Converting Units of Measure

A measurement needs a number and a unit. The number tells how many units you have. The unit tells the size you counted. For example, 5 m means five meters.

Length tells how long, tall, or far something is. Mass tells how heavy something is. Capacity tells how much a container can hold. You use meters for length, grams for mass, and liters for capacity.

Let the prefix help

The start of a metric name is its prefix. Each prefix has a meaning.

The prefix keeps its meaning in different measures. A kilogram is 1,000 grams. A milliliter is one thousandth of a liter, so 1,000 mL fills 1 L.

Build the length ladder

Read these units from largest to smallest:

km → hm → dam → m → dm → cm → mm

Each step takes you to a unit ten times smaller. One meter fills ten decimeters. Each decimeter fills ten centimeters. Together, that makes 10 × 10 = 100 centimeters in a meter.

You often skip the less common units when calculating. Keep these useful links ready:

• 10 mm = 1 cm
• 100 cm = 1 m
• 1,000 mm = 1 m
• 1,000 m = 1 km
• 1,000 g = 1 kg
• 1,000 mL = 1 L

A long jump can use more than 1,000. From kilometers to centimeters, multiply the two links: 1,000 × 100 = 100,000. There are 100,000 cm in 1 km.

Write the symbol carefully

Leave a space after the number: 6 kg or 250 mL. Symbols keep the same form after any number. Write 6 kg, with no plural s or period. Use a capital L in L and mL.

Watch similar symbols: m means meter, mi means mile, and min means minute. Also watch the prefix centi-. A centimeter is a small part of a meter. You need 100 centimeters to make one meter, just as you need 100 cents to make one dollar.

Imagine someone says a pencil is 18 long. You cannot picture its length yet. Eighteen centimeters makes sense, but eighteen meters would stretch across a huge space. The unit matters as much as the number.

Keep a few familiar sizes

A benchmark is a familiar size you can use for comparison. These are rough sizes, so use the word “about.”

Objects vary. Your fingernail helps you estimate a centimeter; a ruler helps you measure it accurately.

Match the unit to the job

Use millimeters for tiny lengths, such as a coin's thickness. Use centimeters for a pencil or a book. Meters fit rooms and playgrounds. Kilometers fit distances between towns.

Grams suit light objects, such as grapes. Kilograms suit heavier things, such as dogs or bags of potatoes. Milliliters fit small amounts of liquid. Liters fit larger containers, such as fish tanks.

Choose a unit that gives a useful number. A nearby town might be 12 km away. Its distance is also 12,000,000 mm, but that huge number is harder to picture.

Estimate and check

Picture meter sticks standing end to end beside a door. A little more than two sticks means a little more than 2 m. Picture four or five sticks along a car. A length of about 4 or 5 m is sensible.

Benchmarks also catch mistakes. An answer of 18 m for a pencil needs another look. Check the number and the unit. The pencil could be about 18 cm long.

The same pencil can measure 18 cm or 180 mm. More small units fit along it, so its number of millimeters is greater. Its actual length has stayed the same.

Keep mass and capacity separate. A liter tells how much a container holds. A kilogram tells how heavy something is. Equal containers of popcorn and water can hold the same amount of space while having very different masses.

You can describe one length in different ways. A ribbon that is 2 m long is also 200 cm long. Converting changes the unit you use to describe it. The ribbon itself stays the same length.

Decide what happens to the number

Smaller units fit more times along the same length. When you change a larger unit to a smaller unit, multiply. The number you multiply by is the conversion factor.

To change kilograms to grams, the factor is 1,000. Each kilogram contains 1,000 grams. For 3 kg, you count three groups of 1,000 g.

3 × 1,000 = 3,000, so 3 kg = 3,000 g.

Work through a conversion

Mia's dog has a mass of 12 kg. Find its mass in grams.

