Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

Opening subject page...

Loading your content

  1. 5th Grade Math
  2. Convert Units and Solve Problems

5TH GRADE MATH • MEASUREMENT AND DATA

Convert Units and Solve Problems

Learn how to switch between measurement units so you can solve real-world problems like a pro!

SECTION 1

Why Do We Need to Convert Units?

Have you ever wondered why your family measures some things in feet and other things in inches? Or why a recipe might use cups, but milk comes in gallons? People have been measuring things for thousands of years. Long ago, different towns and countries all had their own ways to measure. That caused a lot of confusion! Over time, people created measurement systems so everyone could agree on the same units.

3000 BC
Ancient Egypt
Egyptians used body parts like the forearm (called a cubit) to measure length. This was not very exact because everyone's arm is different!
1200s
King's Foot
In England, the king's foot became the standard "foot" of measurement. That's where we get 12 inches = 1 foot!
1790s
The Metric System Is Born
Scientists in France created the metric system. It uses meters, grams, and liters. It is based on the number 10, which makes converting very easy.
Today
Two Systems Side by Side
The United States uses the customary system (inches, pounds, gallons) every day, but also uses the metric system in science. Being able to convert within each system is a super-important skill!

Because we use many different units, we need a way to switch between them. That's what unit conversion is all about. In this lesson, you will learn how to convert between units in the same system and use those skills to solve real-world problems.

SECTION 2

Core Principles of Unit Conversion

Before we start converting, let's learn four big ideas that will guide us every step of the way.

1

Same System, Different Sizes

We convert within one measurement system at a time. Inches, feet, and yards are all in the customary system. Centimeters, meters, and kilometers are all in the metric system.
2

Conversion Factors Are the Key

A conversion factor tells you how two units compare. For example, 1 foot = 12 inches. That "12" is your magic number for switching between feet and inches.
3

Multiply to Go Smaller, Divide to Go Bigger

Going from a bigger unit to a smaller unit? Multiply. Going from a smaller unit to a bigger unit? Divide. Think: more small pieces, fewer big pieces.
4

The Amount Stays the Same

When you convert 3 feet to 36 inches, the actual length hasn't changed. You just described it with different-sized units. It's like trading one dollar bill for four quarters — same value!
✦ KEY TAKEAWAY
Think of converting units like exchanging coins. If you trade 1 dollar for 4 quarters, you have more coins, but the same amount of money. Converting 1 yard into 3 feet works the same way — more pieces, but the same total length!
SECTION 3

Seeing How Units Connect

The diagram below shows common units of length in both the customary and metric systems. Notice how arrows show the conversion factor between each pair. When you move down the chart (to smaller units), you multiply. When you move up (to bigger units), you divide.

CUSTOMARY LENGTHMETRIC LENGTHMile× 5,280Foot× 12Inch÷ to go upKilometer (km)× 1,000Meter (m)× 100Centimeter (cm)× 10Millimeter (mm)÷ to go upREMEMBER⬇ Smaller unit → MULTIPLY | ⬆ Bigger unit → DIVIDE
This chart shows how customary and metric length units relate. Follow the arrows down and multiply by the number shown. Go up and divide instead.

Look at the metric side. Going from meters to centimeters, you multiply by 100. So 5 meters = 5 × 100 = 500 centimeters. Going the other way, 500 centimeters ÷ 100 = 5 meters. The customary side works the same way, just with different numbers.

SECTION 4

The Math Behind Converting Units

Every conversion uses one simple idea: multiply or divide by a conversion factor. Here are the formulas you will use most.

BIG UNIT → SMALL UNIT
Small units = Big units × Conversion factor
Example: feet → inches. Since 1 foot = 12 inches, multiply by 12. So 3 feet = 3 × 12 = 36 inches.
SMALL UNIT → BIG UNIT
Big units = Small units ÷ Conversion factor
Example: centimeters → meters. Since 1 meter = 100 centimeters, divide by 100. So 250 cm = 250 ÷ 100 = 2.5 meters.
METRIC SHORTCUT (LENGTH)
km ×1,000→ m ×100→ cm ×10→ mm
The metric system is built on 10s. To go the other direction, divide by the same numbers.
💡 Quick Tip
When you convert to a smaller unit, your answer should be a bigger number. When you convert to a bigger unit, your answer should be a smaller number. Use this to check if your answer makes sense!
SECTION 5

Common Conversion Factors You Need to Know

Below are the most important conversion factors for 5th grade. You do not need to memorize every single one right away, but the more you practice, the faster you will remember them!

Common conversion factors for customary and metric systems
TypeCustomaryMetric
Length1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5,280 ft1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm
Mass / Weight1 lb = 16 oz, 1 ton = 2,000 lb1 kg = 1,000 g, 1 g = 1,000 mg
Capacity1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 c, 1 c = 8 fl oz1 L = 1,000 mL
Time1 hr = 60 min, 1 min = 60 secSame as customary
CUSTOMARY CAPACITY — The Gallon House1 GALLON2 QUARTS2 QUARTS= 4 QUARTS total1 PT1 PT1 PT1 PT= 8 PINTS total (each quart = 2 pints)CCCCCCCC= 16 CUPS total (each pint = 2 cups)1 gal = 4 qt = 8 pt = 16 cups
The Gallon House shows how customary capacity units nest inside each other. One gallon holds 4 quarts, each quart holds 2 pints, and each pint holds 2 cups.

