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Addition & subtraction

Choose addition or subtraction from the situation and explain a written calculation. Use place-value exchanges and inverse operations to check your result.

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What you’ll learn

Represent combining, removing, and comparing quantities.
Explain an exchange between hundreds, tens, and ones.
Check subtraction by adding the difference back.

Choose the operation from the relationship

Addition can combine amounts or describe an increase. Subtraction can describe what remains or the difference between two amounts. Identify the known quantities and the unknown before calculating.

Exchange without changing the total

A hundred can be exchanged for ten tens, and a ten for ten ones. Written methods record those exchanges so corresponding units can be added or subtracted.

A mistake to avoid

In subtraction, taking the smaller digit from the larger digit in every column can produce the wrong answer. Keep the original order and make any needed place-value exchange.

Worked example

Work out 402 − 178

Rewrite 402 as 3 hundreds, 9 tens, and 12 ones. Subtract 1 hundred, 7 tens, and 8 ones to get 2 hundreds, 2 tens, and 4 ones: 224. Check: 224 + 178 = 402.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.

Primary / elementary foundationsPrimary mathBuild a connected foundation in number, calculation, fractions, measurement, and data. Use the skills in order or return to the first idea that needs attention.Counting & comparing · Place value · Addition & subtraction · Multiplication · +6 more Goal-led refresherAdult math refresherRefresh the mathematics behind a real task, from a percentage or measurement to an equation or graph. Use familiar goals and revisit only the skills you need.Place value · Addition & subtraction · Multiplication · Long division · +12 more

MultiplicationConnect multiplication to equal groups and arrays. Use place value and the distributive property to explain a larger product instead of treating the method as a trick.Signed numbersUse a number line to make sense of positive and negative numbers. Distinguish a value’s position from its distance from zero and explain changes in either direction.

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