1. Start with the unit fact: 1 kg = 1,000 g.
2. Grams are smaller than kilograms, so multiply.
3. Calculate 12 × 1,000 = 12,000.
4. Write the answer: 12,000 g.

The number grew because you counted smaller units. As a check, twelve full 1-liter water bottles would have about this mass.

See the pattern in a table

Each row describes the same mass in two units.

The rule for every row is “multiply kilograms by 1,000.” You can use the rule for a missing row, too. For 7 kg, calculate 7 × 1,000 = 7,000 g.

Place value explains the pattern. Multiplying by 10 moves each digit one place left on a place-value chart. Multiplying by 100 moves it two places; by 1,000, three places. Whole numbers may need zeros to hold the empty places: 8 cm = 80 mm and 7 m = 700 cm.

Join two links when you need them

To change kilometers to centimeters, go through meters:

1 km = 1,000 m, and each meter is 100 cm.

1,000 × 100 = 100,000, so 1 km = 100,000 cm.

For meters to millimeters, you can use 1,000 directly. You can also multiply by 100 to reach centimeters, then by 10 to reach millimeters.

Choose the factor from the two units, not just the direction. For 6 m in centimeters, use 100: 6 m = 600 cm. Using 1,000 would give the number of millimeters instead.

A larger unit gathers small units into a group. One kilogram gathers 1,000 grams. To find how many kilograms fit into 3,000 g, ask how many groups of 1,000 you have.

3,000 ÷ 1,000 = 3, so 3,000 g = 3 kg.

Follow the units

When you change a smaller unit to a larger unit, divide. The number gets smaller because each new unit holds more.

A bike path measures 6,000 m. Write it in kilometers.

1. Use 1 km = 1,000 m.
2. Kilometers are larger, so divide by 1,000.
3. Calculate 6,000 ÷ 1,000 = 6.
4. The path is 6 km long.

Check by multiplying back: 6 × 1,000 = 6,000. You reach the number of meters you started with.

Use place value

Dividing by 10 moves each digit one place right on a place-value chart. Dividing by 100 moves each digit two places; by 1,000, three places.

For whole numbers ending in zeros, you may see zeros disappear:

• 90 mm ÷ 10 = 9 cm
• 400 cm ÷ 100 = 4 m
• 7,000 mL ÷ 1,000 = 7 L
• 15,000 m ÷ 1,000 = 15 km

Choose the factor before calculating. Millimeters to centimeters uses 10, while millimeters to meters uses 1,000. For example, 80 mm is 8 cm. A factor of 100 would wrongly give 0.8 cm.

Keep the leftover

Sometimes you cannot make another whole large unit. Take out the whole units and keep the rest in the small unit.

For 2,350 g, first take out 2,000 g. That makes 2 kg. Then calculate 2,350 − 2,000 = 350. You have 2 kg 350 g.

For 145 cm, take out 100 cm to make 1 m. Keep the remaining 45 cm: 1 m 45 cm. For 63 mm, six groups of 10 mm make 6 cm. The last 3 mm stay as millimeters.

A table can show this direction, too.

Reading from grams to kilograms means dividing by 1,000. Reading back means multiplying. Before accepting an answer, picture its size: 500 cm is five meter sticks, so 5 m is sensible.

A mixed measure names a large part and a small part. For example, 1 m 45 cm means one meter plus another 45 centimeters. Write the larger unit first.

Combine the parts

To change a mixed measure to one small unit, convert the large part first. Then add the small part.

For 3 kg 200 g:

• 3 kg = 3,000 g
• 3,000 g + 200 g = 3,200 g

For 2 L 750 mL, the liters give 2,000 mL. Add 750 mL to get 2,750 mL. Both parts now count milliliters, so you can add them.

Do not join the written numbers together. For 3 kg 45 g, calculate 3,000 + 45 = 3,045 g. The zero holds the hundreds place. An answer of 3,450 g would add 450 g after the kilograms, which is too much.

