Example

Simplifying 78+6.4\frac{7}{8} + 6.4

Simplify the expression 78+6.4\frac{7}{8} + 6.4, which mixes a fraction with a decimal.

Step 1 — Convert 78\frac{7}{8} to a decimal. Because it is generally easier to work with decimals than to convert 6.46.4 into a fraction, divide 7÷87 \div 8:

  • 88 into 7070: 88 times (6464), remainder 66.
  • 88 into 6060: 77 times (5656), remainder 44.
  • 88 into 4040: 55 times (4040), remainder 00.

So 78=0.875\frac{7}{8} = 0.875.

Step 2 — Add the two decimals. Use the decimal addition procedure:

0.875+6.4=0.875+6.400=7.2750.875 + 6.4 = 0.875 + 6.400 = 7.275

Therefore, 78+6.4=7.275\frac{7}{8} + 6.4 = 7.275.

This example shows the general strategy for expressions that combine fractions and decimals: convert to a single form (usually decimals) so that standard decimal arithmetic can be applied.

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Updated 2026-04-21

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