How to Pass Numerical Reasoning (9 page)

Find the lowest common multiple by finding the prime factorization of each denominator:

3 = 1 × 3

6 = 2 × 3

9 = 3 × 3

The lowest common multiple = (1 ×) 2 × 3 × 3 = 18.

Comparing positive fractions

Often you can estimate which of two fractions is the larger. However, if the fractions are too close to estimate accurately, there is a method you can use to work out the relative sizes of fractions. You can also use this technique to find out whether two fractions are equivalent. This is a technique you will find useful to compare ratios and proportions. To compare positive fractions, simply cross-multiply the numerators and denominators.

Worked example

Are the following fractions equivalent?

Cross-multiply denominators and numerators:

Follow the arrows and write the results beside the fraction.

4 × 27 = 108 and 12 × 9 = 108, so the fractions are equivalent.

Worked example

Which is the larger fraction?

5 × 11 = 55 and 9 × 7 = 63. Follow the arrows and write your answers on either side of the fractions. The fraction on the right side of the question is the larger fraction, because 63 > 55.

Comparing positive fractions: practice drill

Decide which is the larger fraction.