Split one measure into two units

Work backward to change 4,060 m into kilometers and meters. Four groups of 1,000 m make 4 km. Calculate 4,060 − 4,000 = 60. The mixed measure is 4 km 60 m.

Check by joining the parts again: 4,000 m + 60 m = 4,060 m. The smaller part is less than 1,000 m, so it cannot make another kilometer.

Compare in one unit

You can compare numbers only after checking their units. Which is longer: 2 m 5 cm or 250 cm?

Change the first length: 2 m 5 cm = 200 cm + 5 cm = 205 cm. Now compare 205 with 250. 250 cm is longer.

The number 900 is greater than 2, but 900 mL is less than 2 L. Two liters is 2,000 mL. Ignoring the units would reverse your answer.

Order several measures

Order these from lightest to heaviest: 1 kg 50 g, 1,500 g, 1 kg 5 g, and 1,200 g.

Put the gram amounts in order: 1,005, 1,050, 1,200, 1,500. Then use the original labels:

1 kg 5 g, 1 kg 50 g, 1,200 g, 1,500 g.

You may also meet 1,300 g written as 1 kg 300 g or 1.3 kg. These describe the same mass. Choose the form that fits the question or makes your next calculation easier.

A decimal can describe part of a large unit. Since 100 cm make 1 m, one centimeter is one hundredth of a meter: 1 cm = 0.01 m. Ten centimeters is 0.1 m. One millimeter is one thousandth of a meter: 1 mm = 0.001 m.

The same idea works with thousands. One gram is 0.001 kg, and one milliliter is 0.001 L.

Multiply toward smaller units

For 2.5 kg in grams, use the factor 1,000. On a place-value chart, every digit moves three places left:

2.5 × 1,000 = 2,500, so 2.5 kg = 2,500 g.

You can also split the mass: 2 kg gives 2,000 g, and half a kilogram gives 500 g. Adding them gives 2,500 g.

The factor depends on the units. For 1.75 m in centimeters, multiply by 100 to get 175 cm. For 4.2 cm in millimeters, multiply by 10 to get 42 mm.

Adding zeros after a decimal does not do this job. The numbers 2.5 and 2.5000 have the same value. You need multiplication to change the number of units.

Divide toward larger units

For 724 g in kilograms, divide by 1,000. Each digit moves three places right on the chart:

724 ÷ 1,000 = 0.724, so 724 g = 0.724 kg.

For 45 g, the 4 ends in the hundredths place and the 5 in the thousandths place. Write 0.045 kg. The zero after the point holds the empty tenths place.

For 5 cm in meters, divide by 100. The 5 moves from ones to hundredths. A zero fills the tenths place: 5 cm = 0.05 m.

Change mixed measures to decimals

Convert the small part before joining it to the whole part.

Writing 2 m 5 cm as 2.5 m would make the small part 50 cm. The number of small units does not simply become the digits after the point.

Use familiar parts and compare

Half a kilogram is 0.5 kg or 500 g. A quarter liter is 0.25 L or 250 mL. Three quarters of a meter is 0.75 m or 75 cm. One tenth of a kilometer is 0.1 km or 100 m.

To compare 0.8 kg with 750 g, change 0.8 kg to 800 g. It is heavier. To compare 1.2 m with 125 cm, change 1.2 m to 120 cm. It is shorter.

Two decimal places in meters can show whole centimeters. Three can show whole millimeters. In kilograms, liters, and kilometers, three places can show whole grams, milliliters, and meters.

You meet US customary units on rulers, road signs, and sports fields. Inches fit small objects. Feet suit rooms and heights. Yards suit fields, and miles suit trips.

Picture a quarter, about 1 inch across. A standard ruler is 1 ft long. A yardstick is 1 yd long, about the width of a front door. A mile is about a 20-minute walk.

Learn the links

Customary length units have different factors.

A yard has 36 inches because its three feet each have 12 inches: 3 × 12 = 36. These units do not follow the metric ladder. Moving digits by place value will not change feet to inches.

