Operations & Algebraic Thinking
Understanding the Equal Sign
What it means for two expressions to be equal.
What the Equal Sign Really Means
You've been writing equations like 3 + 4 = 7 for a while now, using the equal sign as if it just means 'the answer is.' But the equal sign has a more exact job: it says the amount on the left side and the amount on the right side are the same.
Definition — Equal Sign
This means the equal sign doesn't have to sit right before the answer. An equation like 7 = 3 + 4 is just as true as 3 + 4 = 7, and so is 5 + 2 = 3 + 4, since both sides equal 7.
Worked Example — Checking if an Equation Is True
Worked Example — An Equation with Expressions on Both Sides
Tip
Common Mistakes
Assuming an equation is only written correctly when the answer comes right after the equal sign, and treating 7 = 3 + 4 as backward or wrong.
The equal sign can go anywhere between two equal amounts. 7 = 3 + 4 and 3 + 4 = 7 say the exact same true thing.
Comparing only the first numbers on each side of an equation like 4 + 3 = 5 + 2, instead of finding each side's total value.
Always add up each full side before comparing. Find the value of the left side, find the value of the right side, then check whether those two totals match.
Key Takeaways
- The equal sign shows that both sides of an equation have the same value.
- An equation is true only when both sides equal the same amount, no matter which side the equal sign is closer to.
- Work out the value of each side separately before comparing them.
Summary
The equal sign balances two equal amounts, not just a question and its answer. That same balance idea is the key to the next lesson, where one number in an equation is missing and has to be found.
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