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Math 7 · Unit 3, Lesson 1: Adding Signed Numbers · Tile 4 of 5

Fractions, Decimals, and Mixed Numbers

Parts of a dollar work the same way

Fractions and decimals follow the same rules. There are just a few more steps, so do them in the same order every time.

Write it down. Do every change on paper, one line per step. Changing signs in your head is the number one reason for missed problems. If you changed something, it should be on the paper.

ElleMath-speak

The rules for adding signed numbers work for all rational numbers, including fractions and decimals.

FinnPlain English

Money comes in parts of a dollar too. Owing 1 dollar and 25 cents works the same way as owing 1 dollar.

The steps (the same every time)

  1. Change. Subtraction becomes adding the opposite.
  2. Improper fractions. Turn mixed numbers into improper fractions (top heavier than the bottom). Example: 2 12 is the same as 52. If the mixed number is negative, keep the negative sign outside: −2 12 = −(2 12) = −(52).
  3. Common denominator. Fractions need the same bottom (denominator) before you add. Use the least common multiple.
  4. Add. Use the rules for adding and subtracting signed numbers on the tops (numerators). The bottom (denominator) stays the same.
  5. Simplify. Divide the top (numerator) and bottom (denominator) by their greatest common factor.
  6. Check. Estimate with decimals. Does your answer make sense?

Need help with Least Common Multiple (LCM) or Greatest Common Factor (GCF)?

Decimals are dollars and cents

Line up the decimal points. Write in zeros so both numbers have the same number of decimal places.

−1.25 − 3.5−1.25 + −3.50 Change, and write in a zero−4.75 Owe $1.25, then owe $3.50 more

Don't fall into the negative mixed number trap!

−2 12 means −(2 + 12). The negative belongs to the whole thing.

It is NOT −2 + 12. That equals −1 12, a different number.

So −(2 12) = −(52), which is the same as −2 12 = −52. Keep the negative sign outside.

−2 12 is to the left of −2. −1 12 is to the right of −2.
ElleMath-speak

A negative mixed number is negative in both its whole number part and its fraction part. Negative 2 and one half equals negative five halves.

FinnPlain English

If you owe 2 and a half dollars, you owe the 2 dollars and you owe the half dollar too. You don't owe 2 dollars and have a half dollar.

Worked example

−2 12 + 34−52 + 34 Improper fractions−104 + 34 Common denominator: owe 10 quarters, have 3 quarters−74 Add: still owe 7 quarters−1 34 Mixed numberCheck: −2.50 + 0.75 = −1.75. It matches.
ElleMath-speak

Find a common denominator before you add fractions. Write your answer in simplest form.

FinnPlain English

The bottoms, the denominators, have to match before you can add the tops, the numerators. Then make the fraction as simple as you can.

Let me try a few

NC standard: NC.7.NS.1.

Where to go next

Let me try a few5 problems on fractions, decimals, and mixed numbers. Next: Tile 5, Distance and Real-World ProblemsHow far apart, and how much it changed All tilesAll 5 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.