Multiply to smaller units

A rope is 7 ft long. Find its length in inches.

One foot holds 12 inches, so seven feet holds seven groups of 12. Calculate 7 × 12 = 84. The rope is 84 in long.

A two-column table shows the same pattern:

You can use more than one link. For 2 yd in inches, first calculate 2 × 3 = 6 ft. Then calculate 6 × 12 = 72 in. The direct factor gives the same result: 2 × 36 = 72 in.

Divide to larger units

For 15 ft in yards, divide by 3. There are five groups of 3, so 15 ft = 5 yd. For 96 in in feet, divide by 12: 96 in = 8 ft.

If division leaves a remainder, keep it in inches. Count groups of 12 in 50 in: 12, 24, 36, 48. Four groups make 4 ft. There are 50 − 48 = 2 in left. So 50 in = 4 ft 2 in.

For longer distances, use the mile links. Two miles is 2 × 1,760 = 3,520 yd. Feet and yards need different factors, even when the starting number of miles is the same.

Check which unit is larger before choosing an operation. For 6 yd in feet, multiply by 3 to get 18 ft. For 6 ft in yards, divide by 3 to get 2 yd. A foot contains 12 inches, so a factor of 10 would lose two inches from every foot.

An ounce and a fluid ounce sound similar, but they measure different things. Ounces (oz) measure weight. Fluid ounces (fl oz) measure capacity, or how much a container holds.

A cup of popcorn can fill 8 fl oz of space. Its weight is much less than 8 oz. Read the whole symbol before you calculate.

Weight: ounces, pounds, and tons

Keep these facts ready:

• 1 lb = 16 oz
• 1 ton = 2,000 lb

Five quarters weigh about 1 oz. A stick of butter weighs 4 oz, so four sticks weigh 16 oz, or 1 lb. A small car weighs about 1 to 2 tons.

For 3 lb in ounces, multiply: 3 × 16 = 48 oz. For 64 oz in pounds, divide: 64 ÷ 16 = 4 lb.

You can count groups when dividing by 16. In 40 oz, two groups make 32 oz. There are 8 oz left, so 40 oz = 2 lb 8 oz. For 3 tons in pounds, calculate 3 × 2,000 = 6,000 lb.

Capacity: build a chain

The customary capacity units are fluid ounce, cup, pint, quart, and gallon. Imagine a measuring cup, a pint container of ice cream, a quart carton, and a gallon jug.

Join the links to describe one gallon:

1 gal = 4 qt = 8 pt = 16 c = 128 fl oz.

A quart is one quarter of a gallon. You can sketch a big G containing four Qs. Give each Q two Ps, and each P two Cs. You have drawn 4 quarts, 8 pints, and 16 cups.

Follow several steps

How many cups fill 3 gallons?

1. Change gallons to quarts: 3 × 4 = 12 qt.
2. Change quarts to pints: 12 × 2 = 24 pt.
3. Change pints to cups: 24 × 2 = 48 c.

Or use 16 cups in each gallon: 3 × 16 = 48 c.

For the reverse direction, divide. Twelve cups make 6 pints, which make 3 quarts. For 9 qt in gallons and quarts, take out two groups of 4 qt. Eight quarts make 2 gal; 1 qt is left.

The factor between pints and quarts is 2. Four pints make 2 qt because you gather them in pairs. Multiplying would wrongly make the number larger when you switch to the larger unit.

Half a foot is half of 12 inches. Divide 12 into two equal parts to get 6 in. For a quarter foot, divide 12 into four equal parts to get 3 in. Three quarters of a foot is three of those parts: 3 × 3 = 9 in.

Find a fraction of one unit

Start with the conversion fact. Then find the fraction of that number.

Join the whole and fractional parts

To change 2½ ft into inches, handle both parts.

Two whole feet give 2 × 12 = 24 in. Half a foot gives 6 in. Add 24 + 6 = 30 in.

