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Length, Time &
Capacity Units

Master unit conversions across length, time, and capacity: the essential skill for quantitative reasoning on the ISEE.

ISEE Middle Level Quantitative Reasoning

What Is Unit Conversion?

Unit conversion means expressing the same measurement in a different unit. The actual amount stays the same: only the label and number change.

Three Measurement Families

Length
How far or how long something is: inches, feet, yards, miles
Time
How long an event takes: seconds, minutes, hours, days
Capacity
How much liquid a container holds: cups, pints, quarts, gallons

Why Conversions Matter

You cannot compare or combine measurements that use different units. Before adding, subtracting, or comparing, every quantity must share the same unit.

3 feet + 6 inches = ? convert 36 in + 6 in = 42 inches ✓ Same unit → safe to add

Key Length Factors

inches ÷ 12 feet ÷ 3 yards ÷ 1,760 miles × 12 × 3 × 1,760 Bigger unit → smaller number (divide) | Smaller unit → bigger number (multiply)

Key Time Factors

seconds ÷ 60 minutes ÷ 60 hours ÷ 24 days × 60 × 60 × 24 Also: 1 week = 7 days | 1 year = 365 days (≈ 52 weeks)

Key Capacity Factors

cups ÷ 2 pints ÷ 2 quarts ÷ 4 gallons × 2 × 2 × 4 1 gallon = 4 quarts = 8 pints = 16 cups

The Multiply or Divide Rule

Going to a Smaller Unit
Multiply by the conversion factor. More small pieces fit inside, so the number gets bigger.
Going to a Bigger Unit
Divide by the conversion factor. Fewer large pieces are needed, so the number gets smaller.

Multiply vs Divide: Side by Side

Smaller → Bigger Unit Bigger → Smaller Unit
Operation Divide Multiply
Number goes Down Up
Example \(36 \text{ in} \div 12 = 3 \text{ ft}\) \(3 \text{ ft} \times 12 = 36 \text{ in}\)
Think Fewer big pieces More small pieces

Step-by-Step Method

1
Identify the units. What unit do you start with? What unit does the answer need?
2
Recall the conversion factor. For example: \(1 \text{ ft} = 12 \text{ in}\).
3
Choose multiply or divide. Going to a smaller unit? Multiply. Going to a bigger unit? Divide.
4
Compute and check. Does the answer make sense? Smaller unit should yield a larger number.

Example 1: Length

Problem: A ribbon is \(4\frac{1}{2}\) feet long. How many inches is that?

1
Units: feet → inches (bigger → smaller)
2
Factor: \(1 \text{ ft} = 12 \text{ in}\)
3
Multiply: \(4.5 \times 12 = 54\)
4
Answer: \(54\) inches ✓ (bigger number, smaller unit)

Example 2: Time

Problem: A movie is \(150\) minutes long. Express this in hours and minutes.

1
Units: minutes → hours + minutes (smaller → bigger)
2
Factor: \(1 \text{ hr} = 60 \text{ min}\)
3
Divide: \(150 \div 60 = 2\) remainder \(30\)
4
Answer: \(2\) hours \(30\) minutes ✓

Example 3: Capacity (Multi-Step)

Problem: A punch bowl holds \(3\) gallons. How many cups is that?

3 gal start × 4 12 qt quarts × 2 24 pt pints × 2 48 cups Shortcut: 1 gallon = 16 cups → 3 × 16 = 48 cups ✓

Common Mistakes

✕ Multiplying When You Should Divide
Converting inches to feet but multiplying by 12 instead of dividing. Always ask: am I going to a bigger or smaller unit?
✕ Wrong Conversion Factor
Mixing up capacity pairs: using 4 instead of 2 for cups-to-pints. Remember: 2-2-4 (cups → pints → quarts → gallons).
✕ Forgetting Remainders
Writing \(150\) min = \(2.5\) hours when the question asks for hours and minutes. The remainder \(30\) must stay as minutes.

Conversion Reference Table

Category Relationship Factor
Length 1 foot = 12 inches 12
Length 1 yard = 3 feet 3
Length 1 mile = 5,280 feet 5,280
Time 1 minute = 60 seconds 60
Time 1 hour = 60 minutes 60
Time 1 day = 24 hours 24
Capacity 1 pint = 2 cups 2
Capacity 1 quart = 2 pints 2
Capacity 1 gallon = 4 quarts 4

Question 1 of 5

How many inches are in \(7\) feet?

Question 2 of 5

A race lasts \(3\) hours and \(15\) minutes. How many minutes is that in total?

Question 3 of 5

How many cups are in \(2\) gallons?

Question 4 of 5

A board is \(108\) inches long. How many yards is that?

Question 5 of 5

Which is greater: \(5\) quarts or \(9\) pints?