Multi-Step Conversion Problems: Solve, Check and Fix | Grade 5 Math | LevelKite

Some measurement problems take more than one step. A multi-step problem is a problem where you need two or more calculations to reach the answer.

In this lesson, each word problem has at least one conversion step. To convert means to write the same amount in a different unit, such as writing $2$ feet as $24$ inches. The amount stays the same. Only the way you write it changes.

The units may be customary units, such as inches, feet, ounces and pounds. Or they may be metric units, such as meters, grams and liters.

You already know how to convert with a conversion fact. A conversion fact tells you how many of a smaller unit make one larger unit, such as $12$ inches in $1$ foot. The table below lists the facts this lesson uses.

Your new skills are choosing when to convert, checking that an answer makes sense, and finding and fixing conversion mistakes.

Conversion facts used in this lesson

Kind of unit	One larger unit	Same amount in the smaller unit
Customary	$1$ foot (ft)	$12$ inches (in)
Customary	$1$ pound (lb)	$16$ ounces (oz)
Metric	$1$ kilometer (km)	$1{,}000$ meters (m)
Metric	$1$ kilogram (kg)	$1{,}000$ grams (g)
Metric	$1$ liter (L)	$1{,}000$ milliliters (mL)

Key concept

Let the units guide each step

A number in a measurement only has meaning with its unit. $3$ feet and $3$ inches use the same number, but they are very different lengths. That is why two rules guide every problem in this lesson.

Match units before you combine. You can add, subtract or compare the numbers only when the amounts are in the same unit. If they are not, convert first.
Finish in the asked-for unit. The asked-for unit is the unit the question wants for its answer. If your result is in a different unit, convert it before you write your answer.

The big decision is when to convert. This plan helps you decide.

Find the asked-for unit. Read the question and note the unit it wants.
Decide when to convert. If you must add, subtract or compare amounts that are in different units, convert first, before you combine them. If the amounts are already in the same unit, you can calculate first and convert last.
Calculate. Write the unit beside each number, so you always know what the number counts.
Check. Is the answer in the asked-for unit? Is it a sensible size? A sensible size means the number fits the story and the units.

Worked example

Convert last: filling water bottles

A coach fills $6$ water bottles. Each bottle holds $750$ milliliters. How many liters of water does the coach need?

Find the asked-for unit. The question asks for liters. The problem gives one measurement, 750 milliliters, so you do not need to combine amounts in different units. Plan: find the total in milliliters, then convert that total to liters at the end.
Multiply to find the total. There are 6 bottles with 750 milliliters in each one, so the total is 6 groups of 750 milliliters.
$6 \times 750 \text{ mL} = 4{,}500 \text{ mL}$
Convert the total, because the question asks for liters. A liter is larger than a milliliter, so it takes fewer liters to hold the same water. Divide by the 1,000 milliliters in each liter.
$4{,}500 \div 1{,}000 = 4.5, \quad \text{so } 4{,}500 \text{ mL} = 4.5 \text{ L}$
Check the unit and the size. The answer is in liters, as asked. Each bottle holds 750 milliliters, which is less than the 1,000 milliliters in 1 liter. So 6 bottles must hold less than 6 liters. An answer of 4.5 liters fits.
$4.5 \text{ L} < 6 \text{ L}$

Answer

The coach needs $4.5$ liters of water.

Could you convert first in the bottle problem? Yes. The problem gives one measurement, so you do not have to combine amounts in different units. Both orders work. The table below shows each order, step by step.

Both rows end with the same total, $4.5$ L. That is no accident. When both orders work and you do every step correctly, the answer is the same. Converting last kept the numbers whole for longer, so the arithmetic was easier. When you have a choice, pick the order with the easier numbers.

The bottle problem solved in two orders

Order	First step	Second step	Total
Convert last	Multiply: $6 \times 750 \text{ mL} = 4{,}500 \text{ mL}$	Convert: $4{,}500 \div 1{,}000 = 4.5$ , so $4{,}500 \text{ mL} = 4.5 \text{ L}$	$4.5$ L
Convert first	Convert: $750 \div 1{,}000 = 0.75$ , so $750 \text{ mL} = 0.75 \text{ L}$	Multiply: $6 \times 0.75 \text{ L} = 4.5 \text{ L}$	$4.5$ L

Worked example

Convert first: cutting a board

Maya has a board that is $8$ feet long. She cuts off $3$ pieces. Each piece is $18$ inches long. How many inches of board are left?