For 1¾ lb, one whole pound gives 16 oz. A quarter pound gives 4 oz, so three quarters gives 12 oz. Add 16 + 12 = 28 oz.

A mixed measure works similarly. In 5 ft 3 in, change 5 ft to 60 in, then add 3 in. The result is 63 in. In 3 qt 1 pt, change 3 qt to 6 pt, then add 1 pt to get 7 pt.

Divide and label the remainder

To turn 75 oz into pounds and ounces, count groups of 16: 16, 32, 48, 64. Four pounds use 64 oz. Subtract 75 − 64 = 11. The answer is 4 lb 11 oz.

The remainder stays in the smaller unit. A division result of 4 remainder 2 for inches to feet means 4 ft 2 in. It does not mean 4.2 ft.

Change the small part to a fraction

For 2 ft 3 in as feet alone, ask what part of a foot 3 in makes. Three out of twelve inches is 3/12, or ¼. So 2 ft 3 in = 2¼ ft.

Decimals also describe parts of the larger unit. In 4.5 ft, the .5 means half a foot. Half a foot is 6 in, so 4.5 ft = 4 ft 6 in. The decimal digit is not a count of inches.

To compare customary measures, choose one unit. For 1½ lb, 20 oz, and 1 lb 2 oz, use ounces. Their weights are 24 oz, 20 oz, and 18 oz. From lightest to heaviest, write 1 lb 2 oz, 20 oz, 1½ lb.

Time units link together with several different numbers. You use 60 for minutes and seconds, but 24 for days and hours. Start with the correct fact each time.

Multiply or divide

For 3 hr in minutes, count three groups of 60. Calculate 3 × 60 = 180 min. For 2 days in hours, calculate 2 × 24 = 48 hr. For 4 years in months, calculate 4 × 12 = 48 months.

Going toward a larger unit means dividing. There are 72 ÷ 24 = 3 days in 72 hr. There are 35 ÷ 7 = 5 weeks in 35 days.

To divide 240 sec by 60, you can count 60, 120, 180, 240. Four groups make 4 min. For 100 min, one full group makes 1 hr. The remaining 40 min stays as minutes: 1 hr 40 min.

Join time facts

One hour has 60 minutes, each with 60 seconds. Calculate 60 × 60 = 3,600 sec in one hour.

One day has 24 hours, each with 60 minutes: 24 × 60 = 1,440 min. One week has 7 × 24 = 168 hr.

Check the calendar

Months have different lengths:

• April, June, September, and November have 30 days.
• January, March, May, July, August, October, and December have 31 days.
• February has 28 days, or 29 in a leap year.

Four weeks is 28 days. That is shorter than most months, so “1 month = 4 weeks” is not a reliable conversion.

A year has 365 days, or 366 in a leap year. Since 52 × 7 = 364, an ordinary year has 52 weeks and 1 day.

Leap years add February 29. Years divisible by 4 are leap years, with a special rule for century years. A year ending in 00 must also divide evenly by 400. So 2000 was a leap year, but 1900 was not and 2100 will not be.

Do not use 100 for hours and minutes. Two hours contains two groups of 60, giving 120 min. Likewise, converting days to hours needs 24, so 3 days is 72 hr.

A time such as 2 hr 45 min has two parts. You can change it into minutes by converting the hours first, then adding the remaining minutes.

2 hr = 120 min, and 120 + 45 = 165 min.

For 3 min 20 sec, change 3 min to 180 sec. Then add 20 sec to get 200 sec. For 1 day 6 hr, change the day to 24 hr, then add 6 hr to get 30 hr.

Take out whole groups

To turn 200 sec back into minutes and seconds, count groups of 60. Three groups use 180 sec. Subtract 200 − 180 = 20. The mixed time is 3 min 20 sec.

For 50 hr, two groups of 24 make 2 days. The remaining 2 hr gives 2 days 2 hr. The leftover always keeps the smaller unit.

