Math Core

A recipe asks for 2 liters of water, but your measuring cup is marked in milliliters. A race is 3 kilometers long, but the track signs count meters. To compare or combine measurements, you often need to change them into the same unit first. That is called converting units.

Big units and small units

Every measurement has a number and a unit, like 4 feet or 250 grams. The same length can be written with different units. A 1-foot ruler is also 12 inches long.

When you change from a bigger unit to a smaller unit, it takes more of the small units to measure the same thing. One foot is 12 inches, so 3 feet is $3 \times 12 = 36$ inches.

Converting to a smaller unit

To change a bigger unit into a smaller unit, multiply by how many small units fit in one big unit.

\text{number of big units} \times \text{small units in 1 big unit} = \text{number of small units}

Conversion facts to know

Length

Customary	Metric
1 foot (ft) = 12 inches (in)	1 meter (m) = 100 centimeters (cm)
1 yard (yd) = 3 feet = 36 inches	1 kilometer (km) = 1,000 meters

Weight and mass

Customary	Metric
1 pound (lb) = 16 ounces (oz)	1 kilogram (kg) = 1,000 grams (g)

Liquid volume

Metric
1 liter (L) = 1,000 milliliters (mL)

Time

Time
1 minute (min) = 60 seconds (sec)
1 hour (hr) = 60 minutes

Notice the pattern in metric units: "kilo" means 1,000 and "milli" means one thousandth. So a kilometer is 1,000 meters and a liter is 1,000 milliliters.

Worked example: Feet to inches

A bookshelf is 5 feet tall. How tall is it in inches?

Feet are bigger than inches, so multiply. There are 12 inches in 1 foot.

$5 \times 12 = 60$

The bookshelf is 60 inches tall.

Making a conversion table

A table helps you see the pattern. Here is one for kilograms and grams:

kilograms	grams
1	1,000
2	2,000
3	3,000
4	4,000

Each time you add 1 kilogram, you add 1,000 grams. The numbers in the right column are always 1,000 times the numbers in the left column.

Mixed units

Sometimes a measurement uses two units, like 2 hours 15 minutes or 4 feet 7 inches. To change it into the smaller unit, convert the big part, then add the small part.

Worked example: Hours and minutes

A movie is 2 hours 15 minutes long. How many minutes is that?

Convert the hours: $2 \times 60 = 120$ minutes.

Add the extra minutes: $120 + 15 = 135$ .

The movie is 135 minutes long.

Common mistake

Don't forget the small part! 2 hours 15 minutes is not 120 minutes. After you convert the hours, add the 15 extra minutes to get 135.

Solving measurement problems

To add, subtract or compare two measurements, write them in the same unit first. Usually the smaller unit is easiest, because then you work with whole numbers.

Worked example: Comparing weights

A bag of apples weighs 3 pounds. A bag of oranges weighs 50 ounces. Which bag is heavier, and by how many ounces?

Change the pounds into ounces: $3 \times 16 = 48$ ounces.

Now compare: 50 ounces is more than 48 ounces. $50 - 48 = 2$ .

The oranges are heavier by 2 ounces.

Worked example: Cutting ribbon

Mia has a ribbon 2 meters long. She cuts off 3 pieces that are each 45 centimeters long. How many centimeters of ribbon are left?

Change meters to centimeters: $2 \times 100 = 200$ cm.

The 3 pieces use $3 \times 45 = 135$ cm.

Subtract: $200 - 135 = 65$ .

Mia has 65 centimeters of ribbon left.

Tip

Check that your answer makes sense. When you change to a smaller unit, the number should get bigger. If 5 feet turned into a number smaller than 5, something went wrong.

Practice

Practice 1

A garden hose is 3 yards long. How many feet long is it?

Type a number.

Practice 2

A dog weighs 7 kilograms. How many grams is that?

Type a number.

Practice 3

Which measurement is the same as 4 minutes?

Practice 4

Leo is 4 feet 7 inches tall. How tall is he in inches?

Type a number.

Practice 5

A water jug holds 3 liters. Sam pours out 500 milliliters. How many milliliters are left in the jug?

Type a number.

Practice 6

Which is longer: 2 kilometers or 1,900 meters?

Practice 7

A box of crackers weighs 4 pounds. The crackers come in bags that each weigh 8 ounces. How many bags are in the box?

Type a number.

Practice 8

Ava practiced piano for 1 hour 20 minutes on Saturday and $\dfrac{3}{4}$ of an hour on Sunday. How many minutes did she practice in all?

Type a number.