Find the asked-for unit. The question asks for inches. The board is in feet and the pieces are in inches. You need to subtract these amounts, so they must be in the same unit first. Plan: convert the board to inches before you subtract. Then the result will already be in the asked-for unit.
Convert the board length to inches. An inch is smaller than a foot, so it takes more inches to cover the same length. Multiply by the 12 inches in each foot.
$8 \times 12 = 96, \quad \text{so } 8 \text{ ft} = 96 \text{ in}$
Find the total length that Maya cuts off. There are 3 pieces of 18 inches each, so multiply.
$3 \times 18 \text{ in} = 54 \text{ in}$
Subtract the cut length from the whole board. Both amounts are in inches now, so you can subtract the numbers.
$96 \text{ in} - 54 \text{ in} = 42 \text{ in}$
Check the unit and the size. The answer is in inches, as asked. After Maya cuts pieces off, what is left must be shorter than the whole board. The 42 inches left is less than the 96 inches of the whole board, so the answer fits.
$42 \text{ in} < 96 \text{ in}$

Answer

There are $42$ inches of board left.

Both worked examples ended with a check. Here are two ways to judge whether an answer is a sensible size.

Compare with an amount from the problem. After you cut pieces off a board, what is left must be shorter than the whole board. Six bottles that each hold less than $1$ L must hold less than $6$ L together.
Think about the size of the units. For any amount more than zero, changing to a smaller unit makes the number larger, and changing to a larger unit makes the number smaller. In the bottle problem, $4{,}500$ mL became $4.5$ L. The unit got larger and the number got smaller, as it should.

A size check can catch answers that are far too big or far too small. It can miss a smaller mistake, such as a wrong conversion fact, so check each fact too.

The same checks help you find mistakes in finished work. The table below shows three kinds of conversion mistake to look for.

Three conversion mistakes to look for and how to fix them

Kind of mistake	Mistaken work	Why it is wrong	Corrected work
Multiplying when you need to divide	$3{,}000 \times 1{,}000 = 3{,}000{,}000$ , so $3{,}000 \text{ g} = 3{,}000{,}000 \text{ kg}$	A kilogram is larger than a gram, so the number of kilograms must be less than $3{,}000$ , not more.	$3{,}000 \div 1{,}000 = 3$ , so $3{,}000 \text{ g} = 3 \text{ kg}$
Using the wrong conversion fact	$4 \times 12 = 48$ , so $4 \text{ lb} = 48 \text{ oz}$	The fact is wrong. $12$ inches make $1$ foot, but $16$ ounces make $1$ pound.	$4 \times 16 = 64$ , so $4 \text{ lb} = 64 \text{ oz}$
Combining amounts in different units	$3 + 250 = 253$ , so $3 \text{ L} + 250 \text{ mL} = 253 \text{ mL}$	The $3$ counts liters and the $250$ counts milliliters. They need the same unit before you add.	$3 \text{ L} = 3{,}000 \text{ mL}$ , and $3{,}000 + 250 = 3{,}250$ , so the total is $3{,}250 \text{ mL}$

Worked example

Find and fix a mistake: Lena's walk

Lena walks $850$ meters to school and $850$ meters back home each day. How many kilometers does she walk in $5$ days? Here is Lena's work. Line 1: $850 + 850 = 1{,}700$ m each day. Line 2: $1{,}700 \times 5 = 8{,}500$ m in $5$ days. Line 3: $8{,}500 \times 1{,}000 = 8{,}500{,}000$ km. Find and correct her mistake.

Start with the size check. Each trip is 850 meters, which is less than the 1,000 meters in 1 kilometer. Lena makes 2 trips a day for 5 days, which is 10 trips. So she must walk less than 10 kilometers. Her answer of 8,500,000 kilometers is far too big, so there is a mistake to find.
$2 \times 5 = 10 \text{ trips}$
Look for amounts combined in different units. Every amount in Lines 1 and 2 is in meters, so the units match. The addition and the multiplication are also correct. Lines 1 and 2 are fine.
$850 + 850 = 1{,}700 \quad \text{and} \quad 1{,}700 \times 5 = 8{,}500$
Check the conversion in Line 3. The fact is right, because 1 kilometer is 1,000 meters. But Lena multiplied. A kilometer is longer than a meter, so it takes fewer kilometers to cover the same distance. The number must get smaller, so she needed to divide.
Correct Line 3. Divide by the 1,000 meters in each kilometer.
$8{,}500 \div 1{,}000 = 8.5, \quad \text{so } 8{,}500 \text{ m} = 8.5 \text{ km}$
Check the corrected answer. It is in kilometers, as asked. It is less than 10 kilometers, which matches the size check from the first step.
$8.5 \text{ km} < 10 \text{ km}$

Answer

Lena multiplied by $1{,}000$ when she needed to divide by $1{,}000$ . She walks $8.5$ kilometers in $5$ days.

The takeaway: in a multi-step measurement problem, let the units guide you. Find the unit the question asks for. Match units before you add, subtract or compare. When you have a choice, convert at the step that keeps the numbers easy. Finish in the asked-for unit, then check that the size makes sense. Use the same checks to find mistakes, such as multiplying when you need to divide, using a wrong conversion fact, or combining amounts in different units.