Try and represent 85 and −74 on a number line.

Step-by-step solution

Idea: Change each improper fraction to a mixed number to see which two integers it lies between. Then cut that unit gap into as many equal parts as the denominator and count the parts. Positive numbers go to the right of 0, negative numbers to the left.

1. 85 = 135, so it lies between 1 and 2.½ mark
2. Divide the gap from 1 to 2 into 5 equal parts. Starting at 1, move 3 parts to the right. That point is 85.1 mark
3. −74 = −134, so it lies between −2 and −1.½ mark
4. Divide the gap from −1 to −2 into 4 equal parts. Starting at −1, move 3 parts to the left (it is just one part to the right of −2). That point is −74. See the diagram.1 mark

Check: 85 = 1.6 and −74 = −1.75: 1.6 is between 1 and 2, and −1.75 is between −2 and −1 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Counting from 0 instead of from 1: marking 3 parts after 0 gives 35, not 85.
• Marking −74 between −1 and 0 because the numerator 7 is ‘small’. Since 74 > 1, it lies beyond −1.
• Dividing the unit into unequal parts; the parts must be equal.

How this can come in the exam

Try one yourself

Between which two integers does −175 lie, and how would you mark it?

More questions like this

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