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Lesson · Grade 9 · Mathematics

Multiplying and Dividing Negative Fractions

  • Grade 9
  • Mathematics
  • 1 min 48 s
  • British Columbia
  • BC9-MA-03

Working through (−1/3) ÷ (−2/5), the video keeps the first fraction, changes ÷ to ×, and flips only the second fraction to its reciprocal. Then it decides the sign first using the sign rules from integers (two negatives give a positive) before multiplying numerators and denominators to get 5/6. It checks the answer by multiplying back, 5/6 × (−2/5) = −10/30 = −1/3, and ends on the one-line recap: sign first, and to divide, flip the second fraction and multiply.

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In one sentence

The question this lesson answers

Let us work out negative one third divided by negative two fifths.

When you multiply or divide fractions, the sign rules from integers still hold.

Transcript

What the lesson says

Let us work out negative one third divided by negative two fifths.

When you multiply or divide fractions, the sign rules from integers still hold.

Same signs give a positive answer: negative 2 times negative 3 is 6.

Different signs give a negative answer: negative 2 times 3 is negative 6.

To divide by a fraction, multiply by its reciprocal, which is the fraction flipped upside down.

Keep the first fraction, change divide to multiply, and flip the second fraction, never the first.

Negative two fifths becomes negative five over two. Its sign does not change.

Now decide the sign first. Both fractions are negative, so the signs are the same.

So the answer will be positive, not negative.

With the sign decided, multiply the numerators, the top numbers: 1 times 5 is 5.

Then multiply the denominators, the bottom numbers: 3 times 2 is 6.

So negative one third divided by negative two fifths equals five sixths, a positive answer.

To check, multiply the answer by negative two fifths. We should get back to negative one third.

The signs are different, so the answer is negative. 5 times 2 is 10, and 6 times 5 is 30.

Dividing top and bottom by 10 gives negative one third, the number we started with.

To sum up: decide the sign first, and to divide, flip the second fraction and multiply.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)BC9-MA-03

Previous: Adding and Subtracting Negative Fractions and DecimalsNext: Order of operations with rational numbers and powers

The outcomes and strands follow the British Columbia curriculum.

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