q1 Hard

1 chain = 22 yards
1 yard = 3 feet
1 foot = 12 inches

Based on the information above, how many inches are there in 1.5 chains?

A 99

B 396

C 594

D 1,188

E 1,584

Show Solution

To find the total number of inches, convert chains to yards, then to feet, and finally to inches.

First, convert chains to yards: $1.5 \times 22 = 33$ yards.
Next, convert yards to feet: $33 \times 3 = 99$ feet.
Finally, convert feet to inches: $99 \times 12 = 1, 188$ inches.

Answer: D

Q2 Hard

A single sheet of specialized paper is 0.15 millimeters thick. If a stack contains 4,000 sheets of this paper, what is the height of the stack in meters?

A 0.06

B 0.6

C 6

D 60

E 600

Show Solution

First, find the total thickness of the stack in millimeters by multiplying the number of sheets by the thickness per sheet: $4, 000 \times 0.15 = 600$ millimeters. To convert millimeters to meters, divide by $1, 000$ since there are $1, 000$ millimeters in a meter: $\frac{600}{1 , 000} = 0.6$ meters.

Answer: B

Q3 Hard

A drone can lift a maximum payload of 850 grams. A camera weighing 12 ounces is attached to the drone. Of the following, what is the largest mass of additional equipment, in grams, that can be added to the drone without exceeding its lifting capacity? (1 ounce = 28 grams)

A 336

B 414

C 514

D 526

E 838

Show Solution

First, convert the weight of the camera into grams: $12 \times 28 = 336$ grams. The drone can lift a total of $850$ grams. To find the maximum additional mass, subtract the mass of the camera from the total capacity: $850 - 336 = 514$ grams.

Answer: C

Q4 Hard

A leaky faucet drips water at a constant rate of 5 milliliters per minute. How many liters of water will leak from the faucet in exactly 4 hours?

A 0.12

B 1.2

C 12

D 20

E 120

Show Solution

First, find the total number of minutes in $4$ hours: $4 \times 60 = 240$ minutes. Next, calculate the total amount of water leaked in milliliters by multiplying the time by the rate: $240 \times 5 = 1, 200$ milliliters. Finally, convert milliliters to liters by dividing by $1, 000$ : $\frac{1 , 200}{1 , 000} = 1.2$ liters.

Answer: B

Tips & Strategies

Write down your units! When you set up a math problem, treat the unit words (like 'inches' or 'hours') just like numbers. If you have 'hours' on top of a fraction and 'hours' on the bottom, cross them out! ✏️
Memorize the 'Big 4' time fractions for the SSAT: 15 minutes is $\frac{1}{4}$ hour, 30 minutes is $\frac{1}{2}$ hour, 45 minutes is $\frac{3}{4}$ hour, and 60 minutes is 1 full hour. ⏱️
When dealing with the metric system, just move the decimal! Moving from Liters to Milliliters? Move the decimal 3 spots to the right.

Common Mistakes

Watch out for the 'Time Trap'! There are 60 minutes in an hour, NOT 100. If an SSAT question says $1.5$ hours, that is 1 hour and 30 minutes, not 1 hour and 50 minutes! ⏰
Don't forget to check if you are going Big-to-Small or Small-to-Big. A common mistake is dividing when you should multiply. Remember: Big to Small, Multiply All! Small to Big, Divide the Pig! 🐷

Frequently Asked Questions

Do I need to memorize all the conversion rates for the SSAT?

You should memorize the basic ones! Know your time (60 seconds = 1 minute), basic Customary length (12 inches = 1 foot, 3 feet = 1 yard), and basic Metric prefixes (kilo, centi, milli). The SSAT usually gives you a hint for the weird ones, like how many feet are in a mile.

What is the difference between Metric and Customary units?

Customary units are what we mostly use in the USA, like inches, pounds, and gallons. Metric units are used by scientists and most of the world, like meters, grams, and liters. 🌍 Metric is super easy because everything is based on the number 10!

How often do unit conversions show up on the test?

You will definitely see them! They usually pop up in word problems. Sometimes a whole question is just about converting, but often it's a hidden step you have to do before solving the rest of the problem. 🕵️‍♂️

How do I know if I should multiply or divide?

Think about the size of the pieces! If you trade a big 1-dollar bill for small pennies, you get a LOT of pennies (multiply). If you trade lots of small pennies for big 1-dollar bills, you get FEWER bills (divide).

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