Adding and Subtracting Algebraic Expressions: A Grade 6 Guide

Adding and subtracting algebraic expressions means grouping like terms, then adding or subtracting their coefficients, while unlike terms stay put. The one hard part is a minus sign in front of a bracket, because it flips every sign inside. Learn that flip, and the rest is sorting.

I once marked a page where a girl got every addition right and every subtraction wrong. She had flipped only the first sign in each bracket and left the rest alone. One lesson on the flip fixed her whole page, and her face lit up when she saw it.

How Do You Add Algebraic Expressions?

Add algebraic expressions by grouping like terms together, then adding their coefficients while keeping unlike terms separate and writing each term once. Only the coefficients change, because the letters and powers in each group stay exactly the same throughout the whole sum.

Two layouts help, and children can pick the one that keeps their working tidy. The vertical layout lines up like terms in columns, which suits long expressions. The horizontal layout keeps short expressions on one line, which suits quick sums.

Try it: (3x + 5) + (2x – 1). Group the x terms, 3x + 2x, and the constants, 5 – 1. The answer is 5x + 4, and no term appears twice.

Why Does Subtracting a Bracket Change Every Sign?

Subtracting a bracket changes every sign inside it, because the minus sign means you take away the group, so plus terms turn to minus and minus terms turn to plus. Miss one sign and the answer goes wrong, so circle the minus and flip each sign before you combine anything.

Here is the wrong way and the right way side by side. Wrong: (5x + 3) – (2x – 4) becomes 5x + 3 – 2x – 4, which gives 3x – 1. Right: the minus flips both signs, so it becomes 5x + 3 – 2x + 4, which gives 3x + 7.

My sign check step is simple: circle the minus, flip every sign, then combine. I ask children to tick each flipped sign, because an unticked sign is usually an unchanged sign.

What Mistakes Do Children Make When Adding and Subtracting?

Children most often flip only the first sign inside a bracket, combine unlike terms after adding, and forget returned items in multi-step problems. Teach them to tick each flipped sign, group like terms first, and read the story again before they write the final answer.

Grouping comes first, and the grouping like terms worksheet builds that habit before brackets arrive. A child who can sort terms well rarely mixes them when brackets appear.

Standard 6.EE.A.3 covers applying the properties of operations to generate equivalent expressions, and adding and subtracting is the core of that skill. Each correct sum rewrites two expressions as one equivalent expression.

Multi-step problems add one more trap: returned or damaged items. I tell children to list what comes in, what goes out, and what breaks, before they write a single term. The list keeps the story straight.

Practise With the Free Worksheet

The adding and subtracting algebraic expressions worksheet gives focused bracket practice with the sign changes shown step by step. It covers adding and subtracting expressions, including full bracketed subtraction, plus a multi-phase problem with packs, returns and damage to track.

Try These Three Yourself

1. Add: (4a + 3) + (2a – 5). (Answer: 6a – 2, because 4a + 2a is 6a and 3 – 5 is -2.)
2. Subtract: (7a + 2) – (3a – 5). (Answer: 4a + 7, because the minus flips -5 to +5, so 2 + 5 is 7.)
3. Why does (4x – 3) – (x + 2) equal 3x – 5? (Answer: The minus flips +x to -x and +2 to -2, so 4x – x is 3x and -3 – 2 is -5.)

Work one bracket sum together tonight. Circle the minus, flip every sign out loud, and let the flip stop being scary. Find more Grade 6 guides on the Grade 6 hub.