The Gallon House is a great picture to keep in your head. It shows that each big unit breaks into smaller units. For example, if you need to know how many cups are in 2 gallons, you can trace through: 2 gallons × 16 cups per gallon = 32 cups!

SECTION 6

Worked Example: A Multi-Step Problem

Let's solve a real-world problem step by step. Read carefully and follow along!

📐 Problem
Maya's class is building a garden border. They need 3 pieces of wood. The first piece is 4 feet long. The second piece is 36 inches long. The third piece is 2 feet 6 inches long. What is the total length of wood they need, in inches?

Step-by-Step Solution

Step 1 — Identify What You Know

Piece 1 = 4 feet. Piece 2 = 36 inches. Piece 3 = 2 feet 6 inches. The question asks for the total in inches.

Step 2 — Convert Piece 1 to Inches

Since 1 foot = 12 inches, multiply: 4 × 12 = 48 inches.
Piece 1 = 48 inches

Step 3 — Piece 2 Is Already in Inches

Piece 2 is already given as 36 inches. No conversion needed!
Piece 2 = 36 inches

Step 4 — Convert Piece 3 to Inches

First convert the feet part: 2 × 12 = 24 inches. Then add the 6 inches: 24 + 6 = 30 inches.
Piece 3 = 30 inches

Step 5 — Add All Three Pieces

48 + 36 + 30 = 114 inches.
Total = 114 inches
🔑 STRATEGY RECAP
In multi-step problems, always convert everything to the same unit first, then do the math. It's like making sure all your puzzle pieces are the same shape before you try to fit them together!
SECTION 7

Common Mistakes and How to Avoid Them

Even great math students make mistakes with unit conversion. Here are the most common ones and how to fix them.

Avoid these common pitfalls when converting units
Common MistakeWhy It HappensHow to Fix It
Multiplying when you should divide (or the other way around)Forgetting which direction the conversion goesAsk: Am I going to a smaller unit (multiply) or a bigger unit (divide)? Check that your answer makes sense!
Mixing up conversion factorsConfusing 1 ft = 12 in with 1 yd = 3 ft, etc.Keep a conversion chart handy until you memorize the facts. Double-check which units you are converting.
Forgetting to convert all values to the same unitRushing through a multi-step problemUnderline the units in the problem. Before adding or subtracting, make sure every number uses the same unit.
Getting the decimal point wrong in metricLosing track of zeros when multiplying or dividing by 10, 100, or 1,000Count the zeros carefully. Multiplying by 100 moves the decimal 2 places right. Dividing by 100 moves it 2 places left.
✦ KEY TAKEAWAY
Always do a "does this make sense?" check at the end. If you converted feet to inches, your number should be bigger. If you converted grams to kilograms, your number should be smaller. If your answer goes the wrong direction, you probably multiplied when you should have divided, or vice versa.
SECTION 8

Looking Ahead: Where Will This Take You?

The unit conversion skills you are learning now will grow with you through middle school and beyond. Here's a sneak peek at how these skills build over time.

How unit conversion skills grow from 5th grade onward
What You Learn Now (5th Grade)What Comes Next (6th Grade & Beyond)
Convert within one system (customary or metric)Convert between systems (e.g., inches to centimeters)
Use whole numbers and simple decimalsWork with fractions and mixed numbers in conversions
Solve 2–3 step word problemsUse unit rates, ratios, and proportions
Convert length, weight, and capacityConvert area (square units) and volume (cubic units)

In science classes, you will use metric conversions all the time. In everyday life, you will use customary conversions when you cook, build things, or measure distances. The more you practice now, the easier it will be later!

SECTION 9

Practice Problems

Try these five problems on your own. Each one is a little harder than the last. Check your answers when you're done!

PROBLEM 1 — CONCEPTUAL
If you convert 7 meters to centimeters, will your answer be greater than 7 or less than 7? Explain why.
PROBLEM 2 — BASIC CALCULATION
Convert 5 kilometers to meters.
PROBLEM 3 — INTERMEDIATE
Emma has 3 gallons of lemonade. She pours it into pint-sized bottles. How many bottles can she fill? (Hint: 1 gallon = 4 quarts, and 1 quart = 2 pints.)
PROBLEM 4 — APPLIED
Jake runs 2 kilometers on Monday, 1,500 meters on Tuesday, and 3,200 meters on Wednesday. How many total kilometers did he run over the three days?
PROBLEM 5 — CRITICAL THINKING
A recipe calls for 2 pounds 8 ounces of flour. Maria only has a scale that shows ounces. She puts flour on the scale and it reads 36 ounces. Does she have enough flour? If not, how many more ounces does she need?
SUMMARY

Lesson Summary

In this lesson, you learned how to convert measurement units within the same system. The two main systems are the customary system (inches, feet, pounds, gallons) and the metric system (millimeters, meters, grams, liters). The key rule is: multiply when going to a smaller unit and divide when going to a bigger unit. You use a conversion factor to tell you how many of one unit fit in another.

For multi-step problems, always convert every measurement to the same unit before you add, subtract, or compare. Always do a quick check: does my answer make sense? A smaller unit should give a bigger number. A bigger unit should give a smaller number. Keep practicing these conversions and they will become second nature!

Varsity Tutors • 5th Grade Math • Convert Units and Solve Problems