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Lesson · Grade 9 · Mathematics

Adding and Subtracting Negative Fractions and Decimals

  • Grade 9
  • Mathematics
  • 1 min 59 s
  • British Columbia
  • BC9-MA-02

On a single number line, the video works out −3/4 + 5/6 by rewriting both fractions in twelfths while keeping the negative sign, then shows how subtracting a negative adds its opposite in 2/3 − (−1/2) = 7/6. It finishes with the decimal −2.5 − 1.75 = −4.25, checks every answer, and ends on a one-line recap.

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In one sentence

The question this lesson answers

Let's add negative three quarters and five sixths on a number line.

Negative three quarters sits left of zero.

Transcript

What the lesson says

Let's add negative three quarters and five sixths on a number line.

Negative three quarters sits left of zero.

First find a common denominator, a bottom number both fractions share. 12 works: 4 times 3 and 6 times 2 both make 12.

Multiply top and bottom by the same number. Negative three quarters is negative nine twelfths, and five sixths is ten twelfths.

Keep the negative sign. A common mistake is to drop it, giving nineteen twelfths, which is wrong.

From negative nine twelfths, move ten twelfths right to one twelfth. Check: negative 9 plus 10 is 1.

Next, two thirds minus negative one half.

The opposite of a number is the same distance from zero on the other side. The opposite of negative one half is one half.

Subtracting a negative adds its opposite, so this is two thirds plus one half.

With denominator 6, two thirds is four sixths and one half is three sixths.

From two thirds, move one half right to seven sixths. Check: 4 plus 3 is 7.

Decimals work the same way. Try negative 2.5 minus 1.75.

Subtracting 1.75 means adding negative 1.75, so from negative 2.5, move 1.75 left.

Both are negative, so add 2.5 and 1.75 to get 4.25. The answer is negative 4.25.

Recap: keep each sign when you find a common denominator, and subtracting a negative adds its opposite.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)BC9-MA-02

Previous: Negative Fractions and Decimals on a Number LineNext: Multiplying and Dividing Negative Fractions

The outcomes and strands follow the British Columbia curriculum.

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