Find part of an hour

An hour has 60 minutes, so a fraction of an hour is that fraction of 60.

A quarter hour comes from 60 ÷ 4 = 15 min. Three quarters is three groups of 15: 3 × 15 = 45 min. The same method works for other time units. Half a minute is 30 sec; half a day is 12 hr.

Read decimal hours

The decimal part counts a fraction of an hour. Multiply it by 60 to find minutes.

For 1.5 hr, the .5 is half an hour: 0.5 × 60 = 30 min. So 1.5 hr = 1 hr 30 min, or 90 min.

For 2.25 hr, calculate 0.25 × 60 = 15 min. The whole time is 2 hr 15 min. For 0.1 hr, calculate 0.1 × 60 = 6 min.

You can go the other way by dividing minutes by 60. Twelve minutes is 12 ÷ 60 = 0.2 hr. Forty-five minutes is ¾ hr or 0.75 hr.

Writing 2 hr 30 min as 2.30 hr mixes up minutes and hundredths of an hour. Thirty minutes is half an hour, so write 2.5 hr. A stopwatch reading “2:30” in minutes and seconds means 2 min 30 sec, which is 2.5 min.

Compare in minutes

Order 2.5 hr, 140 min, and 2 hr 35 min from shortest. They become 150 min, 140 min, and 155 min. The order is 140 min, 2.5 hr, 2 hr 35 min.

You can add counts of the same unit. You cannot add 1 L and 250 mL by adding 1 + 250. First write the liter as 1,000 mL. Then 1,000 + 250 = 1,250 mL.

Add in one small unit

Find 3 m 45 cm + 2 m 70 cm.

1. Change each length: 345 cm and 270 cm.
2. Add: 345 + 270 = 615 cm.
3. Split the answer: 6 m 15 cm.

Add the parts and regroup

You can also line up meters with meters and centimeters with centimeters. Add the meter parts: 3 + 2 = 5 m. Add the centimeter parts: 45 + 70 = 115 cm.

One hundred centimeters makes another meter. Trade 115 cm for 1 m 15 cm. Add the extra meter to get 6 m 15 cm.

This trade is called regrouping. Use the fact for your units:

For 2 hr 40 min + 1 hr 35 min, the first total is 3 hr 75 min. Trade 60 of those minutes for 1 hr. The answer is 4 hr 15 min.

Subtract by trading first

Find 5 lb 4 oz − 2 lb 10 oz. Four ounces is too small to subtract 10 oz. Trade 1 lb for 16 oz. The first weight becomes 4 lb 20 oz.

Now subtract each part: 4 lb − 2 lb = 2 lb, and 20 oz − 10 oz = 10 oz. The difference is 2 lb 10 oz.

For 3 hr 15 min − 1 hr 40 min, trade one hour. The first time becomes 2 hr 75 min. Subtract to get 1 hr 35 min.

The trade keeps the total the same. Two hours and 75 minutes is still 195 minutes, just like three hours and 15 minutes.

Keep units beside your numbers

Treating 3 hr 15 min as the whole number 315 would use groups of 100. Time uses groups of 60, so ordinary column subtraction on 315 and 140 would give the wrong result.

For a decimal and a small-unit measure, one unit is often easiest. To add 2.4 kg and 650 g, use grams: 2,400 + 650 = 3,050 g, or 3.05 kg.

When an answer uses hours and minutes, regroup until its minutes part is less than 60. If the question asks for minutes alone, a result such as 255 min is already complete.

Equal measures can be multiplied to find their total. A total measure can be divided to find equal shares. Changing to a smaller unit often makes the arithmetic easier.

Multiply equal amounts

Six bottles each hold 750 mL. Their total is 6 × 750 = 4,500 mL. That is 4 L 500 mL, or 4.5 L.

Check the size: each bottle holds less than 1 L, so six bottles hold less than 6 L. The answer 4.5 L fits.

