Which of these fractions lies closest to 1?

Class 7Fractions and DecimalsFractions and Decimals

A $\frac{13}{15}$
B $\frac{5}{6}$
C $\frac{7}{8}$
D $\frac{9}{10}$

Step-by-Step Solution

Measure the gap to 1 for each:

1 - \frac{13}{15} = \frac{2}{15}, 1 - \frac{5}{6} = \frac{1}{6}, 1 - \frac{7}{8} = \frac{1}{8}, 1 - \frac{9}{10} = \frac{1}{10}

. The smallest gap is

\frac{1}{10}

, so

\frac{9}{10}

is closest. The trap is picking the fraction with the biggest denominator,

\frac{13}{15}

, which actually has the largest gap of all.

Answer: D)

\frac{9}{10}

Key idea: Adding and subtracting unlike fractions

Step 1: find the **LCM of the denominators**. Step 2: convert each fraction to an equivalent fraction with that LCM as the new denominator. Step 3: now the fractions are 'like' — add or subtract numerators, keep denominator.

Example: 1/3 + 1/4. LCM of 3 and 4 is 12. Convert: 1/3 = 4/12, 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12.

The whole job is converting once you've picked the right common denominator.

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