KA-0141Number lines and betweenness
3 points, difficulty 1 of 3Level 5–6about 60sWhich of these fractions lies between one third and one half?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Turn them all into decimals.
2The strategy
One third is about 0.33 and one half is 0.5. Convert each choice to a decimal and see which one lands strictly between those two numbers.
3The full solution
1/5 is 0.2, 1/4 is 0.25, 2/5 is 0.4, 3/5 is 0.6, 2/3 is about 0.67. Only 0.4 sits between 0.33 and 0.5.
Solution
The reliable way
Convert everything to decimals so they can be compared on one scale. One third is about 0.33 and one half is 0.5. The choices are 0.2, 0.25, 0.4, 0.6 and about 0.67. Only 0.4, which is two fifths, lies strictly between 0.33 and 0.5. The transferable idea: put fractions on a common footing - decimals or a common denominator - before comparing, because a bigger denominator makes a fraction smaller, not larger.
The elegant way
Over fifteenths, one third is 5/15 and one half is 7.5/15, and two fifths is 6/15 - comfortably between them.
Why this is on the test: Comparing fractions by looking at one number at a time is the most persistent misconception in the number strand.