A runner completes five laps. Each lap takes 3 min 20 sec. First change one lap to seconds: 180 + 20 = 200 sec. Then multiply 5 × 200 = 1,000 sec. Sixteen minutes uses 960 sec, leaving 40 sec. The total is 16 min 40 sec.

Multiply both parts

For three lengths of 2 ft 8 in each, multiply feet and inches:

• 3 × 2 ft = 6 ft
• 3 × 8 in = 24 in

Trade 24 in for 2 ft. The full length is 8 ft.

Or convert one length first: 2 ft 8 in = 32 in. Then 3 × 32 = 96 in, which is 8 ft. Multiplying only the feet would miss two of the three 8-inch parts.

Divide to find each share

Two liters of juice is shared equally among eight cups. Change 2 L to 2,000 mL. Divide 2,000 ÷ 8 = 250 mL in each cup.

Here you know the number of shares, and find the size of each share. Check by multiplying: 8 × 250 = 2,000 mL.

Divide to count the groups

How many 250 g bags can you fill from 3 kg of rice? First convert 3 kg to 3,000 g. Then calculate 3,000 ÷ 250 = 12 bags.

Here you know the size of each group, and find the number of groups. The answer is a count of bags. Multiplying 12 bags by 250 g per bag gets you back to 3,000 g.

Compare with “times as long”

A rope four times as long as a 75 cm rope measures 4 × 75 = 300 cm, or 3 m.

Use the same unit when finding how many times as long. One kilometer is 1,000 times as long as one meter because 1 km = 1,000 m. One foot is 12 times as long as one inch because 1 ft = 12 in.

A word problem may ask you to convert, multiply, and subtract. Read the final question first. It tells you what you must find and which unit your answer needs.

A useful plan is:

1. Name what you need to find.
2. Write down the measures with their units.
3. Change measures to one unit where needed.
4. Choose the operations and solve one step at a time.
5. Write the answer with its unit and check it.

Find a total mass

Sam packs 1 kg 200 g of books, a 450 g lunch, and a 350 g water bottle. Find the total mass in kilograms.

Change the books to 1,200 g. Add 1,200 + 450 = 1,650 g, then 1,650 + 350 = 2,000 g. The question asks for kilograms, so divide by 1,000. The packed items have a total mass of 2 kg.

Show a whole and its parts

A jug starts with 2 L of lemonade. Leah pours three glasses of 300 mL each. How much is left?

Change the jug amount to 2,000 mL. The glasses use 3 × 300 = 900 mL. Subtract 2,000 − 900 = 1,100 mL, or 1.1 L.

A bar diagram makes the story visible. Draw one bar for 2,000 mL. Mark three parts of 300 mL each. Label the unfilled rest with a question mark. The three known parts and the unknown part together make the whole jug.

Check backward: 900 + 1,100 = 2,000 mL. The amount left fits the starting amount.

Work across customary units

Ana has 2 yd of ribbon. She cuts four pieces of 15 in. How much ribbon remains?

First convert: 2 × 36 = 72 in. The pieces use 4 × 15 = 60 in. Subtract 72 − 60 = 12 in, or 1 ft.

Stopping at 60 in would tell you the amount cut off. The question asks for the amount left, so you still need subtraction.

Use a number line

Zoe runs 1,200 m, then another 900 m. A number line diagram can show both distances. Mark equal 100 m spaces. Start at 0, jump to 1,200 m, then jump another 900 m. You land at 2,100 m, or 2 km 100 m.

Label the unit and keep equal distances between the marks. The jump lengths show the distances being added.

For repeated time, multiply before regrouping. Jay practices piano for 45 min each day for five days. Calculate 5 × 45 = 225 min. Three hours uses 180 min, leaving 45 min. His total is 3 hr 45 min.

A final check should fit the story. An amount left must not exceed the starting amount. Equal shares must join back to the total. Read the requested unit again: an answer in liters needs conversion if your calculation ended in milliliters.